One subject that I've always been interested in, but have never found the proper introduction to is signal processing. I thought PF might be an appropriate place to ask (tough, I'm not even sure which forum it would be most appropriate, but since I'm stronger in math than physics, I'm posting here).(adsbygoogle = window.adsbygoogle || []).push({});

This is sort of an open-ended inquery, but I'll list the kinds of problems I'd like to learn how to solve:

1) Given a continuous input signal, you can sample the signal at regular intervals. Given that your sampling rate is sufficiently high (something about the nyquist frequency), you can reconstruct the continuous signal from the samples. How is this done?

2) Given a recording of a violin or piano, how can you analyze what note is being played? I know the fourier series is used for when you know the period of your signal, but with sampled data coming from a microphone, the signal is not guaranteed periodic. I believe this has to do with the fourier transformation, but no source I've found has a clear definition of how it works or what it represents other than it is an extrapolation of the fourier series for aperiodic signals.

3) In music, the pitch of a note generally correlates with the frequency of a signal. If the frequency distribution of a signal is constant, how do you reconcile this with the fact that the pitches (and thus, frequencies) in the music vary with time?

4) I found a listing of some standard functions with their fourier transformations listed in a table. Many of them included a delta (which as far as I understand is being used as a Dirac delta function). The Dirac delta function, is of course, not really a function since it diverges to infinity, (but is still useful because it gives you the correct answer). Is it typical that the fourier transformations of signals diverge like this?

You can see I have some rough notions of the subject already, but I want to know good resources for fitting all the pieces together. Any help would be very much appreciated.

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# Signal Processing

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