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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.

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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..

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.

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