Designing a specific low-pass discrete filter in MATLAB

How would I go about designing a 6th order low pass discrete filter with a 3dB frequency of 12Hz using the FIR (fir1) window approach, with the filter being designed to filter signals sampled at 100Hz?

Thank you in advance.

Answer 1

[Star Strider]

Try this —

Fs = 100;                                               % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency
order = 6;
Fp = 12;                                                % Passband Frequency 
h = fir1(6, Fp/Fn, 'low');

figure
freqz(h, 1, 2^16, Fs)

[h,f] = freqz(h, 1, 2^16, Fs);                              % Get Output
passband_freq = interp1(mag2db(abs(h)), f, -3)              % Check Passband Frequency

passband_freq = 11.8608

The passband frequency is acceptably close to the designed value for ‘Fp’.

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[Jonathan George]

Thank you, Star. And one more question out of curiosity: how would I be able to determine the value of the highest order b coefficient of the discrete system with those results? Many thanks.

[Star Strider]

As always, my pleasure!

The ‘b’ coefficients are actually ‘h’ in my original code, so according to the documentation section on b since ‘The coefficients are sorted in descending powers of the Z-transform variable z’:

Fs = 100;                                               % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency
order = 6;
Fp = 12;                                                % Passband Frequency 
b = fir1(6, Fp/Fn, 'low')

b = 1×7

0.0095 0.0717 0.2442 0.3493 0.2442 0.0717 0.0095

the highest order with respect to z would be b(2). At least that is how I read it.

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