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344 Chapter 7 FIR FILTER DESIGN
then fir1 returns a bandpass filter with passband cutoffs wc1 and wc2.
If wc is a multi-element (more than two) vector, then fir1 returns a
multiband filter with cutoffs given in wc.
• h = fir1(N,wc,’ftype’) specifies a filter type, where ’ftype’ is:
a. ’high’ for a highpass filter with cutoff frequency Wn.
b. ’stop’ for a bandstop filter, if Wc = [wc1 wc2]. The stopband frequency
range is specified by this interval.
c. ’DC-1’ to make the first band of a multiband filter a passband.
d. ’DC-0’ to make the first band of a multiband filter a stopband.
• h = fir1(N,wc,’ftype’,window) or h = fir1(N,wc,window) uses
the vector window of length N+1 obtained from one of the specified
MATLAB window function. The default window function used is the
Hamming window.
To design FIR filters using the Kaiser window, the SP toolbox provides
the function kaiserord, which estimates window parameters that
can be used in the fir1 function. The basic syntax is
[N,wc,beta,ftype] = kaiserord(f,m,ripple);
The function computes the window order N, the cutoff frequency vector
wc, parameter β in beta, and the filter type ftype as discussed. The
vector f is a vector of normalized band edges and m is a vector specifying
the desired amplitude on the bands defined by f. The length of f is twice
the length of m, minus 2; i.e., f does not contain 0 or 1. The vector ripple
specifies tolerances in each band (not in decibels). Using the estimated
parameters, Kaiser window array can be computed and used in the fir1
function.
To design FIR filters using window technique with arbitrary shaped
magnitude response, the SP toolbox provides the function fir2, which
also incorporates the frequency sampling technique. It is explained in the
following section.
7.4 FREQUENCY SAMPLING DESIGN TECHNIQUES
In this design approach we use the fact that the system function H (z)
can be obtained from the samples H(k) ofthe frequency response H(e jω ).
Furthermore, this design technique fits nicely with the frequency sampling
structure that we discussed in Chapter 6. Let h(n)bethe impulse response
of an M-point FIR filter, H(k) beitsM-point DFT, and H(z) beits
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