USE fft(x) as a highpass filter
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fcarl
le 16 Juin 2011
Commenté : Travis Morrison
le 26 Juin 2017
Hi,
I want to use the fft(x) function to create an highpass filter. I want to ask if the following procedure is correct:
1) take the signal x and make an fft(x).
2) Set frequencies up to 0.5 Hz to zero.
3) Make ifft(spectrum).
Is it right to set the first data points to zero or is there anything to pay attention to (e.g.: symmetry of the fft...). So if I set the first data points to zero, is this enough?
Thanks for your efforts!
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Rick Rosson
le 21 Juin 2011
Here are some suggestions for improving the code.
I have inserted several new lines of code indented from the original code, and eliminated some lines of the original code by making them into comments:
signal=load(files{i});
dt = 0.008;
Fs = 1/dt;
N = size(signal,1);
dF = Fs/N;
f = (-Fs/2:dF:Fs/2-dF)';
% Band-Pass Filter:
BPF = ((lower_freq < abs(f)) & (abs(f) < upper_freq));
figure;
plot(f,BPF);
% time=0.008:0.008:size(signal,1)*0.008;
time = dt*(0:N-1)';
figure;
plot(time,signal);
% NFFT=2^nextpow2(size(signal,1));
signal=signal-mean(signal);
% spektrum = fft(signal,NFFT)/(size(signal,1));
spektrum = fftshift(fft(signal))/N;
figure;
subplot(2,1,1);
plot(f,abs(spektrum));
% spektrum(lower_freq:upper_freq,1)=0;
% spektrum(size(spektrum,1)- upper_freq+1:size(spektrum,1)-lower_freq+1,1)=0;
spektrum = BPF.*spektrum;
subplot(2,1,2);
plot(f,abs(spektrum));
% signal=ifft(spektrum); %inverse ifft
signal=ifft(ifftshift(spektrum)); %inverse ifft
HTH.
Rick
4 commentaires
Travis Morrison
le 26 Juin 2017
When converting back to real space you have to multiply by N. Other than that, thanks for the help!
Plus de réponses (5)
Rick Rosson
le 4 Août 2011
You are welcome. If you don't mind, could you please "Accept" the answer that helped resolve this issue?
Thanks!
Rick
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Rick Rosson
le 16 Juin 2011
Before you can solve this problem, you need to know the sampling rate (in samples per second) of the signal x. Otherwise, you will not be able to figure out how many samples of the spectrum correspond to 0.5 hertz (the cut-off frequency).
For convenience, you may want to create the variable Fs to represent the sampling rate and Fc to repreesent the cut-off frequency. For example:
Fs = 200; % samples per second
Fc = 0.5; % hertz
Also, the spectrum returned by the fft function is double-sided. By default, it corresponds to the frequencies from 0 hertz up to Fs hertz. It will be easier to implement your filter if you swap the two halves of the spectrum, so that it will correspond to -Fs/2 up to +Fs/2. You can do so using the fftshift function:
X = fftshift(fft(x));
HTH.
Rick
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