A few final clarifying questions, inline below:
On Sun, Mar 18, 2018 at 8:35 PM, Maximilian Stiefel < stiefel.maximil...@online.de> wrote: > Hi Brad, > > > Taking a step back, maybe the mirroring is a product of the method I'm > > using to interpret the output of the FFT. > > I really do not think so, because, as explained below and in the previous > mail, the phenomenon, we witness here, results from the physics behind > signal theory. > > As I understand your code, you are calculating the Energy Spectrum Density > (ESD), because you take the square of the magnitude of the FFT. The ESD > gives you the energy distribution of the signal over the spectrum. > > https://en.wikipedia.org/wiki/Spectral_density#Definition > > It is legitimate to design audio signal analysis like that, from my point > of view. To interpret your results one can say, that the ESD (let's call it > Psi(w)) has the following properties: > > Psi(w) = Psi(-w) (even) > Psi(w) >= 0 > > This properties also accord to what I explained in my previous mail. A > "natural real signal" such as the output from your wave file consists out > of an odd and even part i.e. > > s(t) = se(t) + so(t). > > We said, that the even part corresponds to an even real part in the > frequency domain and the odd part corresponds to an odd imaginary part in > the frequency domain. However, by taking the square of the FFT's magnitude > (this is what I saw in your code) you will make the whole spectrum even and > real e.g. > > ( j*sin(x) )^2 = -sin^2(x) > ^ ^ > odd and imaginary even and real > > Thus, your output corresponds to the underlying physics. > > > If we listen to a dial tone recording for example, we can clearly tell > > that two and only two tones are present. Is FFT able to tell us the same > > thing (exactly two spikes, at expected frequencies) if given floating > > point samples rather than complex? (Tried this using wx gui FFT plot > > and I don't see mirroring, does the WX GUI FFT suppress the mirroring?) > > Yes, the DFT/FFT/"Fourier transform of the signal" is exactly what you > need. Bin [-512 to -1] are the negative frequencies (which you do not seem > to be interested in) and bin [0 to 511] are the positive frequencies you > want evaluate. > > The sharpness of the frequency peaks you are expecting has something to do > with the window you are using. I saw you used a Blackman-Harris window. Try > playing around a bit with this setscrew if you are not happy with your > results. > Thank you for the suggestion! > > Two further comments: > > 1) If your application is about loudness as perceived by humans you have > to introduce a model for the ear as we do not hear linearly. > This is a good point that I will keep in mind, although my application of this work is not intended for comparison with perceived amplitude, it may be useful to process it that way so I will look into it. > > 2) It is impressive how you visualize your ESD on console, but why are you > not using the mighty QT GUI Time Sink or a python plotting library like > matplotlib to plot your result? (Played around with it recently > https://gist.github.com/m3x1m0m/1d524d560ff2f3e0702ca6c5d73bcff1) > > Thank you for the kind suggestion - I haven't explored the QT UI much but I tried the time sink and found it useful. I went with ascii art initially so that I could gain an intimate familiarity with the vector sink and its behavior. I have to confess I am struggling with the math descriptions provided. If I may, I would like to ask a few questions simplified into terms that I I think I can understand the responses to: - Is it true then that if I have a 100-bin FFT, that each of the "left 50" equals the negative of its corresponding right-side bin? - Is there any use for "negative frequencies" if my goal is to simply measure the ESD for each of the frequency bins? - If I want to get 48 usable frequency bands, each corresponding to a 0-1k, 1k-2k, 2k-3k, etc do I actually need a 96 bin FFT due to the mirroring? - Do the negative frequencies correspond to a phase difference compared to the positive frequencies - in other words if I have two 2600Hz signals that are out of phase by 180 degrees, would this be reflected in the negative vs positive bin associated with 2600Hz? Thanks! Brad > Regards, > > Max > > _______________________________________________ > Discuss-gnuradio mailing list > Discuss-gnuradio@gnu.org > https://lists.gnu.org/mailman/listinfo/discuss-gnuradio >
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