freqs

Signal Processing Toolbox

Frequency response of analog filters.

h = freqs(b,a,w)
[h,w] = freqs(b,a)
[h,w] = freqs(b,a,n)
freqs(b,a)

Description

freqs returns the complex frequency response H(jw) (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 frequencies specified in real vector w.

[h,w] = freqs(b,a)

automatically picks a set of 200 frequency points w on which to compute the frequency response h.

[h,w] = freqs(b,a,n)

picks n frequencies on which to compute the frequency response h.

freqs

with no output arguments plots the magnitude and phase response versus frequency in the current figure window.

freqs works only for real input systems and positive frequencies.

Example

Find and graph the frequency response of the transfer function given by

a = [1 0.4 1];
b = [0.2 0.3 1];
w = logspace(-1,1);
freqs(b,a,w)

You can also create the plot with

h = freqs(b,a,w);
mag = abs(h);
phase = angle(h);
subplot(2,1,1), loglog(w,mag)
subplot(2,1,2), semilogx(w,phase)

To convert to Hertz, degrees, and decibels, use

f = w/(2*pi);
mag = 20*log10(mag);
phase = phase*180/pi;

Algorithm

freqs evaluates the polynomials at each frequency point, then divides the numerator response by the denominator response:

s = i*w;
h = polyval(b,s)./polyval(a,s);

`abs`	Absolute value (magnitude).
`angle`	Phase angle.
`freqz`	Frequency response of digital filters.
`invfreqs`	Continuous-time (analog) filter identification from frequency data.
`logspace`	Generate logarithmically spaced vectors (see MATLAB Function Reference).
`polyval`	Polynomial evaluation (see MATLAB Function Reference).