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Some Sounds Disappear Without Being Noticed有些聲音,消失了也不會被發現

A brief history of MP3 — and a technique of compression, hearing, and learning to forget.MP3 的簡史,以及一套關於壓縮、聽覺與遺忘的技術。

Horris Tse
Horris Tse Founder · HtPiHtPi 創辦人
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My undergraduate final-year project studied MP3 — and the brief was very concrete: make an MP3 decoder run on the low-cost chips used in toys. Those chips had no computing power to spare; calculations that leaned on floating-point arithmetic had to be rewritten in fixed-point before they stood a chance on cheaper, smaller hardware.

我本科的畢業專題,研究的正是 MP3。題目很具體:怎樣把 MP3 decoder(解碼器)放進玩具使用的低成本晶片。這類晶片沒有充裕的運算能力;原本依賴 floating-point(浮點數)的計算,要改寫成 fixed-point(定點數),才有機會在更便宜、資源更少的硬件上運行。

At the time, I treated MP3 as a problem of signal processing and engineering trade-offs: how much numerical precision could be surrendered before the loss became audible? Where would errors accumulate once the representation changed? Years later, what the project left behind was more than an implementation technique.

那時候,我把 MP3 看成一個訊號處理與工程取捨的問題:精度可以少到甚麼程度,仍然不會破壞聽感?數字的表示方式改變後,誤差會在哪裏累積?多年後再回頭看,這個專題留下的卻不只是一套實作方法。

It posed a more interesting question: when resources are limited, what should we keep?

1,411,200 bits

One second of uncompressed stereo CD audio.

MP3 does not try to preserve every one of them. It models how we hear first, then leaves less room for what is hardest to notice. The sound still sounds like itself — with far less data behind it.

Compression is not about making everything smaller.
It is a decision about what need not remain.

None of this is arbitrary deletion. It rests on psychoacoustics, mathematical models, signal transforms, and a great deal of listening. MP3’s achievement is not forgetting a lot — it is forgetting precisely.

它提出了一個更有意思的問題:如果資源有限,我們應該留下甚麼?

1,411,200 bits

未經壓縮的雙聲道 CD 音訊,每一秒的資料量。

MP3 沒有嘗試把每一個 bit 都保存下來。它先理解人耳怎樣聽,再把較少的空間留給較難察覺的部分。聲音仍然像原來的聲音,但資料已經少了很多。

壓縮不是把一切縮小。
而是決定甚麼可以不留下。

這個選擇並非隨意刪除。它建基於心理聲學、數學模型、訊號轉換,以及大量聆聽測試。MP3 的厲害,不是忘得多,而是盡量忘得準。

It does not hear less. It knows what you cannot hear.

The shorthand explanation says MP3 removes frequencies humans cannot hear. That is not exactly wrong, but the real mechanism is finer: whether a sound is audible also depends on when it occurs and what is playing beside it. For each short frame of sound, the encoder takes four steps.

01 · Split — a moment into frequencies. The encoder decomposes the frame into frequency components and watches how energy is distributed across time and frequency.

02 · Estimate — draw the hearing threshold. A psychoacoustic model estimates which components are easy to hear and which will be masked by stronger neighbours.

03 · Trade — spend bits where they matter. Perceptually sensitive components receive more precision; masked components are represented with fewer bits, and quantisation noise is pushed, as far as possible, below the masking threshold.

04 · Pack — record the common more briefly. The quantised values then pass through entropy coding: frequent values get shorter codes, rare values longer ones. This step loses nothing further — but nothing discarded earlier can ever be played back.

它不是聽得少。它是知道你聽不到甚麼。

常有人說「MP3 刪去人耳聽不到的頻率」。這樣說大體不算錯誤,但真正的機制更細緻:同一個聲音是否聽得見,還要看它在甚麼時候出現,旁邊又有甚麼聲音。編碼器每次面對短短一段聲音,會走過四步。

01 · 分拆——把瞬間拆成頻率。編碼器把這段聲音分解成不同頻率成分,觀察能量在時間與頻率之間如何分布。

02 · 估算——畫出聽覺門檻。心理聲學模型估算哪些成分容易被聽見,哪些會被較強的鄰近聲音遮蔽。

03 · 取捨——把 bits 用在刀口。容易察覺的部分得到較多精度;不易察覺的部分用較少 bits 表示,量化誤差盡量藏在遮蔽門檻之下。

04 · 收納——常見的,用更短方式記錄。量化後的數值再經熵編碼:經常出現的值用較短代碼表示,較少出現的值用較長代碼。這一步不再損失資料,但播放時仍無法找回較早前被捨棄的聲音。

One voice once defeated MP3.

During development, American singer-songwriter Suzanne Vega’s near-a-cappella recording of “Tom’s Diner” became a famous test track. With little accompaniment to hide behind, its exposed vocal texture readily revealed coding artefacts; MP3’s core researcher Karlheinz Brandenburg listened to it over and over while tuning the system, and the song was later called the “mother of MP3”.

The story is a reminder that mathematical models must return to human ears. An encoder can calculate a masking threshold; someone still has to hear when the model is wrong.

Low-bitrate MP3 sometimes turns metallic, warbles, or produces pre-echo — a smear of sound leaking out just before a handclap or drum hit has happened. These artefacts say something honest: lossy compression is not the objective removal of the unimportant, but a bet, placed by a model, on which losses will go unnoticed.

What has MP3 forgotten?

Does it simply delete everything above 20 kHz? No. Low-pass filtering may be part of some encoder or bitrate strategies, but MP3’s core is not a blunt cut. It estimates frequency and temporal masking within short frames, then allocates its limited bits.

Can the discarded data be recovered? Not exactly. MP3 is lossy by design; the decoder reconstructs an approximation. Bit-perfect recovery of the original PCM needs a lossless format such as FLAC.

Is 128 kbps a fixed level of quality? Not necessarily. Material, encoder, settings and listening environment all shape the result. A bitrate is a similar data budget, not a guarantee of identical perceived quality.

Why did MP3 succeed, rather than merely work? Because it solved the right constraints at the right time: tiny hard disks, 28.8 kbps modems, and then portable players. Compression turned “sending a song” from impractical into a wait you could accept.

Memory keeps content. Forgetting makes room for structure.

MP3 does not know what a song means to you. It only knows that at a given instant, some signals are likely to be covered by others.

But it leaves an observation worth carrying beyond audio: receiving more is not the same as understanding more. When attention is limited, selection is not a flaw in the system. Selection is the system.

Compression is a judgement about what deserves to remain,
written down as executable technique.

So missing a few days of information is not necessarily falling behind. Sometimes it is simply reallocating limited attention to what has not yet been absorbed.

Sources & notes

  1. Fraunhofer IIS — The mp3 History: Timeline
  2. Fraunhofer IIS — Development
  3. Fraunhofer IIS — Technology
  4. MPEG — MPEG-1 Audio
  5. Fraunhofer IIS — 30 Jahre .mp3
  6. Fraunhofer IIS — Dieter Seitzer: pioneer and founding director
  7. Apple Newsroom — Apple Presents iPod (2001)

File sizes are theoretical estimates, excluding container/metadata overhead. The listening demonstration synthesises tones in the browser to convey the intuition of masking; it is not the full psychoacoustic model of an MP3 encoder.

一把人聲,曾經難倒 MP3。

在研發過程中,美國創作歌手 Suzanne Vega 的〈Tom’s Diner〉成為著名的測試素材。原始錄音以近乎清唱的人聲為主,聲音裸露,細微失真很難躲在伴奏之後;MP3 核心研究者 Karlheinz Brandenburg 在研發期間以它反覆試聽和調整編碼系統,這首歌後來因而被稱為 MP3 的「母親」。

這段故事提醒我們:數學模型最後仍要回到人的耳朵。編碼器可以計算遮蔽門檻,卻仍需要有人聽出甚麼不對。

低 bitrate 的 MP3 有時會出現金屬感、顫動,或 pre-echo:拍手、鼓點等瞬間聲音尚未發生,前方已先滲出一層模糊聲響。這些破綻正好說明:有損壓縮不是把「不重要」客觀地清除,而是根據模型,押注哪些損失不會被察覺。

MP3 忘記了甚麼?

它是否只刪除 20 kHz 以上的頻率?不是。低通濾波可能是部分 encoder/bitrate 的策略,但 MP3 的核心不只是一刀切走高頻。它會在短時間片段內估算頻率遮蔽與時間遮蔽,再分配有限的 bits。

被壓走的資料可以還原嗎?不能完整還原。MP3 是有損壓縮;decoder 重建的是近似聲音。若要逐 bit 還原原始 PCM,需要使用 FLAC 這類無失真格式。

128 kbps 是否等於固定音質?不一定。素材、encoder、設定和聆聽環境都會影響結果。同一 bitrate 只是相近的資料預算,不是相同的知覺品質保證。

為甚麼 MP3 成功,而不只是技術上有效?因為它在對的時代解決了對的限制:容量細小的硬碟、28.8 kbps modem,以及其後的便攜播放器。壓縮率把「傳一首歌」由不切實際變成可以等待的時間。

記憶保存內容。遺忘騰出結構。

MP3 不知道一首歌對你有多重要。它只知道,在某一瞬間,有些訊號較可能被另一些訊號蓋過。

但它留下了一個可以帶到技術以外的觀察:接收得更多,不等於理解得更多。當注意力有限,選擇不是系統的缺陷;選擇本身就是系統。

壓縮,是一套關於「甚麼值得留下」的判斷,
被寫成可以執行的技術。

所以,錯過幾天資訊,不一定是落後。有時只是把有限的注意力,重新分配給還未消化的東西。

資料來源與備註

  1. Fraunhofer IIS — The mp3 History: Timeline
  2. Fraunhofer IIS — Development
  3. Fraunhofer IIS — Technology
  4. MPEG — MPEG-1 Audio
  5. Fraunhofer IIS — 30 Jahre .mp3
  6. Fraunhofer IIS — Dieter Seitzer: pioneer and founding director
  7. Apple Newsroom — Apple Presents iPod (2001)

檔案大小為理論估算,未計 container/metadata overhead。互動聽覺示範以瀏覽器即時合成聲音,只用來呈現 masking 的直覺,不等同 MP3 encoder 的完整心理聲學模型。

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