Design a minimum-order lowpass filter with a 500 Hz passband cutoff frequency and 600 Hz stopband cutoff frequency. Specify a sampling frequency of 2000 Hz. Require at least 40 dB of attenuation in the stopband and less than 3 dB of ripple in the passband.

rp = 3;% Passband ripplers = 40;% Stopband ripplefs = 2000;% Sampling frequencyf = [500 600];% Cutoff frequenciesa = [1 0];% Desired amplitudes

Convert the deviations to linear units. Design the filter and visualize its magnitude and phase responses.

dev = [(10^(rp/20)-1)/(10^(rp/20)+1) 10^(-rs/20)]; [n,fo,ao,w] = firpmord(f,a,dev,fs); b = firpm(n,fo,ao,w); freqz(b,1,1024,fs) title('Lowpass Filter Designed to Specifications')

Note that the filter falls slightly short of meeting the stopband attenuation and passband ripple specifications. Usingn+1in the call tofirpminstead ofnachieves the desired amplitude characteristics.

Design a lowpass filter with a 1500 Hz passband cutoff frequency and 2000 Hz stopband cutoff frequency. Specify a sampling frequency of 8000 Hz. Require a maximum stopband amplitude of 0.1 and a maximum passband error (ripple) of 0.01.

[n,fo,ao,w] = firpmord([1500 2000],[1 0],[0.01 0.1],8000); b = firpm(n,fo,ao,w);

Obtain an equivalent result by havingfirpmordgenerate a cell array. Visualize the frequency response of the filter.

c = firpmord([1500 2000],[1 0],[0.01 0.1],8000,'cell'); B = firpm(c{:}); freqz(B,1,1024,8000)