Filter design parameter: radian/sec or 1/sec?
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Tsung-Ju Yang
il 4 Giu 2017
Risposto: Star Strider
il 4 Giu 2017
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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Star Strider
il 4 Giu 2017
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
The filter passband goes from 1 Hz to 100 Hz.
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