Signals and Systems - Electrical Engineering

6.5 Analog Filtering 407

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% Example 6.11 -- Filter design using analogfil

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clear all; clf

alphamax = 0.1;

alphamin = 60;

Wp =10; Ws = 15;

Wmax = 25;

ind = 4 % elliptic design

% ind = 3 % chebyshev2 design

[b, a] = analogfil(Wp, Ws, alphamax, alphamin, Wmax, ind)

The elliptic design is illustrated above. To obtain the Chebyshev2 design get rid of the comment

symbol % in front of the corresponding indicator and put it in front of the one for the elliptic

design. n

General comments on the design of low-pass filters using Butterworth, Chebyshev (1 and 2), and
Elliptic methods are:

n The Butterworth and the Chebyshev2 designs are flat in the passband, while the others display
ripples in that band.
n For identical specifications, the obtained order of the Butterworth filter is much greater than the
order of the other filters.
n The phase of all of these filters is approximately linear in the passband, but not outside it. Because
of the rational transfer functions for these filters, it is not possible to have linear phase over all
frequencies. However, the phase response is less significant in the stopband where the magnitude
response is very small.
n The filter design functions provided by MATLAB can be used for analog or discrete filters. When
designing an analog filter there is no constrain in the values of the frequency specifications and
an ’s’ indicates that the filter being designed is analog.

General Filter Design
The filter design programsbutter, cheby1, cheby2,andellipallow the design of other filters besides
low-pass filters. Conceptually, a prototype low-pass filter is designed and then transformed into the
desired filter by means of the frequency transformations given before. The filter is specified by the
order and cut-off frequencies. In the case of low-pass and high-pass filters the specified cut-off fre-
quencies are scalar, while for band-pass and stopband filters the specified cut-off frequencies are given
as a vector. Also recall that the frequency transformations double the order of the low-pass prototype
for the band-pass and band-eliminating filters, so when designing these filters half of the desired
order should be given.

nExample 6.12

To illustrate the general design consider:

(a) Using thecheby2method, design a band-pass filter with the following specifications:

n orderN= 10

n α()=60 dB in the stopband