Re: [music-dsp] Nyquist–Shannon sampling theorem
The application is music. I understand the basics, my question is in the constraints that might be imposed on the signal or functon as referenced by the theory. Is it understood to be repeating? for lack of a better term, essentually just a mash of frequencies that bever change from start to finish. I'm thinking the math must consider it this way, or rather the difference is abstracted since the signal is assumed to be band limited, which means infinit, which means you can create any random signal by inject the required freuencies at the reuired amplitides and phase from start to finish, even a 20k 2ms blip in the middle of endless silence. Is that making any sense? I'm struggling with the fine points. I bet this is obvious if you understand the math in the proof. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Nyquistâ?Shannon sampling theorem
consider this from a wiki page A bandlimited signal can be fully reconstructed from its samples, provided that the sampling rate exceeds twice the maximum frequency in the bandlimited signal. This minimum sampling frequency is called the Nyquist rate. This result, usually attributed to Nyquist and Shannon, is known as the Nyquist-Shannon sampling theorem. An example of a simple deterministic bandlimited signal is a sinusoid of the form . If this signal is sampled at a rate so that we have the samples , for all integers , we can recover completely from these samples. Similarly, sums of sinusoids with different frequencies and phases are also bandlimited to the highest of their frequencies. The example may imply that the bandlimited signal to satisfy the theory is at it's most a complex sum of various sinusoids at different frequencies phases, amplitudes. aa9a7b3fc744c653a5629d4b3d6ae5fd.pngfb409984dea7c4b5f093208b3174ac4c.png269e6a3cdee35a7eec719c55abbf640a.png7b8b965ad4bca0e41ab51de7b31363a1.pnge34fd49d79f3869d9033f958be91021e.png-- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Nyquist–Shannon sampling theorem
sorry about all the attachments, didn't see that coming. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Nyquist–Shannon sampling theorem
There is the frequency-sensitive requirement that you can’t properly sample a signal that has frequencies higher than half the sample rate. For music, that’s not a problem, since our ears have a significant band limitation anyway. This is intuitive. I think perhaps what I'm asking has more to do directly with the fourier series than sample theory. It's my understanding that the fourier theory says any signal can be created by summing various frequencies at various phases and amplitudes. So this would answer my question then that it's not really a stipulation of the function persay, since any signal at all can be described this way. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Nyquist–Shannon sampling theorem
so is there a requirement for the signal to be periodic? or can any series of numbers be cnsidered periodic if it is bandlimited, or infinit? Periodic is the best word I can come up with. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
[music-dsp] mangled peaking filter response
I implemented some eq IIR filters from the pages of the dsp site somewhere based on the digital filter cookbook that is quite popular. the peaking flter doesn't always display a symetrical bell curve. I'm not talking about cramping near nyquist, it happens at the top couple db of the bell curve, looks like a gumby head, a flat line from the top left to a couple db down on the right. This only happens with a narrow bandwidth, and the problem get's worse at lower frequencies, where ultimately the bell curve response of the filter gets completely mangled and looks like the snake that ate the elephant from the little prince. Higher sample rates have no effect on the problem. I've triple checked all my variables and everything looks fine. I've resorted to trying to clamp bandwidth based on frequency, but I don't see any evidence of this behaviour anywhere else I've looked. I am plotting the filter using a time domain spectrometer, 12 buckets per db, I really don't think that is the problem. Any idea what is going on here? Is this typical behaviour? Other graphs I've seen on the net show a perfectly symetrical response curve even at very narrow bandwidth settings. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] mangled peaking filter response
ahh, I doubled the buckets on my spectrometer and the lopsided problem went away in the higher frequencies, but the completeluy mangled bell curve stayed on the low end. I guess there is something wrong with my spectrometer, I'll have to double check everything, doesn't make sense though, works fine for shelving filters. I'm supplying it with a unity wave at every bucket frequency as a starting point, guess Ill have to review that code. false alarm, the filters are probably working fine. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] mangled peaking filter response
yep, just visual samplerate aliasing and input data too small for the window function at lower frequencies, sorry to bug anyone :) -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
