6.5 Analog Filtering 405
6.5.5 Filter Design with MATLAB
The design of filters, analog and discrete, is simplified by the functions that MATLAB provides. Func-
tions to find the filter parameters from magnitude specifications, as well as functions to find the filter
poles/zeros and to plot the designed filter magnitude and phase responses, are available.
Low-Pass Filter Design
The design procedure is similar for all of the approximation methods (Butterworth, Chebyshev,
elliptic) and consists of both
n Finding the filter parameters from loss specifications.
n Obtaining the filter coefficients from these parameters.
Thus, to design an analog low-pass filter using the Butterworth approximation, the loss specifications
αmaxandαmin, and the frequency specifications,pandsare first used by the functionbuttordto
determine the minimum orderNand the half-power frequencyhpof the filter that satisfies the
specifications. Then the functionbutteruses these two values to determine the coefficients of the
numerator and the denominator of the designed filter. We can then use the functionfreqsto plot
the designed filter magnitude and phase. Similarly, this applies for the design of low-pass filters using
the Chebyshev or the elliptic design methods. To include the design of low-pass filters using the
Butterworth, Chebyshev (two versions), and the elliptic methods we wrote the functionanalogfil.
function [b, a] = analogfil(Wp, Ws, alphamax, alphamin, Wmax, ind)
%%
% Analog filter design
% Parameters
% Input: loss specifications (alphamax, alphamin), corresponding
% frequencies (Wp,Ws), frequency range [0,Wmax] and indicator ind (1 for
% Butterworth, 2 for Chebyshev1, 3 for Chebyshev2 and 4 for elliptic).
% Output: coefficients of designed filter.
% Function plots magnitude, phase responses, poles and zeros of filter, and
% loss specifications
%%%
if ind == 1,% Butterworth low-pass
[N, Wn] = buttord(Wp, Ws, alphamax, alphamin, ’s’)
[b, a] = butter(N, Wn, ’s’)
elseif ind == 2, % Chebyshev low-pass
[N, Wn] = cheb1ord(Wp, Ws, alphamax, alphamin, ’s’)
[b, a] = cheby1(N, alphamax, Wn, ’s’)
elseif ind == 3, % Chebyshev2 low-pass
[N, Wn] = cheb2ord(Wp, Ws, alphamax, alphamin, ’s’)
[b, a] = cheby2(N, alphamin, Wn, ’s’)
else % Elliptic low-pass
[N, Wn] = ellipord(Wp, Ws, alphamax, alphamin, ’s’)
[b, a] = ellip(N, alphamax, alphamin, Wn, ’s’)
end
