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.
I think the article says, though, that fourier analysis on the music is necessary for digital audio.
Microsoft's ADPCM was always 4 bits encode of the 16-bit sample. The distorted sound in some files was due to reducing the sampling rate.
https://support.microsoft.com/en-us/kb/89879
"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.
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'd be of course happy to hear something more about the work you did.
Yeah, we could have done digital audio without FFTs. Woulda been infeasible though given the circumstances.
ADPCM. No FFT. Worked on my 1991 PC:
https://support.microsoft.com/en-us/kb/89879
"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.
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.
Optics too. People understood geometrically how a lens focuses reflected light to produce an image before the Fourier transform view on it was revealed.
(http://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfor...)
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.