how to design bandpass filter with cut off wavelengths given.

I have a gridded bathymetry data. I have to remove all signals from the data with a wavelength greater than 4000 km and less than 400 km. How can I design a bandpass filter, eg. Butterworth filter? how do I determine the cut off frequencies and order of the filter? the spacing between grid points is 0.16 km.

Answer 1

[Star Strider]

This will work for a filter design:

Ts    = 0.16;                                                   % Sampling Interval (Units: km)
Fs    = 1/Ts;                                                   % Sampling Frequency (Units: 1/km)
Fn    = Fs/2;                                                   % Nyquist Frequency
Freq1 = 1/4000;                                                 % Convert Wavelentgh To Frequency (Units: 1/km)
Freq2 =  1/400;                                                 % Convert Wavelentgh To Frequency (Units: 1/km)
Wp    = [Freq1 Freq2]/Fn;                                       % Passband Frequencies (Normalised)
Ws    = Wp.*[0.8 1.2];                                          % Stopband Frequencies (Normalised)
Rp    =  1;                                                     % Passband Ripple
Rs    = 50;                                                     % Stopband Ripple
[n,Wn] = buttord(Wp,Ws,Rp,Rs);                                  % Filter Order
[z,p,k] = butter(n,Wn);                                         % Calculate Filter
[sos,g] = zp2sos(z,p,k);                                        % Convert To Second-Order-Section

figure(1)
freqz(sos, 2^16, Fs)                                            % Filter Bode Plot
set(subplot(2,1,1), 'XLim',[0  0.05])
set(subplot(2,1,2), 'XLim',[0  0.05])

The Bode plot of the filter amplitude appears to have strange units, with the filter appearing to ‘amplify’ the signal. This is due to the way freqz calculates filter gain, not the design of the filter. The filter will not amplify your signal.

I leave the implementation to you, because I have no idea what you are doing.

[math seeker]

Thank you very much for your explanation. Can You please explain how the passband and stopband frequencies calculated( including how the 0.8 and 1.2 came) and the passband and stopband ripples assumed?

[Star Strider]

As always, my pleasure.

The passband frequencies are those you specified. The stopband frequencies are simply empirical, and chosen to produce a stable filter, as are the passband and stopband ripples (for a Butterworth filter, the stopband ripple is the stopband attenuation).

I invite you to experiment with them to see how they affect the filter Bode plot.

[math seeker]

The line

freqz(sos, 2^16, Fs)

gives me an error.

error: freqz: B must be a vector

[Star Strider]

The code in my Answer runs without errors in R2017b. (I copied it from my post and ran it again just now, to be sure.)

I have no idea what your problem could be, since you only posted the freqz call.

Answer 2

[Abhishek Ballaney]

https://in.mathworks.com/help/signal/ref/butter.html