Re: Re: Sound Spectrogram over time, in 3D, using Fourier?

*To*: mathgroup at smc.vnet.net*Subject*: [mg95000] Re: [mg94993] Re: Sound Spectrogram over time, in 3D, using Fourier?*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Fri, 2 Jan 2009 06:54:45 -0500 (EST)*References*: <gjict6$c7k$1@smc.vnet.net> <200901020130.UAA23871@smc.vnet.net>*Reply-to*: drmajorbob at longhorns.com

That's an excellent tutorial (to my ears) on DFT. Thanks! Bobby On Thu, 01 Jan 2009 19:30:35 -0600, Sjoerd C. de Vries <sjoerd.c.devries at gmail.com> wrote: > Hi Justin, > > A couple of remarks with respect to your question: > > 1. Fourier returns the discrete fourier transform (DFT) of a list of > numbers. There is no way the Fourier function could know how these > were sampled. The same list of numbers may be the result of sampling > at a rate of one sample a day or at 44.1 KHz or whatever. Therefore, > you cannot interpret the output in terms of frequencies. At least, not > directly. If you know the duration of your set of samples (T) then a > number at position s of the output list corresponds to a frequency of > (s-1)/T Hz. > > 2. The value of a Fourier result at position s equals the complex > conjugated value at position n-s+2 for 1<=s<=n/2, with n the number of > samples. Look for instance at this: > > res = Fourier[Table[Sin[2 \[Pi] 1 t], {t, 0, 1, 1/99}]] > > Table[Conjugate[res[[i]]] - res[[Length[res] - i + 2]], {i, 2, Length > [res]/2}] > > The DC term (the average value) of your samples is at position 1. So, > the result can be expressed as the first n/2 complex numbers, the > remainder of the output is redundant. Therefore, the highest > representable frequency is n/2/T (Nyquist frequency). It therefore > makes no sense to plot the whole range of the output of Fourier[ ]. > Half of it suffices. If Fs is the sample frequency, then n = Fs T and > the highest representable frequency equals Fs/2. > > BTW: note that n/2 complex numbers contain the same amount of > information as n real numbers, so no information is lost in the > transformation. > > 3. The size of the numbers in the output depends on the choice of the > normalization term in the fourier transform. Look for > FourierParameters in the documentation. > > 4. The decibel scale is a relative scale in which values are related > to a given reference level. You have to provide this reference level > yourself (it will have a dB level of 0). Given a certain ref power > level P0, the value of a power level P1 in dB is given by 10*Log10[P1/ > P0]. Often, power is related to the amplitude squared so the value of > P1 in dB will be 20* Log10[A1/A0] when using amplitudes. > > 5. As to the 3D plot: should not be too difficult. Collect a number of > DFTs of some windows in your data set. Add them all to a list and you > have a 3D set that can be plotted by ListPlot3D. > > Cheers -- Sjoerd > > > On Jan 1, 2:28 pm, Justin <carillona... at gmail.com> wrote: >> I'm rather new to Mathematica, and am attempting to make a 3D plot >> showin= > g how the frequency profile of a sound sample changes over time. I've > impor= > ted a .5 second audio file: >> >> wave = Import["clip.wav","Data"] >> >> which returns a list of amplitude values of the wave (The file is >> sampled= > at 44.1 kHz, so there are about 22k numbers in the list). I can get a > n= > ice 2D plot of the frequency spectrum for the length of the whole clip > with= > : >> >> ListLinePlot[Take[Abs[Fourier[wave]],650],PlotRange -> {0,2.5}] >> >> where 650 is the max frequency shown (in Hz I think?) and 0-2.5 is the >> in= > tensity range (I'm not sure what these values mean, but I'd like to see > it = > in dB). >> >> What I would like to do is plot a 3 second long clip in 3D and show how >> t= > he frequency profile changes over those 3 seconds, so x=frequency, y=in= > tensity, z=time. >> >> I understand that my above 2D plot is one fat slice, and that I need to >> m= > ake hundreds or thousands of similar slices over the 3 second clip to > make = > the 3D plot, I'm just not sure how to do it. >> >> Any help would be greatly appreciated, thanks!!! >> >> J > > -- DrMajorBob at longhorns.com

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