MATLAB: Cut off frequency for butterworth filters

butterworth

Hi All,

I have a very basic question.

I am trying to use a butterworth filter but the instructions make no sense. Matlab on accepts a frequency between 0 and 1. The specific instructions say:

"The cutoff frequency Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to half the sample rate."

Lets say my data was sampled at 2500 Hz. I want to low pass filter at 20 Hz. What exactly would I need to enter for Wn and how can I figure it out on my own.

Thanks in advance!

Mostafa

Best Answer

The ‘frequency between 0 and 1’ refers to a normalised frequency with respect to the Nyquist frequency (Nyquist frequency = sampling frequency/2).

For your low-pass filter with a cutoff of 20 Hz and a sampling frequency (Fs) of 2500 Hz, you would define:

Fs  = 2500;
Fco =   20;
Fn  = Fs/2;
Wn  = Fco/Fn;

Since ‘Wn’ is the upper passband frequency, and you will want to use the buttord function to help you design your filter, you will set the stopband frequency at about 1.25 times the passband frequency, and the passband ripple to be 1 dB and the stopband ripple at 10 dB. (These have no relevance to a Butterworth design, but buttord wants them.)

Also, use tf2sos to create the most stable (second-order-section) representation of your filter.

Related Solutions

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.)

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.

Best Answer

Related Solutions

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

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.

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