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Comment by aatish | Hacker News Reader

Thanks for your feedback. Sure, any digital signal is by definition finite in its resolution (the sample rate or bits). I was trying to address the distinction between wave files of the type stored on audio CDs, and MP3s - both digital signals. I agree that the Fourier transform is in principle lossless, but it's particularly useful to use it in a lossy way, i.e. to throw out the least important (to us) components of the signal. If I was particularly misleading about this, I'd like to know.

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Well, if you want to be 100% accurate, I think the section talking about how the high notes aren't important could be clarified. The really high "notes" have already been lost when you recoded the wav file digitally. The lossy step of mp3 encoding is not a result of the transform, but what you do with that information and is more complex than just discarding high frequency components.

Also, the the word "note" is confusing in the context of music, since really low notes usually contain a lot of high frequency information.

Correct. (For the author's benefit) We usually call them harmonics, in the context of pitched sounds, but more accurately, the sinusoidal components of any sound are called its partials. Partials differ from harmonics in that harmonics are restricted to be sinusoids with frequencies that are integer multiples of a fundamental frequency. Real world musical notes don't often exactly fit this paradigm [1].

In any case, if discarding high frequency information is all you needed to do to compress, you could simply low-pass filter the time-domain signal. A better description of what goes into MP3 compression is that it omits frequency components in sound that we can't hear because they are shadowed by nearby (in time and/or frequency) components that are louder.

[1] http://en.wikipedia.org/wiki/Piano_tuning#Stretch

For what it's worth, mp3s do not store the signal as a DFT. The frequency domain data is produced as a MDCT (modified discrete cosine transform). A DFT is performed during MP3 encoding, but it's used to apply the psychoacoustic model (which is much more complex than just throwing out high frequencies) to figure out how to layout the frequency bands in the MDCT. I don't believe JPEG uses a DFT at any point, just a DCT.

I think you were kind of hand-wavy, but that's just how it has to be for this kind of article. If you're trying to explain this stuff to a general audience, you can't just jump right into talking about nyquist limits and stuff.

But maybe you could allude to the fact that there's more going on.

Anyways, I liked the article.

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