Apply frequency domain filter on PSD

Hi,

I'm trying to apply a High pass filter on a digital (from sensor capture) signal. I set my cutoff frequency to "cutoffFreq/(sampleFreq/2)" however, I still have low frequency under my cutoff Frequency and the filter seems to not work...

I'm wondering if the problem does not come from the fact that the HP filter act on the frequency in Hz and my PSD is not expressed in Hz but in number of points. Actually, to plot the PSD in frequency domain, we need to use :

plot(f, PSD);

If we plot only PSD, the X axis will be the number of point. I'm not sure but i suppose that my filter act on number of point and not on frequency. Could you confirm or not my thought ?

If i'm right, how can I proceed to filter my sample at 0.5Hz ?

Best.

My PSD with my fundamental frequency and high peaks on low frequency under 0.5Hz :

My code :

 %import csv file
 M = load("10.csv");

 %select the gx column
 gx = M(:,1);
 %select the gy column
 gy = M(:,2);
 %select the gz column
 gz = M(:,3); 

 t = M(:,4);

 %size of M (same size for each column)
 s = length(gz);
 %because of loop, need s/2
 s2 = fix(s/2);
 %acquisition frequency
 sampleFrequency = 30;
 %calculate x axis (frequency)
 f = sampleFrequency/s*(0:s2);

 %compute the angle from angular velocity
 angle = zeros(s, 1);
 angle(1, 1) = 0;
 for i = 2:s
     dt = t(i,1) - t(i-1,1);
     angle(i,1) = angle(i-1) + (gz(i,1)* dt);
 end

 %normalize the values to center on 0 and avoid first huge peak on 0 frequency
 angle = angle - mean(angle(:));

 %apply Hanning window of angle 
 angle = angle.*hanning(length(angle));

 % figure
 Yangle = fft(angle, s);

 %order of the HP filter
 n = 2;
 %cutoff frequency (Hz)
 cutoffFrequency = 0.5;
 wc = cutoffFrequency/ (sampleFrequency/2);

 %create the filter
 b = fir1(n, wc, "high");

 PSD = Yangle.*conj(Yangle)/s;

 filteredPSD = filter(b, 1, PSD);

 figure  
 plot(f, filteredPSD(1:s2+1));
 title('Power Spcetral Density for gyroscope')
 xlabel('Frequency (Hz)')
 ylabel('Power (g²/Hz)')

Answer 1

[Star Strider]

I would use the Signal Processing Toolbox function fftfilt for frequency domain filtering. (I have no experience with it since I don’t use frequency domain filtering. The documentation is extensive, so you should have no problems using it in your code.)

[Maxence]

I'm applying the same filter with fftfilt and the result is the same. No action...

[Star Strider]

I’m not certain what you actually want to filter, or the characteristics of your signal. I always use time-domain filtering because it’s generally easier.

Your signals of interest have very low frequencies, so unless you have a relatively high sampling frequency (on the order of 100 Hz or higher), any filter design to filter one or more of your peaks may be difficult to realise.

[Maxence]

I just want to cut off all the frequencies on my the PSD under 0.1 Hz. Indeed, on some samples, the 0.05Hz peaks is a bit higher than the 1Hz peak and the fundamental detected is 0.05Hz which is actually noise.

[Star Strider]

My filter design procedure is here: How to design a lowpass filter for ocean wave data in Matlab? If your sampling frequency is high enough, you should be able to realise your filter in the time domain. That’s much easier than trying to do frequency domain filtering.