MATLAB: Fourier

fourierfourier serieshomeworkno attempt

Hello,

I want to display certain functions as a fourier series (I want to perform 5 partial fourier series, or more). I want the output to be displayed as a plotted function, and also the frequency spectrum.

F.e.:

F(t)= x^3 for x=]0,3[ and (1/2)*x for x=]3,6[ with period of 2.

I've searched in the file exchange section, but didn't find anything satisfactory. Perhaps I used the wrong search items, or perhaps someone of you is having something like this?

Greetings from Germany, Manfred

Best Answer

Check out this resource from Steve Eddins: http://blogs.mathworks.com/steve/category/fourier-transforms/

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MATLAB: Suggestions for quantifying spectral leakage

"But then I realised this wouldn't work as if there was a 1MHz bin, there wouldn't be any spectral leakage."

The above statement is not correct. The spacing of the DFT bins is determined by the number of samples and the sampling frequency.

Leakage is a result of the convolution of the signal's spectrum with that of the window -- they are separate things.

For example:

      Fs = 4e6;
      t = 0:1/Fs:0.2-1/Fs;
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      xdft = fft(x'.*hamming(length(t)));
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The frequency spacing is 5 Hz, you see that there is power not only at 1 MHz, but also at +/- 5 Hz

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Here are few things: Your plot shows the amplitude of Fourier transform, not the original signal. So, the amplitude may not be 4 (amplitude of the signal). Indeed, the amplitude of fft is determined so that the power of the signal remains same before and after the transform. Lets say, Y = x'.*fn

Y = x'.*fn; 
Power_Y = sum(Y.^2) % power in time domain
fftY = fft(Y); 
Power_fftY = sum(fftY.*conj(fftY))/length(fftY) % power in frequency domain

The amplitude after transformation is set so that Power_Y = Power_fftY

To get the amplitude back, use ifft that is shown in subplot(313) below. Compare these three plots:

subplot(311), plot(Y); % original signal
subplot(312), plot(abs(fftY)); % fft
subplot(313), plot(ifft(fftY)); % ifft

Best Answer

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MATLAB: Suggestions for quantifying spectral leakage

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