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Comment by ar7hur | Hacker News Reader

Also, the fact that 44,100 can be factored as 2^2 * 3^2 * 5^2 * 7^2 makes it very efficient to do Fast Fourrier Transforms on moving windows. Which we do a lot in Speech Recognition and DSP in general.

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What you say actually makes no sense whatsoever. What is forcing you to consider 1 second windows?

Also, 48kHz is 2^7 * 3 * 5^3 so it actually avoids the larger prime factor of 7. Not that anyone cares: just use an actual power of two as your window size to begin with!

What you say actually makes no sense whatsoever. Why are you talking about 1 second windows? If 44100 can be decomposed easily in small prime numbers, it means that you can split 44100 into windows that are themselves products of small prime numbers.

The length of a second is arbitrary and irrelevant to audio processing. The fact that there are 44100 samples in an arbitrary length of time is meaningless. You would only care about the prime factorization of 44100 if the second was some special amount of time, which it is not.

Why are you splitting 44100 samples into windows? That's the number of samples in one second. Where did you get one second from? You could have started from any duration.

I see what you mean, but since the 1970s speech researchers have been splitting seconds into 10ms or 25ms intervals, that's not my decision. They could have started from any duration but they haven't. And you could start to express time with the Aztec calendar if you wanted. But you won't.

It's not (entirely) arbitrary. Speech is variable, our vocal tract shape changes all the time, but not arbitrarily fast. From a source-filter theory perspective it does make sense to consider speech production over short time frames as linear time-invariant systems.

What this has to do with 44.1 kHz is beyond me, however..

Actually 44.1kHz is unhelpful for that... a lot of infrastructure exists that expects things to work on 10 and 20ms intervals (and multiples there-of), e.g. the normal windows audio apis work in 10ms chunks.

10ms of 44.1kHz is 441 samples, which is odd and thus a not really fantastic size for easily implemented factorizations.

Of course, if you can pick your own analysis interval you can pick some nice power of two or other very smooth number. But thats true regardless of the sampling rate.

Almost all ASR engines use 25ms windows, not 10ms (they typically overlap and are processed every 10ms).

25ms of 44.1kHz isn't even an integer. So the original argument is even less compelling with 25ms windows than it was with 10ms windows.

10-20 msec is the neighborhood of the Haas Limit. That's why, sfaik.

Yep. But understanding Fourier Transforms takes some effort. Luckily, HN user 'bsilvereagle' posted this earlier today:

"Linear Systems and Optimization | The Fourier Transform and its Applications"

https://news.ycombinator.com/item?id=7789767

http://see.stanford.edu/see/courseInfo.aspx?coll=84d174c2-d7...

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