MATLAB: Whats this line do

fftmatrixmatrix manipulationplotzeros

y=[zeros(10,20000),x,zeros(10,20000)];
y2=abs(fftshift(fft(real(y(2,:)))))/length(y);

thanks!!!

Best Answer

It defines y as x padded with 20000 columns on both sides
It takes the DFT of the real part of the second row of y, shifts it to 0 takes the absolute value and divides by the length of the row.

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MATLAB: Does values of fft change when length changes

You have zero-padded both of your ‘x’ signals, extending ‘x1’ from 4 to 10 by adding 6 zeros at the end, and ‘x2’ by zero-padding it out to a length of 512. The ‘energy’ in the signal are in the non-zero-padded data (zeros within the data are of course permitted). It is necessary to ‘normalise’ the fft by dividing the results by the length of the original (non-zero-padded) signal.

Compare the plots for these two normalised results:

X1 = fft(x1)/xlen;
X2 = fft(x,512)/xlen;

They come very close to overlapping. The blue curve has increased frequency resolution, so appears more continuous.

MATLAB: Difference between ‘conv’ & ifft(fft) when doing convolution

You have to keep in mind that the product of the DFTs of two vectors is Fourier transform of the circular convolution, not linear convolution. To establish equivalence between linear and circular convolution, you have to extend the vectors appropriately first before computing the circular convolution. The length of the linear convolution of two vectors of length, M and L is M+L-1, so we will extend our two vectors to that length before computing the circular convolution using the DFT.

 x = [5 6 8 2 5]; 
 y = [6 -1 3 5 1];
 x1 = [x zeros(1,4)];
 y1 = [y zeros(1,4)];
 c1 = ifft(fft(x1).*fft(y1));
 c2 = conv(x,y);

Now compare c1 and c2

Best Answer

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MATLAB: Does values of fft change when length changes

MATLAB: Difference between ‘conv’ & ifft(fft) when doing convolution

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