design a filter using only fft

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Áron Laczkovits 2012-9-26

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I want to design a low pass filter without any toolboxes, only using fft. My plan is, that i read a wav file into matlab, then i fft it and i reload into a 1D vektor. I have to zeroing for example the first 100 elements. Then ifft it. Unfortunatelly doesnt work. Anyone can help me in the m code or any idea how can i do it?

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Answer 1

Wayne King 2012-9-26

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编辑：Wayne King 2012-9-26

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From your description it sounds like you are not also zero-ing out the complex conjugates. You are zero-ing out only the "positive" frequencies, but you also have to zero the corresponding negative frequencies. I'll illustrate this in the following example with two sine waves in noise. I'll remove the 200-Hz sine wave.

 t = 0:0.001:1-0.001;
 x = cos(2*pi*100*t)+cos(2*pi*200*t)+randn(size(t));
 % get rid of the 200-Hz component.
 xdft = fft(x);
 % 200 Hz lives at bin 201
 xdft(201)
 % but look at bin length(x)-201+2
 xdft(length(x)-201+2)

You see the difference between those is that one is the complex conjugate of the other. You have to zero them both.

 xdft([201 length(x)-201+2]) = 0;
 xrec = ifft(xdft);
 plot(abs(fft(xrec)))

You see now that the 200-Hz component is gone.

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Áron Laczkovits 2012-9-26

Is it work with a wave signal? I mean if i use a wav file instead of the 2 sine wave.

Wayne King 2012-9-26

Yes, the principle is the same. I'm not advocating this as a way of filtering a signal, but the point is, you have to remove both the "negative" and "positive" frequencies before you take the inverse Fourier transform.

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