UploadFile_6417

Lowpass Filter Design Using MATLAB 443
matched-z transformation does not preserve either the impulse response
or the frequency response characteristics. Hence it is suitable when designing
using pole-zero placement, but it is generally unsuitable when the
frequency-domain specifications are given.
8.5 LOWPASS FILTER DESIGN USING MATLAB
In this section we will demonstrate the use of MATLAB’s filter design
functions to design digital lowpass filters. These functions use the bilinear
transformation because of its desirable advantages as discussed in the
previous section. These functions are as follows:
1. [b,a]=butter(N,wn)
This function designs an Nth-order lowpass digital Butterworth filter
and returns the filter coefficients in length N +1 vectors b and a. The
filter order is given by (8.49), and the cutoff frequency wn is determined
by the prewarping formula (8.68). However, in MATLAB all digital
frequencies are given in units of π. Hence wn is computed by using the
following relation:
ω n = 2 π tan−1 (
Ωc T
2
The use of this function is given in Example 8.21.
2. [b,a]=cheby1(N,Rp,wn)
This function designs an Nth-order lowpass digital Chebyshev-I filter
with Rp decibels of ripple in the passband. It returns the filter coefficients
in length N +1 vectors b and a. The filter order is given by
(8.59), and the cutoff frequency wn is the digital passband frequency
in units of π; that is,
ω n = ω p /π
The use of this function is given in Example 8.22.
3. [b,a]=cheby2(N,As,wn)
This function designs an Nth-order lowpass digital Chebyshev-II filter
with the stopband attenuation As decibels. It returns the filter coefficients
in length N +1 vectors b and a. The filter order is given by
(8.59), and the cutoff frequency wn is the digital stopband frequency
in units of π; that is,
ω n = ω s /π
The use of this function is given in Example 8.23.
)
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.