real FFT (in theory)....
in [DSP]
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From: dbd on 24 Jun 2010 18:40 On Jun 24, 8:40 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com> wrote: > > ... > just to confirm your suggestions: > > I tried A=[1 2 3 3 2 1], where N=6(even number) and fft(A) has a nonzero > imaginary part. This A is symmetric but not DFT-even so it has nonzero imaginary part in the frequency domain. "fftshift" will not change thst. > Instead, if A[0 1 2 3 3 2 1] things work out well and fft(A) has > imag(fft(A))=0. > This A is DFT-even. To see what that means, read the second section in harris' paper: http://www.utdallas.edu/~cpb021000/EE%204361/Great%20DSP%20Papers/Harris%20on%20Windows.pdf > I guess, as a rule of thumb, for a sequence to be even it needs to have an > odd number of entries and the evenness determination must start from the > second entry: > ... Wrong, see above. Read the reference. Ask new questions. You persist in trying to apply continuous/infinite domain concepts to the discrete/finite domain in ways that do not work. "Insanity: doing the same thing over and over again and expecting different results." Albert Einstein, (attributed) Dale B. Dalrymple
From: Greg Heath on 25 Jun 2010 09:42 On Jun 24, 12:46 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com> wrote: > Hello forum, > > I can easily calculate the fft of a 1D Gaussian function, which is a real, > even function. In theory, Its FFT should be real (zero imaginary part). > Instead the simulation shows an imaginary part definitely not zero and > oscillating...Why? where is my mistake? > > Here my brief matlab code: > > mu=0; %mean > sigma2=.2; %variance > sd = sqrt(sigma2); % std deviation > x = mu-30:0.02:mu+30; % location of points at which x is calculated > g = 1*exp(-0.5*(x-mu).^2/sigma2); > plot(fftshift(imag( fft(g) ))) % See my explanation of the shift functions in % % http://groups.google.com/group/comp.soft-sys.matlab/msg/ecedcba94094f742 close all, clear all, clc, p = 0 mu = 0; % mean sigma2 = .2; % variance sd = sqrt(sigma2); % std deviation x = mu-30:0.02:mu+30; % location of points g = 1*exp(-0.5*(x-mu).^2/sigma2); p = p+1,figure(p) plot(x,g) N = length(x) % 3001 is odd dx = x(2)-x(1) % 0.02 dk = 1/(N*dx) kb = dk*[-(N-1)/2 : (N-1)/2]; Gb = fftshift(fft(ifftshift(g))); % defined over a bipolar interval rGb = real(Gb); iGb = imag(Gb); aGb = abs(Gb); pGb = angle(Gb); minmaxiGb = minmax(iGb) % -1.0914e-014 6.0254e-014 p=p+1,figure(p) subplot(221) plot(kb,rGb) subplot(222) plot(kb,iGb) subplot(223) plot(kb,aGb) subplot(224) plot(kb,pGb) % Snapshot ind = find(aGb > max(aGb)/100); minmaxind = minmax(ind) % [ 1437 1565] kbint = kb(ind); % Snapshot interval p=p+1,figure(p) subplot(221) plot(kbint,rGb(ind)) subplot(222) plot(kbint,iGb(ind)) subplot(223) plot(kbint,aGb(ind)) subplot(224) plot(kbint,pGb(ind)) % Hope this helps. % % Greg
From: Greg Heath on 25 Jun 2010 09:52 % See my explanation of the shift functions in % % http://groups.google.com/group/comp.soft-sys.matlab/msg/ecedcba94094f742 close all, clear all, clc, p = 0 mu=0; % mean sigma2=.2; % variance sd = sqrt(sigma2); % std deviation x = mu-30:0.02:mu+30; % location of points g = 1*exp(-0.5*(x-mu).^2/sigma2); p=p+1,figure(p) plot(x,g) N = length(x) % 3001 is odd dx = x(2)-x(1) % 0.02 dk = 1/(N*dx) kb = dk*[-(N-1)/2 : (N-1)/2]; Gb = fftshift(fft(ifftshift(g))); % defined over a bipolar interval rGb = real(Gb); iGb = imag(Gb); aGb = abs(Gb); pGb = angle(Gb); minmaxiGb = minmax(iGb) % -1.0914e-014 6.0254e-014 p=p+1,figure(p) subplot(221) plot(kb,rGb) subplot(222) plot(kb,iGb) subplot(223) plot(kb,aGb) subplot(224) plot(kb,pGb) % Snapshot ind = find(aGb > max(aGb)/100); minmaxind = minmax(ind) % [ 1437 1565] kbint = kb(ind); p=p+1,figure(p) subplot(221) plot(kbint,rGb(ind)) subplot(222) plot(kbint,iGb(ind)) subplot(223) plot(kbint,aGb(ind)) subplot(224) plot(kbint,pGb(ind)) % Hope this helps. % % Greg
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