Remove specific frequencies from FFT signal and reconstruct the signal after filtering those frequencies

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paloma paleo 2020-11-12

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https://ww2.mathworks.cn/matlabcentral/answers/645653-remove-specific-frequencies-from-fft-signal-and-reconstruct-the-signal-after-filtering-those-frequen

编辑： Bjorn Gustavsson 2020-12-7

采纳的回答： Bjorn Gustavsson

data_t_tichkness.txt

Hi,

I have a signal that shows a very distinctive peaks in the FFT.

Those high amplitudes are the 'noise' of the signal. I would like to remove that values from the original signal and to plot the filtered signal.

Fs = 4500; % Sampling frequency (fps)

T = 1/Fs; % Sampling period (s)

L = 900; % Length of signal (how many frames)

tt = (0:L-1)*T; % Time vector

thickness = detrend(thickness);

Y = fft(thickness);

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2*P1(2:end-1);

f = Fs*(0:(L/2))/L;

figure(1111)

h1=plot(f(1:end),P1(1:end)) ;

title('Amplitude Spectrum')

xlabel('f [Hz]')

ylabel('Power [mm]')

ylim auto

[B,IX] = sort(P1); %order the amplitudes

A1=B(end); %amplitude of the first peak

A2=B(end-1); %amplitude of second peak

f1=f(IX(end)); %frequency of first peak

f2=f(IX(end-1)); %frequency of second peak

AmpTab=[A1 A2];

FreTab=[f1 f2];

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Answer 1

Bjorn Gustavsson 2020-11-12

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Those high amplitudes are a noise in the signal. Not the noise in the signal. To remove such interference-components you will be better off doing it this way (remember the Fourier-transform of a real signal has symmetric real components and an anti-symmetric imaginary components, and also that the DC-component is real.):

fD = fft(data_t_tichkness(:,2)); % Discrete Fourier-transform of your data
subplot(2,1,1)
plot(abs(fD)) % Plot of its absolute values
hold on
[safD,idx] = sort(abs(fD),'descend'); % Sort in descending order, this makes indexing simpler
plot(idx(2:5),abs(fD(idx(2:5))),'r.') % DC-component will be the first, then 
                                      % the positive and negative components will 
                                      % have equal magnitudes and appear consecutively in idx
fD(idx(2:5)) = 0;  % Set the Fourier-components of the first and second spike to zero.
plot(abs(fD))      % Yup, they're gone.
subplot(2,1,2)
ifD = ifft(fD);    % inverse-Fourier-transform
plot(data_t_tichkness(:,2))          
hold on
plot(ifD)

HTH

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paloma paleo 2020-12-5

Dear Bjorn,

I would like to do exactly the opposite. I want to leave the low frequencies with the high peaks and to remove the high frequencies. I estimated that the high frequencies are any frequency higher than 216Hz. Therefore, in the fft graph, it will be between 86 and 814. I wrote the following code, but when I reconstruct the signal it doesnt make sense.

fD = fft(thickness); % Discrete Fourier-transform of your data

subplot(2,1,1)

absolute=abs(fD);

plot(abs(fD)) % Plot of its absolute values

hold on

%[safD,idx] = sort(abs(fD),'descend'); % Sort in descending order, this makes indexing simpler

%plot(idx(2:5),abs(fD(idx(2:5))),'r.') % DC-component will be the first, then

% the positive and negative components will

% have equal magnitudes and appear consecutively in idx

%fD(idx(2:5)) = 0; % Set the Fourier-components of the first and second spike to zero.

fD(86:814) = 0;

plot(abs(fD)) % Yup, they're gone.

subplot(2,1,2)

ifD = ifft(fD); % inverse-Fourier-transform

plot(thickness,'r')

hold on

plot(ifD,'b')

I would appreciate it if you could explain me what is going on.

I wonder if I could use in instead the following command:

fs=4500;

fpass=216;

yl = lowpass(thickness,fpass,fs);

Thanks

paloma paleo 2020-12-7

I can see the issue. I am not too queen to use a 'semi-manually' method since I have a huge number of tests and it would be tricky.

I am not sure what your low-pass filtering does. The type of filter that I need, it is a very simple. I just want to remove the values of the signal from certain frequency. In my case, the frequency is factor of the rotational speed, so I can use e.g., 5x rpm to define the threshold of the frequency. All values with higher frequency than the threshold will be consider a noise. So I would like a filter that only takes in considaration the frequency value.

I have been reading about the type of filters and how to define them and I believe I need something really simple. The type of filters that I found are too fancy for what I need. I work also with image procesing/anaylisis.

So I thought that something like

yl = lowpass(I_raw,fpass,fs);

But I am not 100% sure if this is the correct filter.

Thanks again for you kind responses.

Bjorn Gustavsson 2020-12-7

编辑：Bjorn Gustavsson 2020-12-7

Well the lowpass filter should do what you want. If you're unsure about the filter characteristics you can reasonably easy simply check the documentation (it contains a lot of juicy information!), test what frequency response you get from a single delta-spike as input etc.

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