Plotting the Frequency Response Using MATLAB

The frequency response of a system is the major way of characterizing how a system behaves in the frequency domain. It is important to understand the frequency characteristics of a given system rather than time domain characteristics alone for many practical applications like filter design.

The frequency response of a system, is just the transfer function, evaluated at . Frequency response is usually a complex valued function, so it can be written as , where is the magnitude response and is the phase response. You can use MATLAB to plot the magnitude and phase responses as follows:

Example: , to plot magnitude and phase responses use the following command lines. Define two vectors b and a where b is the coefficients of the polynomial in the numerator, and a is the coefficients of the polynomial in the numerator.
Note that they have to be the same length and start with the coefficient of the highest order term. Then define w as the vector of frequencies over which you want to plot the magnitude and phase responses.

b=[0 1 -1];
a=[1 8 8];
w=[0:.1:2*pi];
freqs(b,a,w)