Re: Any FFT expert around?

[Brian Kaczynski]

2014-02-19 10:49 GMT+01:00, oxy <address@hidden>:
> hi brian,
>
> now it works ... great!!!!!!!
>
> Look at the code below ajusted according to your hints.
>
> Just one question more: you are calculating the frequency
> vector as:
>
>          freq1=-linspace(-Fs1/2,   Fs1/2-1/at,   Fs1*at)';
>
> that makes it non-symetric. Isn't it better ...
>
>          freq1=-linspace(-Fs1/2+1/at,   Fs1/2-1/at,   Fs1*at)';
>
> ...? Then it's symetric. Hey, thanks a lot! Great help!!!!!

That would be "better" if you really want to insist on having a
symmetrical frequency vector at the expense of accuracy.
Unfortunately, it's inaccurate.  For one thing, your symmetrical
frequency vector does not contain a DC term if you have an even number
of FFT points (which you should based on your examples).

If you want the FFT value at the nth point to really correspond to
freq1(n) you should use the slightly offset frequency vector that I
provided.

If it is more important to whatever you're doing that the frequency
vector be exactly symmetrical and you can live with sacrificing the
true 1-to-1 correspondence between frequency points and FFT points,
you can use your symmetrical frequency vector.

> oxy
>
> %======== DEMONSTRATION CODE =========
> % TTF Demo: this code shows how to calculate the
> % frequency domain when doing FFT of td-signals.
>
> %--- parameter setup: same signal, 2 sampling rates ---
> clear all
> nu=10;            % signal frequency
> at=5;             % acquisition time
> T1=2              % signal decay constant in time domain
> FsFactor1=4;      % sampling rate factor 1, Fs1/nu
> FsFactor2=16;     % sampling rate factor 2, Fs2/nu
>
> %----------- calculating -------------------
> Fs1 = FsFactor1*nu;            % Sampling rate 1
> Fs2 = FsFactor2*nu;            % Sampling rate 2
>
> t1 = ((0:(at*Fs1-1))/Fs1)';    % Time vector 1
> t2 = ((0:(at*Fs2-1))/Fs2)';    % Time vector 2
>
> tdsig1=exp(-i*2*pi*nu*t1).*exp(-t1./(T1)); % time domain signal 1
> tdsig2=exp(-i*2*pi*nu*t2).*exp(-t2./(T1)); % time domain signal 2
>
> % I realized, the signal was appearing negative, thus minus...
> freq1=-linspace(-Fs1/2,Fs1/2-Fs1/(Fs1*at),Fs1*at)'; % freq. vector 1
> freq2=-linspace(-Fs2/2,Fs2/2-Fs2/(Fs2*at),Fs2*at)'; % freq. vector 2
>
> freqsig1=fftshift(fft(tdsig1));  % signal vector 1
> freqsig2=fftshift(fft(tdsig2));  % signal vector 2
>
> %----------- end ------------------
>
> =================================================
> On 2/19/14, oxy <address@hidden> wrote:
>> On 2/12/14, Brian Kaczynski <address@hidden> wrote:
>>> Hi Oxy,
>>>
>>> Since you're taking the FFT of a complex vector it will have unique
>>> terms
>>> for negative vs. positive frequency.  You are correct that it makes more
>>> sense to think of the FFT from -Fs/2 to +Fs/2.  It's just that the
>>> Octave
>>> fft function doesn't compute the bins in that order.  Due to aliasing,
>>> any
>>> frequency Fs/2 + df is equivalent to (-Fs/2 + df) so it's more a matter
>>> of
>>> choice how you want to display the data.
>>>
>>> If you prefer plotting from -Fs/2 to +Fs/2 I would change these two
>>> lines
>>> of your code as follows:
>>>
>>> freq=linspace(-Fs/2,Fs/2-Fs/(Fs*at),Fs*at)'
>>> freqsig=fftshift(fft(tdsig);
>>>
>>> Let us know if that gives you what you want!
>>>
>>> -Brian
>>>
>>>
>>> 2014-02-12 17:15 GMT+01:00 oxy <address@hidden>:
>>>
>>>> Hi Brian,
>>>>
>>>> > The frequency vector for FFT should go from DC as bin 1 to slightly
>>>> > less
>>>> > than Fs in the last bin (Fs - Fs/N where N is the number of FFT
>>>> > points).
>>>>
>>>> If i understand u correctly, the frequency vector (freq) must be
>>>> written
>>>> as in this modified version of code below. However, according to
>>>> Nyquist
>>>> we
>>>> cannot measure a frequency higher than Fs/2. Thus i do not see
>>>> the meaning of plotting up to ~Fs.
>>>>
>>>> Also, if I rerun the code below changing FsFactor, I again see this
>>>> dependency of the signal frequency on FsFactor.
>>>> I cannot understand it. Looks like basics, yet not that obvious.
>>>>
>>>>   #---------- start code ------------
>>>>   clear all
>>>>   nu=10;                    % signal frequency
>>>>   at=5;                       % acquisition time
>>>>   T1=2                       % signal decay constant in time domain
>>>>   FsFactor=16;             % the ratio (sampling rate)/(signal
>>>> frequency), or Fs/nu
>>>>
>>>>   clf
>>>>   Fs = FsFactor*nu;                             % Sampling rate
>>>>   t = ((0:(at*Fs-1))/Fs)';                         % Time vector
>>>>   % freq=linspace(-1,1,Fs*at)' * Fs/2;         % frequency vector,
>>>> first
>>>> version
>>>>   freq=linspace(0,1,Fs*at)' * Fs- Fs/(Fs*at);  % frequency vector
>>>> suggested by Brian
>>>>   tdsig=exp(-i*2*pi*nu*t).*exp(-t./(T1));    % time domain signal
>>>>   freqsig=fft(tdsig);                                % freq. domain
>>>> signal
>>>>   subplot(1,2,1)
>>>>   plot(t,tdsig)
>>>>   axis([ 0 0.4])       % zooming time domain to see that period=1/nu
>>>>   subplot(1,2,2)
>>>>   plot(freq, freqsig)
>>>>   #---------- end code ------------
>>>>
>>>> thx guys ...
>>>>
>>>>
>>>> > 2014-02-12 14:22 GMT+01:00 oxy <address@hidden>:
>>>> >
>>>> >> hey guys,
>>>> >>
>>>> >> the (simple) code bellow is how i ve learned to do FFT according to
>>>> >> several docs online. However i observe a dependency of the signal
>>>> >> frequency in the spectrum on the constant FsFactor. In other words,
>>>> >> the signal frequency depends on the sampling rate. I should'nt be,
>>>> >> right? So what is wrong here?
>>>> >>
>>>> >>   #---------- start code ------------
>>>> >>   clear all
>>>> >>   nu=10;                    % signal frequency
>>>> >>   at=5;                       % acquisition time
>>>> >>   T1=2                       % signal decay constant in time domain
>>>> >>   FsFactor=8;             % the ratio (sampling rate)/(signal
>>>> >> frequency), or Fs/nu
>>>> >>
>>>> >>   clf
>>>> >>   Fs = FsFactor*nu;                             % Sampling rate
>>>> >>   t = ((0:(at*Fs-1))/Fs)';                         % Time vector
>>>> >>   freq=linspace(-1,1,Fs*at)' * Fs/2;         % frequency vector
>>>> >>   tdsig=exp(-i*2*pi*nu*t).*exp(-t./(T1));    % time domain signal
>>>> >>   freqsig=fft(tdsig);                                % freq. domain
>>>> >> signal
>>>> >>   subplot(1,2,1)
>>>> >>   plot(t,tdsig)
>>>> >>   axis([ 0 0.4])       % zooming time domain to see that period=1/nu
>>>> >>   subplot(1,2,2)
>>>> >>   plot(freq, freqsig)
>>>> >>   #---------- end code ------------
>>>> >>
>>>> >> Do it yourself. Just rerun the code trying different values of
>>>> >> FsFactor (eg: 2, 4, 8).
>>>> >> Thx a lot for any hint!!!
>>>> >>
>>>> >> oxy
>>>> >>
>>>> >> ps: cross post
>>>> >>
>>>> http://www.mathworks.com/matlabcentral/answers/115700-fft-why-signal-frequency-depends-on-sampling-rate
>>>> >> _______________________________________________
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>>>> >>
>>>> >
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>>
>