14 Commits

Author SHA1 Message Date
wan c307df8f87 dsp: fixing discretisation progression to 'good enough' 2026-03-24 16:34:10 +09:00
wan c5650d002a dsp: major reworks surrounding filters and discretisation 2026-03-24 15:56:27 +09:00
wan 7d4ed4da0f dsp: tone and stuctural improvements around section 4/5 2026-03-23 15:27:14 +09:00
wan 1fd30d6716 dsp: tone rework and better transitions 2026-03-20 15:23:42 +09:00
wan 18bf55f5da dsp: tone rework ~section 3 2026-03-19 19:26:10 +09:00
wan 7ada45a6e7 dsp: tone rework until section 2 2026-03-17 17:33:38 +09:00
wan e08980cd81 minor wording change 2026-03-17 14:20:01 +09:00
wan a48d1c344b dsp: multiple reworks
- deadpan tone adjustment
- added summary section
- inline LaTeX for symbols and exprs
2026-03-17 14:08:49 +09:00
Mikkeli Matlock 3621ff049c manual merge from dsp notes 2026-03-13 21:05:26 +09:00
wan f24b777d95 detailed general tone 2026-03-13 13:40:19 +09:00
wan 6d9564af66 added some notes 2026-03-13 13:38:37 +09:00
Mikkeli Matlock 61ea53780f dsp: more drafting 2026-03-10 23:10:13 +09:00
Mikkeli Matlock f351086490 dsp: drafting 2026-03-10 22:51:12 +09:00
Mikkeli Matlock a66154d701 dsp: initial commit 2026-03-10 20:27:17 +09:00
20 changed files with 340 additions and 868 deletions
-19
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@@ -1,19 +0,0 @@
on:
push:
branches: [master]
paths-ignore:
- "wip/**"
- "README.md"
- ".gitignore"
- ".claude/**"
workflow_dispatch:
jobs:
publish:
uses: novoyuuparosk-wiki/novoyuuparosk-auto-wiki/.gitea/workflows/publish-songs.yml@master
with:
SOURCE_REF: ${{ github.sha }}
# Empty on workflow_dispatch — the reusable workflow treats that as
# "publish everything", same as a first push.
SOURCE_BASE_REF: ${{ github.event.before }}
secrets: inherit
+1 -50
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@@ -1,51 +1,2 @@
# Northwich committee of magic researches songs repository
Just a collection of lyrics of songs. Probably will be managed into proper folders. Probably will have LRCs.
## Publishing to the wiki
Song pages are auto-published to <https://wiki.novoyuuparosk.org> by the
**songs pipeline** in the companion repo `novoyuuparosk-auto-wiki` (the
"repo next door"). It triggers on push to `master`.
- **Source-file contract** (frontmatter fields, body conventions): see
[`pipelines/songs/SCHEMA.md`](../novoyuuparosk-auto-wiki/pipelines/songs/SCHEMA.md)
in `novoyuuparosk-auto-wiki`.
- **Pipeline overview** (branch convention, triggers, categories, LRC, etc.):
[`pipelines/songs/README.md`](../novoyuuparosk-auto-wiki/pipelines/songs/README.md).
In short: a file is published when its frontmatter has `wiki.publish: true`
and it isn't under `wip/`. The `title` field becomes the wiki page name.
## Side-by-side lyrics (columns shorthand)
To lay two (or more) versions of a song next to each other — e.g. an original
and its translation — use a fenced code block tagged `columns`, with each
column separated by a line containing only `===`:
````markdown
```columns
**原題**
一行目
二行目
===
**Title**
first line
second line
```
````
Notes:
- Line breaks and blank lines are preserved verbatim (each column is rendered
with line breaks intact).
- `N` columns ⇒ `N 1` `===` separators.
- Use Markdown emphasis inside the block: `*italic*`, `**bold**`,
`***bold-italic***`. (No need for raw HTML.)
This is implemented entirely by the auto-wiki pipeline at publish time; the
authoritative description lives in
[`SCHEMA.md`](../novoyuuparosk-auto-wiki/pipelines/songs/SCHEMA.md#columns-side-by-side-shorthand).
See [`kairo/kimito_en.md`](kairo/kimito_en.md) for a real example.
Just a collection of lyrics of songs. Probably will be managed into proper folders. Probably will have LRCs.
+1 -95
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---
title: You and me and a gentle journey
album: kairo III
categories:
- kairo
wiki:
publish: true
release_date: 2026-06-14
---
# You and me and a gentle journey
The classic. Old working notes in [another page](Looking_into_You_and_me_\(ry_and_a_brand_new_translation).
## Lyrics
```columns
**君と私と穏やかな旅**
いつか見た夢の話
遠い遠い国のこと
仕舞い忘れた
私たちの旅
忘れ物
置いてきた
網棚の上にあった
まだ時間が
かかるみたい
寝てていいよ
ほら肩にもたれて
深い深い眠りに落ちると
聞こえるの
ほら 懐かしい声
君の声
二人ならどこまででも
行けると信じていると
笑う君を
ああ愛しいと思う
流れてく景色
揺れる列車とこの思いが
紡ぐ旅に
今は身を任せよ
二人で歩けないなら
そこに意味はないんだと
泣いた君を
ああ美しいと思う
境界を越えて届け
あの日の記憶の欠片
いつか思い出すよ
この旅路を
===
**You and me and a gentle journey**
You know there was a dream I had long ago
Of a somewhere that is far away
And a journey for the two of us
An end I am yet to have you see
All of the lost stuff
Collecting but dust
Forgotten up there on overhead racks
Its going to take time
Until the end and should
(should) you feel like dreaming
Youre always welcome on my shoulder
A voice of comfort
A voice of yours
The scenery a-flowing by
The swaying train, and this feeling merged and intertwined
In a stream of journey to which
For now I shall give myself away
If not with me you abide
There wont be not such meaningful events left
To go across the borderline
```
placeholder until I remember what the new title actually would be
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[ar:Northwich committee of magic researches]
[ti:transform (feat. 結月ゆかり)]
[al:kairo II]
[00:48.62]いつか夜空に響いた
[00:55.20]星の歌を探すために
[01:00.48]周波数を回しながら私は
[01:09.41]旅に出た。
[01:12.48]
[04:58.42]失われた電波は
[05:04.43]探さなくていいよ
[05:10.52]地を歩き続けて
[05:16.18]会いに行かなくていいよ
[05:22.12]
[05:22.49]星の心が歌った旋律は
[05:30.27]境界を越えた
[05:34.48]この片隅にいる魂に
[05:42.23]まだ振れているから
[05:46.99]
+1 -20
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@@ -1,20 +1,5 @@
---
title: transform
album: kairo II
categories:
- kairo
wiki:
publish: true
release_date: 2025-11-21
lrc: transform.lrc
---
# transform
The title is stylised in full lowercase: `transform`
## Lyrics
いつか夜空に響いた
星の歌を探すために
周波数を回しながら私は
@@ -29,8 +14,4 @@ The title is stylised in full lowercase: `transform`
星のこころが歌った旋律は
境界を越えた
この片隅にいる魂に
まだ振れているから
## Notes
I'll write something here when I feel I should. Or when 556t finally gives me her polished vocals.
まだ振れているから
-31
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[ar:Northwich committee of magic researches]
[ti:复兴岛]
[al:Post-alternative extended progressive technojazz, Part II: rovers]
[01:11.01]六小时后太阳就要落山
[01:14.15]但当下阳光还在洒满路面
[01:18.88]除了树荫
[01:20.08]和高耸的曾是酒店的
[01:24.41]建筑的阴影
[01:26.48]
[01:26.92]地下人来人往地铁车厢穿梭
[01:30.63]而无人驻足
[01:33.49]
[01:34.71]地上的卡车
[01:36.08]水中的驳船
[01:37.60]掉色的塔吊
[01:40.14]是常驻的过客
[01:42.48]
[02:14.92]七公里外灯光开始璀璨
[02:18.64]停滞的车辆与车辆与车辆
[02:22.14]与沉醉的人
[02:24.14]忘记了或者从不知道(没知道过)
[02:27.85]波涛的寂静和汹涌
[02:30.45]
[02:30.67]今天的鸡蛋灌饼已经收摊
[02:35.06]那明天呢
[02:37.47]
[02:38.93]时代走得太快
[02:40.84]即将追上这缓慢的
[02:43.88]从未停止的步伐
[02:46.46]
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---
title: 复兴岛
album: Post-alternative extended progressive technojazz, Part II
categories:
- Paxprotej
wiki:
publish: true
siblings:
release_date: 2023-12-25
lrc: fuxingdao.lrc
---
# 复兴岛
## Lyrics
六小时后太阳就要落山
但当下阳光还在洒满路面
除了树荫
@@ -38,4 +24,4 @@ lrc: fuxingdao.lrc
时代走得太快
即将追上这缓慢的
从未停止的步伐
从未停止的步伐
-71
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[ti:Paranoma (full version)]
[ar:Northwich committee of magic researches]
[al:Post-alternative extended progressive technojazz, Part II: rovers]
[00:00.00]Paranoma[1]
[00:27.20]
[00:30.06]馴染みのなかった街に降りて
[00:33.90]人の流れに潜り込んで
[00:38.57]痺れる日常からの
[00:40.76]僅か数千分の逃避行は
[00:44.35]今から始まる。
[00:45.79]
[00:46.68]地図でしか見てなかった世界を
[00:49.13]足と目で確かめながら
[00:51.85]呼び方も知らない、意味も分からない全てを
[00:56.19]密やかにこの脳に
[00:58.50]パノラマで写す。
[01:01.16]
[05:25.10]他人の枠組みに入れない旅人は
[05:28.44]旅先をふるさとにするつもりもない。
[05:32.96]期間限定の旅を終わらせないと
[05:36.80]逃げられない常設に墜ちてなるから。
[05:39.28]
[07:13.74]Paranoma[0]
[07:36.89]
[07:44.64]私は…私たちは…
[08:08.28]私たちは道です。私たちは、生命のない、旅を支えたものです。
[08:15.52]
[08:31.07]足の代替としての私たちはただ、人を行きたいところに運ぶ。
[08:38.76]生命じゃなく寿命がある私たちは、寿命が終わるまで人間と付き合い続けている。
[08:46.95]人間が出会いをする時。
[08:50.04]人間が別れをする時。
[08:53.66]人間が喜びを感じる時。
[08:57.07]人間が寂しさを感じる時。
[09:00.41]人間が人間らしいことをする時。
[09:04.29]人間が人間らしく感情を感じる時。
[09:09.16]生命も感情もない私たちは、生命も感情も有する人間たちの記憶の一部になる。
[09:17.53]
[09:19.00]それが楽しいことであろうか、私たちはわからないけど。
[09:24.70]それが悲しいことであろうか、私たちはわからないけど。
[09:31.27]それが素晴らしいことであろうか、私たちはわからないけど。
[09:37.59]それがくだらないことであろうか、私たちはわからないけど。
[09:43.55]
[09:44.59]それが美しいことであろうか、私たちはわからないけど。
[09:49.44]
[09:49.97]わかるはずもないけど。
[09:51.78]
[10:51.54]道は旅の目的ではなく、手段であるはずでした。
[10:58.08]でも道にも美しさが宿っている。
[11:06.90]私たちの旅は道に刻まれ、道は私たちの旅に刻まれた。
[11:13.98]例え私たちが消えても、道が消えても、
[11:18.59]記憶は生き続けるだろう。
[11:21.85]
[11:55.79]Paranoma[2]
[12:16.05]
[12:18.87]ひとりで旅立つのは好きです。
[12:24.58]ひとりで見た景色と、通った道が好きです。
[12:30.61]孤独が嫌いではないけど、
[12:36.31]ひとりの旅は決して孤独の旅ではない。
[12:40.71]
[15:27.69]湯のない風呂と煙のない煙突
[15:30.76]崩れ続ける鉄道橋と解体されている発電所
[15:34.76]錆びた道路標識と剥がれた防錆塗装
[15:38.01]トンネルを終わらせる光と雪に埋めた電波塔
[15:41.24]人気のない街とアスファルトに残った足跡
[15:45.31]誰かがそれを見たでしょう。誰かがそれを見るだろう。
[15:50.05]
[17:11.95]いつか見た景色が
[17:15.08]幾千の目に映ったことを想像して
[17:19.79]世界と非同期に繋がる
[17:23.76]
+2 -16
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---
title: Paranoma
album: Post-alternative extended progressive technojazz, Part II
categories:
- Paxprotej
wiki:
publish: true
siblings:
release_date: 2024-06-09
lrc: paranoma.lrc
---
# Paranoma
## Lyrics
**[1]**
馴染みのなかった街に降りて
人の流れに潜り込んで
@@ -78,4 +64,4 @@ lrc: paranoma.lrc
いつか見た景色が
幾千の目に映ったことを想像して
世界と非同期に繋がる
世界と非同期に繋がる
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[00:32.41]Where next should I go?
[00:34.63]I ask myself
[00:39.25]One thing I certainly hold
[00:42.43]There is no home
[00:45.67]
[00:46.90]In the sauna with different other souls
[00:50.77]I speak a language no one else knows
[00:55.08]My voice quite low
[00:59.42]Purposely so
[01:01.49]
[01:02.18]The trip goes on without a terminal
[01:06.01]To places that grow or dwindle
[01:09.68]Where folks young or old
[01:13.68]Have their stories often yet never told
[01:19.18]
[02:45.15]All the people going somewhere in heat or cold
[02:53.37]On the trains, on the ships, on the decorated personal vehicles
[03:01.15]Are waiting for a whistle to blow
[03:07.74]In the real thin air or a simulated role
[03:16.16]
[03:16.69]Around the corner in the artificial tide
[03:21.96]Someone sings a song about another day in life
[03:28.01]Routines I have witnessed with my own eyes
[03:36.28]None of which mine
[03:39.79]
[04:10.33]From the concrete jungle where hopes and dreams die
[04:15.32]To the lonely northern monument covered in ice
[04:20.29]In the silent alley in decay stuck in time
[04:24.16]Between the rails and rails cut off by the keep out signs
[04:29.45]Off the reflective glass walls lit by the neon lights
[04:34.54]Amidst the snowstorm with lorries at roadsides
[04:39.51]Under the memorial tents singing Irene goodnight
[04:44.61]There's a ghost passing by
[04:48.63]
[06:05.38]Random footprints scatter
[06:08.04]Over the imaginary hills and far away
[06:13.16]Visualised memories of all the journeys
[06:17.16]Etched into my skin and bones
[06:20.61]
[06:21.08]Rearranged faces from the past
[06:24.66]Orient towards a new crossroad
[06:28.93]Visions of the future destinations
[06:31.70]Emerge to remind Ill be a
[06:34.41]Rover till I die
[06:36.80]
+1 -15
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---
title: rover over virtually eternal roundabouts
album: Post-alternative extended progressive technojazz, Part II
categories:
- Paxprotej
wiki:
publish: true
siblings:
release_date: 2023-11-03
lrc: rover.lrc
---
# rover over virtually eternal roundabouts
## Lyrics
In the sauna with different other souls
I speak a language no one else knows
My voice quite low
@@ -85,4 +71,4 @@ Rover till I die
*新しい交差点へ向かう*
*次々の目的地の幻影が現れ*
*再び思い出させた私は*
*死ぬまでローヴァー*
*死ぬまでローヴァー*
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[ar:Northwich committee of magic researches]
[ti:sauna as ubiquitous neural analeptic]
[al:Post-alternative extended progressive technojazz, Part II: rovers]
[00:34.84]Waking up from the illusions last night
[00:39.11]In a desert of cliches and mirages
[00:42.95]They have beautiful names and murderous decorations
[00:47.64]For them starry-eyed storm chasers
[00:51.34]While we are rovers that no one would come after
[00:55.46]My stereo blasting unsung classics
[01:00.13]On our way of an escape from
[01:02.49]Psychedelic asphyxiation
[01:06.73]
[01:24.49]Come is the cloud with boots of rain
[01:28.18]Pouring down into the fjords and lagging the train
[01:32.61]Our last umbrella lost in vain
[01:36.46]Only tears remain on the radar display
[01:40.25]The lonely arctic spring creeps into my brain
[01:45.00]The circuit in my vein weeps
[01:47.46]Over the birth and destined death of yet another
[01:54.41]Poetic creation
[01:56.83]
[02:30.95]I try to be a seeker, a lover and a distributor
[02:36.01]Of the ultimate hype about
[02:39.30]A multitude of neural communications
[02:42.43]Excited by the raving steam coming off your stone
[02:46.55]My songs are the fuel for the heating solution
[02:51.55]So we set out for the poet annihilation
[02:54.99]In search for a salvation to both parties
[02:59.93]Existential problems
[03:03.62]
[03:54.80]The setting sun and an extended lack of daylight
[03:59.10]I crave for my sanity veering out of my sight
[04:02.65]The teletext says itll snow again tonight
[04:07.68]To extinguish every endless fight
[04:11.19]We still cant resist the temptation to hate
[04:15.12]And we strive to avoid devastation as fate
[04:19.31]Then we just recover the remains
[04:23.39]Of our own conclusions
[04:27.05]
[04:28.36]Some other day when the time has come
[04:32.50]All the radio stations down and gone
[04:37.09]Unchained emotional outbursts
[04:41.12]Necessarily overrides our internal
[04:45.56]Appropriate libidos
[04:48.94]
[04:53.39]Say goodbye to the beautiful dreams
[04:57.62]As the engine sings against the drums
[05:02.01]Usurping the memories of the fallen
[05:06.15]Noise overwhelmed by the melodies
[05:10.56]Absurdly comforting
[05:14.01]
[05:18.41]Some other day when the time has come
[05:22.62]All the radio stations down and gone
[05:27.28]Unchained emotional outbursts
[05:31.24]Necessarily overrides our internal
[05:35.64]Appropriate libidos
[05:39.03]
[05:43.44]Say goodbye to the beautiful dreams
[05:47.68]As the engine sings against the drums
[05:52.03]Usurping the memories of the fallen
[05:56.22]Noise overwhelmed by the melodies
[06:00.70]Absurdly comforting
[06:04.89]Absurdly comforting
[06:08.25]
+1 -17
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---
title: sauna as ubiquitous neural analeptic
album: Post-alternative extended progressive technojazz, Part II
categories:
- Paxprotej
wiki:
publish: true
siblings:
release_date: 2024-06-13
lrc: sauna_v2.lrc
---
# sauna as ubiquitous neural analeptic
This is the acoustic refurbished version of the 2022 song `sauna as universal neural analeptic` (which is yet to get a page).
## Lyrics
Waking up from the illusions last night
In a desert of cliches and mirages
They have beautiful names and murderous decorations
@@ -76,4 +60,4 @@ As the engine sings against the drums
Usurping the memories of the fallen
Noise overwhelmed by the melodies
Absurdly comforting
Absurdly comforting
Absurdly comforting
-12
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@@ -1,12 +0,0 @@
[02:15.45](narration)
[02:39.56]
[04:28.83]黒い黒いダイヤは
[04:35.43]二度眠りに落ちた
[04:42.08]煤けた煙突は
[04:48.75]一つずつ土に帰った
[04:54.99]
[04:55.36]見慣れた日常が
[05:02.12]なくなり続けても
[05:08.78]清い水はこの沢に
[05:15.44]ただ流れていく
[05:22.09]
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---
title: Shimizusawa
album: Post-alternative extended progressive technojazz, Part II
categories:
- Paxprotej
wiki:
publish: true
siblings:
release_date: 2023-12-09
lrc: shimizusawa.lrc
---
# Shimizusawa
[Shimizusawa Project](https://www.shimizusawa.com/)
## Lyrics
黒い黒いダイヤは
二度(ふたたび)眠りに落ちた 
煤けた煙突は
@@ -23,4 +8,4 @@ lrc: shimizusawa.lrc
見慣れた日常が
なくなり続けても
清い水はこの沢に
ただ流れていく
ただ流れていく
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[ar:Northwich committee of magic researches]
[ti:pulse under latent semantic envelopes]
[al:Shirakaba Express Service]
[00:14.29]第一部。
[00:15.73]
[01:20.23]Surface.
[01:23.91]The equilibrium of silence between the static magnetic noise, the watery planes, and the optical waves.
[01:36.03]Blurred and mangled electronic signs over the outbound atmospheric leeway.
[01:44.25]Distant stations estimated in abnormal heat perform the inconsistent collimation rite.
[01:50.32]
[01:53.04]Dive.
[01:56.03]The black screen of stalemate conceals the massive stars, the charred comets, and the meteorites.
[02:04.45]Their questionable glitters, once emissions of brave borderers and dark adventurers,
[02:11.56]now the only traces, obscured and indifferent to all but those with a special breed of faith.
[02:22.22]
[02:24.20](title: pulse\Nunder\Nlatent\Nsemantic\Nenvelopes)
[02:36.05]
[03:27.90]The noise floor of a receiving environment is the aggregate of all background signal energy present across a given frequency band at any instant.
[03:37.14]In urban contexts, primary contributors include electromagnetic emissions from power distribution infrastructure, wireless communications networks, and consumer electronic devices.
[03:50.85]The noise floor is not centrally coordinated; no single source generates it.
[03:56.21]It emerges from the cumulative output of many independently operating transmitters, each functioning within its own parameters, whose combined effect is persistent and largely uniform.
[04:08.45]Under standard conditions, this background level is treated as a fixed baseline rather than a variable of interest.
[04:16.56]Signals whose amplitude falls at or below this baseline remain physically present in the medium but cannot be distinguished from the background by a receiving system, and are not considered recoverable.
[04:30.07]
[04:32.10]An impulse signal, also referred to as a unit impulse, is defined as a signal with zero value at all points in time
[04:40.26]except a single instant, at which its value is notionally unbounded, subject to the constraint that its total integrated area equals unity.
[04:51.22]In practice, true impulse signals cannot be physically produced; they are approximated by short-duration, high-amplitude pulses of sufficient bandwidth.
[05:04.06]The impulse response of any linear time-invariant system — that is, the output produced when an impulse is presented as input — fully characterises that system's behaviour under any subsequent input.
[05:17.81]In the absence of any input, a system at rest produces no output and exhibits no properties that distinguish it from any other inactive system.
[05:27.34]From a single impulse and its measured response, the complete transfer function of the system can be derived.
[05:34.91]
[05:36.57]第二部。
[05:38.05]
[06:08.96]Subdued sonic scalars vectorise
[06:14.98]
[06:16.73]Acoustic aberrations dissipate
[06:23.13]
[06:23.99]Isotropic funnel strikes a packet rain
[06:31.54]
[06:32.08]Fine-grained bags of acks ground astray
[06:38.04]
[06:40.02]Ocean as a desert buries all of its life
[06:46.05]
[06:48.05]Deck the shell with a perfect thermocline
[06:53.87]
[06:57.01]Curtain shut before the Fresnel bights
[07:02.01]
[07:04.07]Plasma buildup swells your rovers' thighs
[07:10.05]
[09:11.97]第三部。
[09:13.33]
[09:25.62]Particulate pressure across a landlocked island
[09:32.52]Ultraviolet utilitarian paints every third crag bland
[09:40.99]Lossy lies lament the ludicrous lawful liberty
[09:48.97]Siren sounds soaken in the sauna of substantiality
[09:57.02]Eccentric sediments launch unbidden perpetuity
[10:10.00]
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---
title: pulse under latent semantic envelopes
album: Shirakaba Express Service
wiki:
publish: true
siblings:
- path: pulse_dev.md
tag: PULSE_DEV
label: Dev gibberish
release_date: 2026-06-18
lrc: pulse.lrc
---
# pulse under latent semantic envelopes
The name of the song is stylised in all-lowercase, `pulse under latent semantic envelopes`, but Mediawiki loves a Capital letter.
For more behind-the-scene shenanigans, see PULSE_DEV.
*This page is proudly the first to be maintained by Gitea actions.*
## Lyrics
### Raw (what you get in the audio)
*第一部。*
Surface.
The equilibrium of silence between the static magnetic noise, the watery planes, and the optical waves.
Blurred and mangled electronic signs over the outbound atmospheric leeway.
Distant stations estimated in abnormal heat perform the inconsistent collimation rite.
Dive.
The black screen of stalemate conceals the massive stars, the charred comets, and the meteorites.
Their questionable glitters, once emissions of brave borderers and dark adventurers,
now the only traces, obscured and indifferent to all but those with a special breed of faith.
The noise floor of a receiving environment is the aggregate of all background signal energy present across a given frequency band at any instant. In urban contexts, primary contributors include electromagnetic emissions from power distribution infrastructure, wireless communications networks, and consumer electronic devices. The noise floor is not centrally coordinated; no single source generates it. It emerges from the cumulative output of many independently operating transmitters, each functioning within its own parameters, whose combined effect is persistent and largely uniform. Under standard conditions, this background level is treated as a fixed baseline rather than a variable of interest. Signals whose amplitude falls at or below this baseline remain physically present in the medium but cannot be distinguished from the background by a receiving system, and are not considered recoverable.
An impulse signal, also referred to as a unit impulse, is defined as a signal with zero value at all points in time except a single instant, at which its value is notionally unbounded, subject to the constraint that its total integrated area equals unity. In practice, true impulse signals cannot be physically produced; they are approximated by short-duration, high-amplitude pulses of sufficient bandwidth. The impulse response of any linear time-invariant system — that is, the output produced when an impulse is presented as input — fully characterises that system's behaviour under any subsequent input. In the absence of any input, a system at rest produces no output and exhibits no properties that distinguish it from any other inactive system. From a single impulse and its measured response, the complete transfer function of the system can be derived.
*第二部。*
Subdued sonic scalars vectorise
Acoustic aberrations dissipate
Isotropic funnel strikes a packet rain
Fine-grained bags of acks ground astray
Ocean as a desert buries all of its life
Deck the shell with a perfect thermocline
Curtain shut before the Fresnel bights
Plasma buildup swells your rovers' thighs
*第三部。*
Particulate pressure across a landlocked island
Ultraviolet utilitarian paints every third crag bland
Lossy lies lament the ludicrous lawful liberty
Siren sounds soaken in the sauna of substantiality
Eccentric sediments launch unbidden perpetuity
### Chinese translations
**潜在语义包络下的脉冲**
*第一部分。*
上浮。
静磁噪声、水的平面、还有光波之间是沉默的平衡。
模糊而残损的电子牌匾,掠过向外敞开的那一线大气余隙。
热异常里估算出来的远方站点定期执行和上一次不一样的校准仪式。
下潜。
僵局的黑屏掩住了庞大的恒星、焦黑的彗星,还有陨石。
它们存疑的微光是勇敢拓边者与黑暗冒险者放出的辐射,
如今只是晦暗不明,无人在意的痕迹,只有一些信仰特殊者关心。
任何接收环境的本底噪声,指的是某一频段内任一时刻全部背景信号能量的总和。在城市环境中,其主要来源包括配电设施、无线通信网络以及各类消费电子产品的电磁辐射。本底噪声没有统一来源,也不受集中调度,而是众多独立运行的发射源累积叠加的结果:各发射源均在自身参数范围内工作,叠加之后形成一种持续而大致均匀的背景。通常将这一背景电平视为固定基线,而不作为需要关注的变量。幅度等于或低于该基线的信号,在物理上仍存在于介质之中,但接收系统无法将其同背景区分开来,因而被认为无法恢复。
冲激信号,又称单位冲激,是指这样一种信号:它在所有时刻的取值均为零,仅在某一瞬间例外;在该瞬间,其取值理论上为无穷大,但总积分面积须恒等于一。实际中,理想的冲激信号无法物理实现,通常以持续时间极短、幅度极高、带宽足够的脉冲来近似。对任一线性时不变系统而言,其冲激响应(即以冲激作为输入时所得到的输出)足以完整描述该系统在此后任意输入下的行为。若没有输入,处于静止的系统不产生输出,也不表现出任何可与其他静止系统相区别的特性。仅凭一个冲激及其测得的响应,即可推导出系统完整的传递函数。
*第二部分。*
压低的声音标量,化作矢量
声学的像差,渐渐耗散
各向同性的烟囱砸中一场数据包之雨
一袋袋细碎的应答被研磨得迷路
海洋作为荒漠埋藏自己所有的生命
完美的温跃层敲打外壳
菲涅尔拐角前的帷幕关闭
等离子堆积,肿胀了流浪者的大腿
*第三部分。*
颗粒状的压力遍历一座内陆的孤岛
紫外功利主义者把每三个石头里的第三个涂成无色
有损的谎言哀悼荒唐的合法自由
警笛声音浸泡在实在的桑拿里
诡异的沉积物发射了没人要求的永恒
### Japanese translations
**潜在意味包絡下のパルス**
*第一部。*
浮上。
静磁ノイズと、水の平面と、光波との間の、沈黙の平衡。
ぼやけて潰れた電子の標識が、外へ開いた一筋の大気の余地の上を過ぎていく。
熱異常のなかで推定された遠方の局が、一貫性のない合わせの儀式を行う。
潜航。
停滞した黒い画面が、巨大な恒星と、焦げた彗星と、隕石を覆い隠す。
それらの疑わしい微光は、勇敢な辺境者と闇の冒険者が放った放射であり、
いまや、ただおぼろげで、誰にも顧みられない、ひとつの痕跡にすぎない。特殊な信仰を持つ者だけが、それを気にかける。
ある受信環境のノイズフロアとは、ある周波数帯域内の任意の瞬間に存在する背景信号エネルギーの総和をいう。都市環境では、その主要な発生源として、配電設備・無線通信網・各種民生用電子機器からの電磁放射が挙げられる。ノイズフロアには統一された発生源はなく、集中的に制御されているわけでもない。それは、独立して動作する多数の送信源の累積的な出力から生じるものであり、各送信源はそれぞれの諸元の範囲内で動作しながら、合わさることで持続的かつほぼ一様な背景を形成する。通常、この背景レベルは着目すべき変数としてではなく、固定された基準値として扱われる。振幅がこの基準値に等しいか、それを下回る信号は、媒質中に物理的には依然として存在するものの、受信系がそれを背景から区別することはできず、復元不能とみなされる。
インパルス信号は、単位インパルスとも呼ばれ、次のような信号として定義される。すなわち、ただ一つの瞬間を除くすべての時刻で値が零であり、その一瞬においてのみ値は概念上無限大となるが、全体を積分した面積はつねに一に等しくなければならない。実際には、理想的なインパルス信号を物理的に生成することはできず、持続時間がきわめて短く、振幅がきわめて高く、十分な帯域幅をもつパルスによって近似される。任意の線形時不変システムのインパルス応答(すなわち、インパルスを入力として与えたときに得られる出力)は、その後のいかなる入力に対するそのシステムの挙動をも完全に特徴づける。入力がまったくない場合、静止した系は何も出力せず、ほかのいかなる不活性な系とも区別しうる性質を示さない。ただ一つのインパルスと、その測定された応答とから、システムの完全な伝達関数を導くことができる。
*第二部。*
抑えられた音響スカラーがベクトル化する
音響の収差が散逸していく
等方的な煙突が、パケットの雨を打つ
きめ細かな応答の袋が、すり潰されて地に迷う
砂漠としての海は、自らの生命を埋める
完璧な水温躍層が、その殻を叩く
幕がフレネルの曲がりの前で閉じる
プラズマのたまりがローバーたちの太ももを腫れ上がらせる
*第三部。*
微粒子の圧力が、内陸の孤島の隅々まで行き渡る
紫外線の功利主義者が、三つに一つの岩山を無色に塗る
劣化した嘘が、ばかげた合法な自由を悼む
サイレンの音が、実在性のサウナに浸かっている
奇妙な堆積物が、誰も求めていない永遠を放つ
## Notes about this song
I will be just writing about anything I think of related to this song. At least for the first go. It's not really creative when you set yourself an agenda and duly follow it.
### Why pulse
Some time after witnessing the rover song go locally viral at the second transparent fes I said to myself there will be a third. Almost immediately after that, I was sure the keyword would be 'pulse'. Then it took me several months to figure out the third recursive acronym composition. Maybe more than several months.
The choice in 'pulse' is for a very apparent reason. It's literally the last kairo (original) song. That is, the last song in the last album. I know they had more 2hu released after that but that's a different business, isn't it.
It also is a very good word in itself because there is vitality, there is machinery, there is electronics and engineering, all in one package. It's kairo plus Northwich committee of magic researches.
### Educational rock
It's now a traditional practice to sample random people speaking random stuff in a post-rock / prog rock / chill hip-hop / shoegaze / you name it song. There is a hip-hop remix of Niinistö's new year's day address but I can't really dig it out of the Internet rabbit hole. And to start with literally the first post-rock I ever listened to was the 2hu band 'the distant journey to you' by our Veto guy and there was an excerpt of Kon Satoshi's 'Paprika' in one of the songs.
When I really started to shape this song I was listening to way more Snakes Don't Belong In Alaska than I should. Two of their later songs sampled someone presumably giving a lecture or speech or that sort of presentation. I very much liked it as I'm a big podcast person. It's like listening to your podcasts with psychedelica music accompanying.
I also have been a firm believer that signal processing is something any music-aware people should have at least a slightest idea about. So here we are. It's only natural to make my own mini lecture about some signal basics and incorporate that audio signal into the song.
The other parts of the song are intentionally cryptic, evasive, indirect, fuzzy, ambiguous but the educational bit should be factual enough it can be considered a decent crash course on what it talks about. Aside from being the catalyst for the song's underlying emotional progressions. We'll talk about that later or never.
### Football manager ruined my life and LLM agents severed it into pieces
Back in your 2022s and 2023s, I wasn't aware of Anthropic and ChatGPT was basically chat powered by GPT. But this time I approach my songwriting as a relatively heavy Claude user. I never fully hand the lyric composition to LLM agents or raw LLMs as that's the fun bit, not the chore bit.
What I personally do is usually tell the Claude 'hey I'm thinking about something like this' in either the plainest of languages or just a draft verse. 9 out of 10 times its response pisses me off. Which is consistent with the experience when you do these exchanges with any verified decent human counterpart. No disrespect to my verified 'I can talk poetic bullshit with them' friends but that just happens. And it happens for good.
You see the key here is I have someone to talk to, 24/7, super fluent in languages I speak or not, only restricted by usage limits. For writing lyrics I never hit the limits, by the way. An adversary is an essential upgrade to a rubber duck as it gives you feedback. LLM at the core means this adversary is complex enough to be considered unpredictable and thus inspiring.
Your Claudes and ChatGPTs and maybe Geminis out of the box loves proposing verses after verses which is less helpful. Fortunately, I've tweaked my instances to hold fire and communicate in a more atmospheric way. In a convo I get myself immersed in the atmosphere I initiated and the agent amplified. I guess that's where all the fever dreams root from.
### On professionalism and why I consider myself pro enough even if I have no proper proof
In a way, I think it's probably true that flair and discipline has a dance of balance in many things, and I take music and association football as two seemingly irrelevant examples. Simply because I'm somewhat invested in those two.
A classical piece in the broadest sense takes many, many players with their respective instruments. There would be a leader violinist or a pianist or similar role but let's face it, for like 99% of the time, orchestra players don't play flashy solo phrases. I feel it's like how you have no-nonsense centre backs and anchor defensive midfielders like Jordan Rossiter, that in a sense stand out even less than a goalkeeper.
Your rock and pop bands of 3, 4, 5 people is something else. Basically everyone needs to be a star. Everyone will have flashy, tricky solo riffs.
And don't get me wrong, I by no means am stating that playing simple notes correctly is inferior to smashing an outrageous riff, or that only getting the ball and passing to the nearest full back is inferior to dribbling over 5 defenders and driving home with a full bollocks swing. That is just not true. Doing the less fancy 'basic' but proper and well is just a slightly, or very different dimension of professionalism. I personally very like no-nonsense centre backs because I played as one because I couldn't do fancy stuff on the pitch.
I don't think I can do fancy stuff in my FL studio either. The justification around all this equity of professionalism had a big portion of making myself feel less useless when I tried and mostly failed to learn to play the guitar then bass. Today I'm totally ok and free of complexes like that.
The financial stability is also very real. My plan about music has always been 'find a job so I can play with music' and I've finally done it. I mean I never got anywhere around trying to be self-sustainable with music alone or as the main means, but having that peace of mind of a roof above is certainly helpful even for a hobby. Having music to unleash my creativity buildup when there is any also helps me cope with the 'boring' day job so it's a win-win. Probably.
### Music, bloody hell
I don't think one should be expecting me to elaborate on how delicate my music craftsmanship is after the revelation and identification as a no-nonsense FL Studio user at best of Conference National level. But you see, there are people who watch Conf Nat as devoted as they themselves watch the Prem, or even more. Absolute skill levels are not that much of a matter.
I opted to go for a classic dual-bass, dual-telecaster setup with various other helper instruments because that's simply my favourite. The second bass actually turned out to be utilised less than I originally planned. The plan was based on how things went in 'rover over virtually eternal roundabouts'.
Also, the song started as my experiment of a more techno-heavy style. It didn't end well, but the techno leftovers might be (I'm doubtful) spotted around the place.
Then I switched to the target of making this one the third piece in the recursive acronym trilogy, so essentially I'm doing humble plagiarism on the previous two songs. 'sauna as universal neural analeptic' and 'rover over virtually eternal roundabouts' if you're wondering (no one asked).
Like stated elsewhere the psychedelica influence from SDBIA is faintly visible (audible). I also applied some of the minimalism principles to the guitar lines, they should be perceivably sparser than some contemporaries.
Drums and percussions have always been my passion but I think I just got too lazy to fine tune every loop pattern. A drum track of eternally-morphing patterns is not realistic in some sense after all.
### Vocal synthesis masterclass
Could be stating the obvious, but I'm much better at English than Japanese. When it comes to songwriting I might even argue English enjoys priority over my first language, which is Chinese. So it's a bit of a hassle when there is no good enough Yukari TTS on the shelf. On a side note, Kotonoha sisters got their official English / Chinese TTS but that's a shambles. To put it mildly.
When I discovered GPT-SoVITS which in English is something that allows you to generate many languages in person A's voice and person B's accent (partly), it's only natural that I immediately went for it. It fit like a glove on the foot.
You see, the problem with many voice changers, even in the l'époque de l'intelligence artificielle, is that they end up with English (simplified) pronunciations. Some give you RP but that's not what I want either. It's the models that are my problem and I needed something more weird.
The goal was to mix rallienglanti, Bristolian, and some Aussie flavour to produce the random and weird English I usually speak. The end product is nowhere near that, but equally far from 'standard' English. Which is very acceptable.
Also, this synthesised voice should not be considered truly Yukari in the copyright or trademarks sense. I credited Yukari because I included pieces of Japanese voice made with the authentic A.I.VOICE 2 editor with a valid license. Just saying.
For the sung parts, Synthesiser V Studio Pro 2 is the weapon of massive destruction of choice as always. The actual labour is rather boring so I'll leave it as 'I mix-matched mostly Spanish and English phonemes'.
### So what is this song about?
It's all in the title mate.
Keep reading if you think that alone is not meaningful enough.
I'm firmly against providing an answer as standard yet very happy to write my personal interpretations.
On condition that no one promotes the following text as the only valid official explanation to the song, I can give this:
There is atmospheric pressure around every one of us. It is like the environmental noise that suffocates signals without malice. The noise itself also contains various meaningful, info-bearing signals but all piled up together as a big blob of something, apparently less meaningful than any component was. This is the 'latent semantic envelopes' bit.
The pulse is an object as well as an action. It's both the signal that gets sent (and drowned, most of the time) and the action of sending such signals. Not to mention it also means one's heart beats which is a necessary condition for that guy to be alive.
Pulsing, under 'latent semantic envelopes' or more straightforwardly, under overwhelming noise, is absurd. But if you subscribe to the absurd, it's not really a problem.
That's it.
In more straightforward laymen's language, the song states the fact that those dumb people like me who keeps sending out pulses nobody else cares (or cared by only a significantly minor group) are probably not doing it to get responses or replies. They do it for the sake of it.
I probably should have required signing an EULA to have access to this.
### A personal crusade against claims of superhuman frequential cognitive abilities
The decision to use the 192 kbps MP3 as a source of truth, converting from that to nominally WAV and everything else was based on several grounds. But the dominant one is that I never liked high fidelity above a certain threshold of good enough. And that threshold for me is roughly 192 kbps of MP3. Another reason is that I would like even one more person to think outside of the box, into the channels, towards the corner flag, that this is a form of proper, intentional digital lofi rather than lossy media.
It's totally fair to consider this shithousery because shithousery is what I see it as. I'm not doing this digital lo-fi for the sake of art, I do this as reactive banter invoked by phonophile nonsense. If 192 kbps MP3 is good enough to me, then it's good enough.
I do think at 128 kbps I start to sense that something is missing and more information density would be appreciated. So the personal threshold is there or thereabouts.
### Trivia
- In case you didn't notice, the title forms a recursive acronym.
- In case you didn't notice, the final verse is an acrostic of 'pulse'.
- In case you didn't notice, the last line is a reverse acrostic of 'pulse'.
- Brave Borderer and Dark Adventurer are RN fast patrol crafts, or in English, torpedo boats. And I believe both are playable in War Thunder which is why I know them.
- 'Ocean as a desert buries all of its life' is a blatant steal from America's 'A horse with no name'. The original line is 'ocean is a desert with its life underground'.
- I have to sneak in the exact words 'rover' and 'sauna', sorry. And in case you didn't notice, they are two related songs.
- Many of the words could be understood with a leaning towards their optical engineering aspects. That said, I was more on the electronics end of my opto-electronic science and engineering syllabus.
- Meta-trivia: this note is plagued by football cliches, and the song has contracted some.
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---
title: Tunnels
album: Shirakaba Express Service
wiki:
publish: true
siblings:
release_date: 2026-03-01
lrc: tunnels.lrc
---
# Tunnels
## Lyrics
The long dark road spanning within the mountains
is plagued by tunnels
and an illusion induced by mechanical and neural fatigue
@@ -24,9 +12,3 @@ the long dark road spanning within the mountains.
集中すればするほど、
輪郭が、溶けていく。
The long dark road spanning within the mountains
is plagued by tunnels
and an illusion induced by mechanical and neural fatigue
that the night sky is but an arch over
the long dark road spanning within the mountains.
+297
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@@ -0,0 +1,297 @@
# digital signal processing
A boring lecture about signals and systems, and its digital implementation in DSP.
Borderline 'song' less 'poetic'.
The actual material (text that is read out by a vocal synthesiser) is in Japanese.
## Simple notes
For things that are not easily pronounced (e.g. formulae, expressions, symbols), inclusive either:
- Mark how the thing should be pronounced in a pair of adjacent parentheses
- e.g. $H(\omega)$ (エッチオメガ)
- (inclusive) Or don't embed these elements too deep into the flow of sentences; use common, laymen's language instead
- e.g. not `Fs/2(サンプリング周波数の半分)までの帯域を忠実に再構成できる` but `サンプリング周波数の半分までの帯域を忠実に再構成できる`
The general direction is to stay boring, but the deadpan kind of boring. Keep technical language appearing but explain things in more laymen's language.
## Outline
### 1. Signals and systems
- What is a signal
- A function of one or more variables carrying information; here, amplitude over time
- What is a system
- A system maps an input signal to an output signal
- Characterized entirely by its behavior on inputs — the internals are not required
- Most systems are nonlinear — linearity is a special property, not the default
- Linearity: superposition holds — scaling and additivity
- Most physical systems violate this under sufficient conditions (e.g. overdrive: linear below clip threshold, nonlinear at and above it)
- Time-invariance
- A time-invariant system responds identically regardless of when the input arrives
- Violation: any system with time-varying parameters (e.g. modulated effects)
- LTI as the restricted, studied case
- Satisfies both simultaneously — analytically tractable
- A deliberate simplification; not a description of typical reality
- The impulse signal; impulse response
- The impulse: unit energy concentrated at a single point in time
- The impulse response: what an LTI system outputs when fed an impulse
- Completely characterizes the system
- The impulse response is a function — it exists in the same space as signals; systems are absorbed into signal space
### 2. LTI and convolution
- An LTI system is fully characterized by its impulse response
- Any input decomposes into scaled, shifted impulses
- By linearity and time-invariance, the output is the corresponding sum of scaled, shifted impulse responses
- Convolution as the operation
- That sum is convolution: $y = x * h$
- In continuous time, this is an integral: $y(t) = \int x(\tau) \, h(t - \tau) \, d\tau$
- Symmetric in its arguments: $x * h = h * x$
- Signal and system are interchangeable operands — both are functions; convolution makes no distinction between them
- Commutativity: for LTI systems, order of composition is irrelevant
- Two LTI systems in series have a combined impulse response equal to the convolution of each
- $h_1 * h_2 = h_2 * h_1$ — order does not affect the result
### 3. Signal transformation
- A signal can be represented equivalently in the frequency domain
- The Fourier transform: $s(t) \leftrightarrow S(\omega)$; any signal is a sum of sinusoids at different frequencies
- Each sinusoid has a frequency, amplitude, and phase
- $S(\omega)$ is the spectrum: how much of each frequency is present
- Analog signals carry components from DC to arbitrarily high frequencies
### 4. Filters
- A filter is an LTI system — characterized by its frequency response $H(\omega)$
- $H(\omega)$ is the Fourier transform of the impulse response $h(t)$
- Filtering: shaping a signal's spectrum by selectively attenuating or preserving frequency bands
- Basic types: lowpass, highpass, bandpass
- Lowpass: passes low frequencies, attenuates high
- Highpass: passes high frequencies, attenuates low
- Bandpass: passes a target band, attenuates above and below
- In discrete time: finite impulse response (FIR) and infinite impulse response (IIR) filters
### 5. Discretization
- Moving from continuous to discrete: two axes require discretization
- Amplitude: $N$ bits → $2^N$ discrete levels
- Each sample is mapped to the nearest representable level; the error is quantization noise
- The representable range is fixed by design and hardware (ADC/DAC reference voltage)
- Hard clip at the boundary — analog degrades gradually toward its physical limits; digital does not
- Time axis: sampling captures only finitely many values per second
- Analog signals contain frequency components up to infinity — a discrete system cannot represent all of them
- Discrete time is viable when the high-frequency components that would be lost are not needed
- Nyquist: given sampling rate $F_s$, faithful reconstruction is guaranteed up to $F_s/2$
- What $F_s/2$ should be is an applied engineering question — Nyquist does not answer it
- Components above $F_s/2$ are lost: aliasing
- LTI and convolution hold in discrete time — commutativity survives
- Convolution becomes a sum (finite for FIR, infinite for IIR)
### 6. Nonlinearity and consequences
- Real systems violate LTI: time-varying parameters, feedback, saturation
- Each breaks a different condition: time-variance breaks TI, feedback and saturation break linearity
- Examples
- Modulated delay (chorus, flanger): delay time varies with time → time-invariance breaks; same input at different times yields different output
- Overdrive: saturation above threshold → linearity breaks; EQ before overdrive ≠ overdrive before EQ
- Commutativity breaks — order of composition is no longer irrelevant
- $h_1$ followed by $h_2$ ≠ $h_2$ followed by $h_1$ in general
- No universal rule; behavior must be examined per case
### 7. Summary
- Most of the framework rests on the LTI assumption
- Signalsystem equivalence, convolution, commutativity, frequency-domain analysis — all require linearity and time-invariance
- Real systems break the assumption routinely
- Nonlinearity is not binary — it is a spectrum
- Some systems are close enough to linear that the theory applies as a practical approximation
- Others are not — linear theory offers no useful prediction
- Judging where a system falls requires knowing what linearity is in the first place
- The framework is studied not as a description of reality, but as a baseline against which deviations are measured
## Text (lyrics if you insist)
今度は、信号とシステム、そしてデジタル信号処理について説明する。
### 1. 信号とシステム
信号とシステムを知るには、信号とシステム両方を知る必要がある。
信号とは情報を運ぶものである。
ここでは時間の経過とともに振幅がどう変化するか、その関数として扱う。
システムとは、入力信号を受け取り、出力信号を出す箱である。
箱の中身は問わない。何を入れたら何が出るか、その関係だけがシステムを定義する。
システムにはいくつか性質がある。線形性。
線形システムとは、重ね合わせの原理が成り立つシステムである。
入力を2倍にすれば出力も2倍になる。二つの入力を足し合わせたときの出力は、それぞれ単独で入れたときの出力を足したものと等しい。
この二つの条件が揃ったとき、そのシステムは線形である。
ただ、多くの物理システムはこの条件を満たさない。線形性は特殊であり、当たり前ではない。
そして時不変性。
時不変システムとは、入力を時間軸上でずらしたとき、出力も同じだけずれるシステムである。
今日と明日で同じ入力を与えれば、同じ出力が返ってくる。
パラメータが時間とともに変わるシステムは、この条件を満たさない。
線形かつ時不変なシステムを、線形時不変システムと呼ぶ。ここから先は一旦これだけを扱う。
これは解析的に扱いやすい、意図的に絞った特殊ケースである。現実の大半はこれに当てはまらない。けど、解析的に扱いやすいから線形時不変だけを考える。
ここで道具を一つ出す。インパルス信号である。
単一の瞬間に単位エネルギーが集中した信号で、実際には存在しない理想だが、使える。ちなみに瞬間とは無限に短い間のことである。
このインパルスをある線形時不変システムに通した出力を、そのシステムのインパルス応答と呼ぶ。
インパルス応答は、そのシステムを完全に表現できる。システムが確定したらインパルス応答も唯一になり、インパルス応答があれば唯一に対応するシステムも特定できる。
任意の入力はインパルスの積み重ねとして分解できる。インパルス応答さえ分かれば、どんな入力に対する出力も計算できる。
それと、インパルス応答はシステムの出力でありながら、信号と同じ種類の関数である。
つまりインパルス応答によって、システムは信号と同じ空間に置ける。操作の上では、システムと信号の区別は消える。
### 2. 線形時不変システムと畳み込み
インパルス応答がシステムを決定すると言った。なぜだろう。
任意の入力信号は、大きさの異なるインパルスを時間軸上に並べたものとして表せる。
線形時不変システムはそれぞれのインパルスに独立に反応し、その応答を全て重ね合わせる。
この重ね合わせ全体の操作を、畳み込みと呼ぶ。
連続時間では、畳み込みは積分になる。連続じゃない時間の場合は後ほど。
時間軸に沿って入力を少しずつずらしながら、そのずれに対応するインパルス応答を強さに応じて足し合わせる。その積分の結果が出力である。
$y = x * h$ y イコール x 畳み込み h)
畳み込みはその二つの引数に対して対称である。
$x * h = h * x$ (x 畳み込み h イコール h 畳み込み x)
これは計算上の偶然ではない。x と h が同じ種類の対象だからそうなる。前の節で言った、インパルス応答で、システムが信号空間に変換される話の続きである。
この対称性には実用上の意味がある。
二つの線形時不変システムを直列につないだとき、合成されたシステムのインパルス応答は、各インパルス応答の畳み込みである。
$h_1 * h_2 = h_2 * h_1$ h1 畳み込み h2 イコール h2 畳み込み h1)
どちらを先につないでも、結果は変わらない。
数学ではこれを可換性と呼ぶ。一応。
### 3. 信号変換
これまで信号を、時間に対する振幅の変化として扱ってきた。同じ信号を、周波数に対する振幅の分布として見ることもできる。
厳密には各周波数成分に位相もあるが、ここでは振幅に注目する。
そのためにフーリエ変換がある。というか、フーリエがその変換の仕方を決めたのでフーリエ変換と呼ばれた。
$s(t)$(エス ティー)と $S(\omega)$(エス オメガ)は同じ信号の二つの顔である。
一方は時間の経過を、もう一方は周波数の分布を示す。
つまり、どんな信号も、周波数の異なる正弦波をいくつか重ね合わせたものとして表せる。
楽器かエンジンの音がわかりやすい。どちらも複数の周波数成分が混ざっている。その配合が音色を決める。
$S(\omega)$ はその内訳である。どの周波数の成分がどれだけの強さで含まれているか、それがスペクトルである。
アナログ信号は原理的には、ゼロから無限大まであらゆる周波数成分を持ちうる。
これが後で問題になる。
### 4. フィルタ
信号は原理的に無限の周波数成分を持ちうると述べた。
実用上、その全てが必要なことはまずない。例えば人間の聴覚はおよそ20kHzまでしか知覚できない。
聞こえないので、人間に聞くための信号では要らない。必要な帯域だけを残し、不要な成分を落とす。それがフィルタの仕事である。
フィルタは線形時不変システムであり、フーリエ変換の言葉で言えば、信号のスペクトルを形作るシステムである。
フィルタを特徴づけるのは周波数応答 $H(\omega)$(エイチ オメガ)である。
これはインパルス応答 $h(t)$ をフーリエ変換したものである。
インパルス応答が時間領域でシステムを表すように、周波数応答は周波数領域でそのシステムを表している。
フィルタの働きは、周波数によって信号をふるいにかけることである。
基本的な分類としてローパス、ハイパス、バンドパスがある。
ローパスフィルタは低い周波数だけを通し、高い周波数を削ぎ落とす。
ハイパスフィルタはその逆で、高い周波数を通し、低い周波数を削ぐ。
バンドパスフィルタは特定の帯域だけを通し、それより低い成分も高い成分も減衰させる。
バンドパスフィルタは普通にローパスとハイパスを組み合わせたものと見なせる。
どちらを先に適用しても結果は変わらない。線形時不変システムだからの可換性です。
これらのフィルタは全て、カットオフ周波数という境界を持つ。
理想的には、境界の手前までゲインが1、超えた瞬間にゲインが0になる。垂直な壁である。
しかし、そのような理想は実現できない。
現実のフィルタは、カットオフ周波数の周辺に曲線を持つ。急な減衰ではなく、緩やかに下る斜面になる。
理想の壁に近づけようとすると、設計が複雑になり、部品が増え、コストが上がる。
時には、緩やかな斜面で十分である。
離散時間においては、有限インパルス応答フィルタと無限インパルス応答フィルタの区別がある。
前者のインパルス応答はある時点で終わる。後者は終わらない。
### 5. 離散化
フィルタはアナログにもデジタルにも存在する。
アナログ空間では、振幅も時間も連続である。最小単位というものがない。なめらかに、切れ目なく続く。
デジタル空間では、切れ目がある。
デジタルシステムが振幅を表現できる精度は、ビット深度によって決まる。
$N$ ビットのシステムは $2^N$ 個の離散的な振幅レベルを持つ。別にこういう二進数の話はしなくていいはずですが。
各サンプルの値は、最も近いレベルに丸められる。この丸め誤差を量子化ノイズと呼ぶ。
表現できる振幅の上限と下限は、設計とハードウェアによって固定されている。ADCやDACの基準電圧がそれを決める。
その境界を超えると、ハードクリップが起きる。
アナログ回路は限界に近づくにつれて少しずつ歪む。デジタルにそういう曖昧さはない。境界は硬い。
次に時間軸について。
デジタルシステムは、連続した時間の流れから、一定間隔で値を取り出す。これがサンプリングである。
ここで問題がある。前の節で述べたように、アナログ信号は原理的には無限大まで周波数成分を持ちうる。
しかし有限のサンプリング頻度では、表現できる周波数に上限がある。全てを保存することはできない。
その上限を超える成分がサンプリング時に残っていると、消えるわけではない。
折り返される。上限を超えた分だけ、反対側に折り返して、低い周波数の成分として現れる。
サンプリング周波数が40kHzのとき、25kHzの成分は15kHzとして記録される。存在しないはずの周波数が信号に混入する。
これをエイリアシングと呼ぶ。
対策は、サンプリングの前にローパスフィルタをかけておくことである。
ではそのフィルタのカットオフ周波数をどこに設定するか。
それは用途次第である。例えば人間の聴覚はおよそ20kHzまでしか知覚できない。
音声信号であれば、20kHz以上を保持する理由はない。
ただし、ここで単純に20kHzでローパスをかけて20kHzでサンプリングすると、情報は失われる。
サンプリング周波数と保存したい帯域の上限が同じでは、再構成できない。余裕が要る。
ナイキストの定理が、その余裕を定量化する。
サンプリング周波数を $F_s$ としたとき、$F_s/2$ より低い周波数成分は忠実に再構成できる。
つまり保存したい帯域の上限の2倍でサンプリングすれば、再構成が保証される。
人間の聴覚が20kHzまでなら、$F_s$ が40kHzを超えていれば聞こえる範囲はカバーできる。
余裕を持たせて、一般的には44.1kHzや48kHzが使われる。192kHzは人間以外の何かのためにあるのだろう。
定理が言うのはそれだけである。$F_s$ をどこに設定すべきかは用途が決める。
$F_s/2$ を超える成分は再構成できない。それがエイリアシングである。
補足しておく。この離散化によって、線形時不変システムの性質が崩れるわけではない。
連続時間において積分であった畳み込みは、離散時間においては和になる。有限インパルス応答なら有限和、無限インパルス応答なら無限和である。
可換性を含む全ての性質は引き継がれる。
### 6. 非線形性とその影響
では、現実のシステムに戻る。
先ほど線形時不変システムは特殊ケースであると述べた。
現実のシステムは線形時不変システムの条件を様々な形で破る。
時変パラメータは時不変性を破る。
フィードバックと飽和は線形性を破る。
例を挙げる。
モジュレーテッドディレイを考える。コーラスやフランジャーがその例である。
ディレイタイムが時間とともに変化するとき、同じ入力でも入力するタイミングによって出力が異なる。
これは時不変性の破れである。
次にオーバードライブを考える。
入力が閾値を超えると飽和が生じ、出力は入力に比例しなくなる。
これは線形性の破れである。
そして順序が問題になる。EQの後にオーバードライブを適用した結果と、オーバードライブの後にEQを適用した結果は、一般に異なる。
このとき、畳み込みの可換性は成立しない。
非線形システムでは、一般に
$h_1$(システム1)の後に$h_2$(システム2)を適用した結果と、
$h_2$(システム2)の後に$h_1$(システム1)を適用した結果は、等しくない。
普遍的な規則は存在しない。
各ケースを個別に検討する必要がある。
### まとめ
以上がデジタル信号処理の基本的な枠組みである。
振り返ると、ここで述べたことの大半は線形時不変システムという前提の上に成り立っている。
信号とシステムが同じ空間に住むこと。畳み込みによる合成。可換性。周波数領域での見通しのよさ。
これらは全て、線形性と時不変性が揃っているからこそ成り立つ性質である。
そして最後で述べた通り、現実のシステムはその前提をしばしば破る。
では、なぜこの枠組みを学ぶのか、現実のシステムはほとんど非線形なのに。
非線形性は白黒ではないから。線形と見なして良いシステムもあれば、線形理論が全く通用しないシステムもある。
その見極めには、何が破れているのかを知る必要がある。線形の理論はそのためにある。
線形時不変システムの理論は、現実そのものの記述ではない。現実を測るための基準線である。
+34 -47
View File
@@ -1,17 +1,6 @@
---
title: pulse under latent semantic envelopes - development notes
categories:
- Songwriting notes
wiki:
publish: true
siblings:
- path: pulse.md
tag: PULSE_SONG
---
# pulse under latent semantic envelopes
# pulse under latent semantic envelopes: personal dev notes
The remaining bits of how I came to all this. For the actual song page, see PULSE_SONG.
*(WIP. Description and pieces only now)*
## Planning area
@@ -33,33 +22,32 @@ Submarine, underwater, subsonic and supersonic pings as well as passive hydroaco
Literally, there can be long, essay-like, paragraphs (not too many) with structurally interconneting statements and sentences. But flairs of fragmented fractures of language (almost alliteration) is also appreciated and desired.
**Structural proposal**
1. "Surface." - the breach, the fever-dream opener
2. Instrumental - let the image settle
3. Essay/documentary - the explanatory core, almost clinical, "semi-boring scientific" (this is where the concept gets stated plainly before the rest of the song complicates it)
4. Instrumental - going into the poemic verses
5. Poem-ic verses - emotional density, maybe climax, maybe not
6. P-U-L-S-E 5-liners - trademark closer, acrostic constraint
7. Instrumental outro
**Structural proposal**
1. "Surface." - the breach, the fever-dream opener
2. Instrumental - let the image settle
3. Essay/documentary - the explanatory core, almost clinical, "semi-boring scientific" (this is where the concept gets stated plainly before the rest of the song complicates it)
4. Instrumental + fragments - the logic starts dissolving
5. Poem-ic verses - emotional density, maybe climax, maybe not
6. P-U-L-S-E 5-liners - trademark closer, acrostic constraint
7. Instrumental outro
## Construction zone
The first locked in draft version of the song. Things got developed even after this version.
*and yes, I did use a C++ code block to write my lyrics.*
```cpp
// Opener
Surface.
The equilibrium of silence between the static magnetic noise, the watery planes, and the optical waves.
Blurred and mangled electronic signs over the outbound informational motorway.
Distant stations estimated in abnormal heat perform the collimation rite.
The equilibrium of silence between the static magnetic noise, the watery planes, and the optical waves
blurring the electronic signs over the outbound informational motorway.
Images imagined in the imaginary region of the protruding obelisks many kilometres away
from this here expanding entropy killing various variables as abnormal heat usually may.
// think a submarine surfacing at night to do some radio comms as the starting point, then infuse it with a fever dream
// 'Images imagined in the imaginary region' is half wordplay, half multimedia transmission with a loss (signal-wise). the obelisks are basically antennae.
Dive.
The black screen of stalemate conceals the black stars, the black comets, the black meteorites
their questionable glitters, once emissions of brave borderers and dark adventurers
their questionable glitters and gleams, once emissions of brave borderers and dark adventurers
now the only traces, obscured and indifferent to all but those with a special breed of faith.
// 'Dive' - an opposite to 'Surface'. This is on the receiving end.
// Just see this as 'receiving other guys' pulses'.
@@ -69,9 +57,9 @@ now the only traces, obscured and indifferent to all but those with a special br
// The pseudo documentary narration, half-blended into the background music
// in a metalingual sense the music is the background noise and the narration is the signal with a low SNR. Or one could consider the roles swapped.
The noise floor of a receiving environment is the aggregate of all background signal energy present across a given frequency band at any instant. In urban contexts, primary contributors include electromagnetic emissions from power distribution infrastructure, wireless communications networks, and consumer electronic devices. The noise floor is not centrally coordinated; no single source generates it. It emerges from the cumulative output of many independently operating transmitters, each functioning within its own parameters, whose combined effect is persistent and largely uniform. Under standard conditions, this background level is treated as a fixed baseline rather than a variable of interest. Signals whose amplitude falls at or below this baseline remain physically present in the medium but cannot be distinguished from the background by a receiving system, and are not considered recoverable.
The term "ambient frequency" refers to the aggregate of background signals present in a given environment. In urban contexts, this includes electromagnetic interference from power infrastructure, wireless communications networks, and consumer electronic devices. The ambient field is not centrally coordinated. No single source generates it. It emerges from the cumulative output of many transmitters operating within similar parameters. The resulting noise floor is persistent and of low significance under normal circumstances. Signals that fall below this threshold remain technically present but are not distinguishable from the noise itself, and are not considered practially receivable.
An impulse signal, also referred to as a unit impulse, is defined as a signal with zero value at all points in time except a single instant, at which its value is notionally unbounded, subject to the constraint that its total integrated area equals unity. In practice, true impulse signals cannot be physically produced; they are approximated by short-duration, high-amplitude pulses of sufficient bandwidth. The impulse response of any linear time-invariant system that is, the output produced when an impulse is presented as input fully characterises that system's behaviour under any subsequent input. In the absence of any input, a system at rest produces no output and exhibits no properties that distinguish it from any other inactive system. From a single impulse and its measured response, the complete transfer function of the system can be derived. This property is considered foundational to systems analysis.
An impulse signal, sometimes referred to as a unit impulse, is defined as a signal with zero amplitude at all points except for a single instant, at which point its amplitude approaches infinity while its total energy remains finite. In practical applications, true impulse signals cannot be generated; they are approximated by short-duration waveforms of high amplitude. The impulse response of any linear system - that is, the system's output when presented with an impulse input - fully characterises that system's behaviour. From a single impulse and its response, the complete identity of the system can be derived. This property is considered fundamental to signal analysis.
// build some tension with bass and drum and fiddle here
@@ -79,27 +67,26 @@ An impulse signal, also referred to as a unit impulse, is defined as a signal wi
// more 'rhythmic yelling' than singing, you get the idea
Subdued sonic scalars vectorise
Acoustic aberrations dissipate
// sahb - duwd - sao - nihk - skay - lahrs - vehk - tahr - rayz,
// (ah - ) kaws - tihk - ax - bahr - ray - shaxns - dihs - sah - payt
// --- stanza: the receiving end ---
Isotropic funnel strikes a packet rain
Fine-grained bags of acks ground astray
Spectral broadcast lossy with a narrow sight
No perceived replies per design
// needs further tweaking
Ocean as a desert buries all of its life
The ocean as a desert buries all of its life
Deck the shell with a perfect thermocline
// 'deck the shell': intentional vagueness between 'decorate the outer shell' and 'knock on the border surface'.
// (thax - ) ao - sheh(n) - naes - ax - deh - zahrt - bah - riys - ao(l) - lahv - ihts - layf
// (dehk - thax - ) shehl - wit - ax - pahr - fekt - thahr - mow - klayn
Curtain shut before the Fresnel bights
Plasma buildup swells your rover's thighs
A dim light dies in the rover's eyes
Or the next one could never come otherwise
// Thoughts: 'the light dies' because a pulse is mostly dormant you wanker. You have to let the light die so it lights up again, simple as
// ending verse(s) before the painfully long instrumental outro
// P:
particulate pressure plagues across a landlocked island
// U:
ultraviolet utilitarian paints every third crag bland
// L:
lossy lies lament the ludicrous lawful liberty
// S:
siren sounds soaken in the sauna of substantiality
// E-S-L-U-P:
essential sentiments leave unbidden perpetually
p.....
u.....
l.....
s.....
essential sentiments lay unconditionally permanent
```