Designing a specific low-pass discrete filter in MATLAB

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Jonathan George
Jonathan George 2022-3-25
评论： Star Strider 2022-3-26
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.

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Star Strider
Star Strider 2022-3-26
Ran in:
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’.
.
  2 个评论
Jonathan George
Jonathan George 2022-3-26
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
Star Strider 2022-3-26
Ran in:
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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