Frequency response of analog filters
h = freqs(b,a,w)
[h,w] = freqs(b,a,n)
freqs returns the complex frequency response H(jω) (Laplace transform) of an analog filter
given the numerator and denominator coefficients in vectors b and a.
h = freqs(b,a,w) returns the complex frequency response of the analog filter specified by coefficient vectors b and a. freqs evaluates the frequency response along the imaginary axis in the complex plane at the angular frequencies in rad/s specified in real vector w, where w is a vector containing more than one frequency.
[h,w] = freqs(b,a,n) uses n frequency points to compute the frequency response, h, where n is a real, scalar value. The frequency vector w is auto-generated and has length n. If you omit n as an input, 200 frequency points are used. If you do not need the generated frequency vector returned, you can use the form h = freqs(b,a,n) to return only the frequency response, h.
freqs works only for real input systems and positive frequencies.
Find and graph the frequency response of the transfer function
a = [1 0.4 1]; b = [0.2 0.3 1]; w = logspace(-1,1); freqs(b,a,w)
You can also compute the results and use them to generate the plots.
h = freqs(b,a,w); mag = abs(h); phase = angle(h); phasedeg = phase*180/pi; subplot(2,1,1), loglog(w,mag), grid on xlabel 'Frequency (rad/s)', ylabel Magnitude subplot(2,1,2), semilogx(w,phasedeg), grid on xlabel 'Frequency (rad/s)', ylabel 'Phase (degrees)'
Design a 5th-order analog lowpass Bessel filter with an approximately constant group delay up to rad/s. Plot the frequency response of the filter using freqs.
[b,a] = besself(5,10000); % Bessel analog filter design freqs(b,a) % Plot frequency response