Filter design parameter: radian/sec or 1/sec?

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Tsung-Ju Yang 2017-6-4

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回答： Star Strider 2017-6-4

Dear All, I am confused with some fundamental problem in Matlab. Sorry to as such a basic problem.

Signal: x[n]= cos(2*pi*(n-1)*Ts)+2*cos(2pi*f*(n-1)*Ts), n=1,2,3,...,1000 and Ts=0.002

I want to design filter to get the first term and the second term respestively with 16-order filter. But I am not sure the passband should be

"1Hz, f Hz" or "2pi, 2pi*f"

when I call the filter function such as butter, cheby1, cheby2, ellip in IIR or in FIR. May you so kind give me an example?

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Answer 1

Star Strider 2017-6-4

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The passbands and stopbands for the Signal Processing Toolbox filter functions are actually normalised to the closed interval [0, pi] radians. It is calculated as the passband and stopband frequency in Hz divided by the Nyquist frequency.

Example for frequency calculations for the filters your signal:

Ts = 0.002;                                             % Sampling Interval (seconds)
Fs = 1/Ts;                                              % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency

Note that the highest frequency you can design in your filter is the Nyquist frequency, here 250 Hz.

An example of a Chebyshev Type II filter design for filtering an EKG signal is here:

Fs = 250;                                               % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency (Hz)
Wp = [1.0   100]/Fn;                                    % Passband Frequencies (Normalised)
Ws = [0.5   101]/Fn;                                    % Stopband Frequencies (Normalised)
Rp = 10;                                                % Passband Ripple (dB)
Rs = 50;                                                % Stopband Ripple (dB)
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);                         % Filter Order
[z,p,k] = cheby2(n,Rs,Ws);                              % Filter Design
[sosbp,gbp] = zp2sos(z,p,k);                            % Convert To Second-Order-Section For Stability
figure(3)
freqz(sosbp, 2^17, Fs)
EKG_filt = filtfilt(sosbp, gbp, EKG_original);          % Filter EKG Signal