Digital music could absolutely exist without the Fourier Transform.
The author should familiarize himself with the history of digital audio, and its milestones such as the development of the compact disc format: long before MP3, Ogg and the popularization of the Internet, and its use for media streaming.
At its bare bones, digital audio requires time domain sampling and reconstruction, sandwiched between some filters that can be analog. It requires understanding of the Nyquist limit, which can be purely in time domain terms (sampling frequently enough to avoid an temporal aliasing ambiguity in the reconstruction).
Digital synthesis of music can also be as simple as playing recorded samples in loops, and scaling them in the time domain for various pitches (or changing the sample rate, or both), which doesn't require Fourier.
Claiming that the FT is not necessary for digial audio is like claiming that the you don't need the rocket equation in order to build a missile. Sure, its technically possible, and yes, there were probably early pioneers that forged ahead before the mathematical theory was fully sketched out, but our understanding of the fourier transform has drastically increased our ability to design acoustical systems.
Those analog anti-aliasing and anti-imaging filters are designed using LTI systems theory, that fundamentally rely on the Fourier tranform to reason about their transfer functions. The Nyquist-Shannon sampling theorem was proven using the fourier transform. Without the fourier transform, you need to rely entirely upon time domain representations of signals, and perform your analysis using tedious convolutions. You can't use a spectrum analyzer to examine the signal to noise ratio of your CD player. While it's true that digital music could technically exist without the fourier, there is no way in hell it would be as pervasive as it is today.
The Windows 95 startup sound, created by Brian Eno, was coded ADPCM. Seemed to work okay. A billion people heard it. (8 bit MS ADPCM also sounded horrible.)
You surely mean 8 bit PCM (without "AD") sounded horrible? ADPCM encodes differences in just 4 bits but the decoded values are in the range of 16 bits.
"ADPCM stores the value differences between two adjacent PCM samples and makes some assumptions that allow data reduction. Because of these assumptions, low frequencies are properly reproduced, but any high frequencies tend to get distorted. The distortion is easily audible in 11 kHz ADPCM files, but becomes more difficult to discern with higher sampling rates, and is virtually impossible to recognize with 44 kHz ADPCM files."
I've already linked this article and it has even more details, highly recommended.
I wrote some of those original codecs. I'm aware of what they do. :) The original SoundBlaster card was 8-bit. Creative ADPCM is 8 bit. Dialogic ADPCM -- basically every recorded sound you've ever heard over a telephone -- is 12 bit. You are correct with the modern definition but I'm talking about 20 years ago so let's not stomp on history for sake of Hacker News karma points.
The Microsoft article gets a few things wrong. The distorted sound is not due to reducing the sample rate. The distorted sound comes from taking a perfectly-good 11k file and then ADPCM compressing it. This is obviously due to throwing away information on each sample as part of the encoding process, not anything due to sample rate. (Of course it sounds better at higher sample rates. More data, more better.)
ADPCM for telephony seldom even hit 11k rates. 6000 and 8000Hz ADPCM files are common. (And nope, not 16 bit either.)
I fully agree with you re 8-bit SoundBlasters and phones. I was talking about the music recorded for CDs, 16-bits. Converting that to ADPCM was certainly not a process that was guaranteed to automatically give the good results but it was at least possible to produce reasonably good sound and save some space.
I'd be of course happy to hear something more about the work you did.
Most people don't appreciate the transition to digitized images & audio went thru early on: as the technology went mainstream, there was an extreme insufficiency of storage space & network bandwidth that had to be overcome as a chicken-and-egg problem. In a day where multi-mile wireless >10Mbps bandwidth & >32GB storage to your pocket is cheap, we forget how painful desktop wired dialup bandwidth & ~100MB storage was, and the crazy contortions we had to go thru to transfer & store digital images & audio. FFTs and subjective image extraction solved those problems, leaving artifacts which utterly baffle today's users who can, say, store a full year's worth of HD video for $50, or 200GB wireless cloud hosting for $4/mo.
Yeah, we could have done digital audio without FFTs. Woulda been infeasible though given the circumstances.
"22 kHz mono ADPCM can be decompressed real-time (that is, while playing) on a 386SX/16 megahertz CPU"
Note: 16 MHz 386SX was effectively slower than the 286 of the same speed.
I had all the Beatles albums on one CD, all encoded with ADPCM, and the sound was not bad.
If I remember correctly, the guys at Bell Labs had also some server filled with the digital music. But I can't locate the story (maybe somebody remembers, was it Ritchie or Thompson?) and don't remember when actually.
If the Fourier transform didn't exist I don't know that any music could exist, since lack of it would imply that sounds of different frequencies could not be linearly combined. For example, imagine if playing a drum and violin simultaneously produced crackling static!
That being said, it's a poor linkbait title for a superficial article that's missing nuance, rigor, and causality. Anyone who takes interest in this subject should read Wikipedia or an actual textbook, lest they feed their Dunning-Kruger.
Music exists without a man-made technology that is the result of a conscious application of the Fourier transform.
Optics too. People understood geometrically how a lens focuses reflected light to produce an image before the Fourier transform view on it was revealed.
The fourier transform is just means to transform one abstract representation to another. There isn't anything inherently physical about the concept that says that music couldn't exist without it.
I think you didn't read much of the article past the headline -- the article is about how FFT allows for efficient compression of just about any human-audible sound, which allows us to send around the files more easily & efficiently. Your first example is about classic lossless formats, and your second example is about synthesis (which for the time being is significantly less expressive than recorded sound)
The author should familiarize himself with the history of digital audio, and its milestones such as the development of the compact disc format: long before MP3, Ogg and the popularization of the Internet, and its use for media streaming.
At its bare bones, digital audio requires time domain sampling and reconstruction, sandwiched between some filters that can be analog. It requires understanding of the Nyquist limit, which can be purely in time domain terms (sampling frequently enough to avoid an temporal aliasing ambiguity in the reconstruction).
Digital synthesis of music can also be as simple as playing recorded samples in loops, and scaling them in the time domain for various pitches (or changing the sample rate, or both), which doesn't require Fourier.