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06:05:31  <jjjohnny>mikolalysenko: T/F i should only care about 1/2 of the returned sample set for an FFT?
06:05:47  <mikolalysenko>jjjohnny: is it real valued?
06:05:54  <jjjohnny>yes
06:06:17  <mikolalysenko>for a real valued fft then it satisfies the property that f(-w) = conj(f(w))
06:06:40  <mikolalysenko>where f(w) the value of the ft at w
06:06:52  <mikolalysenko>and conj(z) is the complex conjugate of some number
06:07:21  <mikolalysenko>so from this equation, given half of the frequencies ie those >=0, you can deduce the other half
06:07:31  <mikolalysenko>so in some sense: yes, you only need half the frequencies
06:07:55  <mikolalysenko>however to apply the convolution theorem or do most manipulation you need the whole spectrum
06:08:34  <mikolalysenko>there are advantages to working with half the frequencies though, and some packages like fftw have options for real valued ffts that only return the positive half of the fourier transform
06:08:57  <jjjohnny>mikolalysenko: but can one accurately know the value of ie. 7000Hz with a 8k soet of samples?
06:08:59  <mikolalysenko>see this page for more info: https://en.wikipedia.org/wiki/Hermitian_function
06:09:35  <jjjohnny>ftr i do ndarray-complex.mag the fft reals
06:10:21  <mikolalysenko>generally to get a frequency domain accuracy of 1/n hz, you need at least 2n samples
06:10:51  <mikolalysenko>err I mean for n hz
06:11:24  <mikolalysenko>so you would need 14k samples/second to encode a 7kHz signal losslessly
06:13:02  <mikolalysenko>the reason for the doubling is actually related to that hermitian symmetry in a sense
06:13:22  <mikolalysenko>so you can think of hermitian symmetry as killing 1/2 the degrees of freedom in the signal
06:13:57  <mikolalysenko>or because the output of the ft is complex valued you have 2x as much data as the real side does
06:16:50  <jjjohnny>mikolalysenko: can i get values up to 48k Hz fft analyzing 2 seconds of a samplRate 48k signal
06:18:27  <jjjohnny>seems legit to me
06:19:48  <mikolalysenko>yeah
06:20:23  <mikolalysenko>the units on this always get a little weird and I sometimes find it hard to keep straight sometimes
06:20:43  <mikolalysenko>but morally you need 2x as many time samples to get up to some frequency
06:21:05  <mikolalysenko>though you have to be a little careful with the units you use for time/frequency
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17:21:31  <substack>this doesn't look fun: https://github.com/nodejs/node-eps/pull/3
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