MATLAB: Normalizing frequency for fir1() matlab function:?

fir filterlow-pass filternormalized frequency

I am trying to implement an FIR low pass filter using fir1() function but I am confused in normalizing the frequencies.Whether I had to divide my frequencies by fs or fs/2 for normalization to be used as Wn. Which one will give me the correct results?

Best Answer

Always normalise by the Nyquist frequency, in your example ‘fs/2’ if ‘fs’ is your sampling frequency.

Related Solutions

MATLAB: How to design FIR lowpass filter with cutoff frequency, fc1 = 20 Hz and FIR bandpass filter with cutoff frequency fc2 = 10 Hz and fc3 = 35 Hz.

Déjà vu

how to design IIR highpass filter with cutoff frequency of 20Hz and FIR bandpass filter with cutoff frequency of 10Hz and 15Hz?

Make the appropriate changes to get the cascaded filter you want.

MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

You have to divide your passband and stopband frequencies by the Nyquist frequency to normalise them:

Fs = 1000;                                          % Sampling Frequency
Fn = Fs/2;                                          % Nyquist Frequency
Wp = [10  495]/Fn;                                  % Norrmalised Passband Frequencies
Ws = [5   499]/Fn;                                  % Normalised Stopband Frequencies
Rp =  1;                                            % Passband Ripple (dB)
Rs = 25;                                            % Stopband Ripple (dB)
[n,Wn] = buttord(Wp, Ws, Rp, Rs);                   % Optimal Filter Order
[b,a] = butter(n, Wn);                              % Calculate Filter Coefficients
[sos,g] = tf2sos(b,a);                              % Convert To Second-Order Sections For Stability
figure(1)
freqz(sos, 4096, Fs)                                % Filter Bode Plot

You cannot have any frequency exactly at zero or exactly at the Nyquist frequency, so I designed your passband to be close enough to them to be stable. In your filter, you can also use a high-pass design with a lower cutoff of 10 Hz, since your upper passband is at the Nyquist frequency. The passband and stopband ripple values are necessary to specify in the design but irrelevant to a Butterworth filter. These are acceptable values for most filter designs (for example Chebyshev) that require them.

You would use the ‘sos’ and ‘g’ variables in your actual filter:

filtered_signal = filtfilt(sos, g, signal);

(This design works well in R2016a and should also work in earlier releases.)

Best Answer

Related Solutions

MATLAB: How to design FIR lowpass filter with cutoff frequency, fc1 = 20 Hz and FIR bandpass filter with cutoff frequency fc2 = 10 Hz and fc3 = 35 Hz.

MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

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