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Frequency Sampling Design Techniques 357
Hilbert Transformer, frequency sampling design : M = 51
Amplitude response
1
0.39
0
0 0.2 0.4 0.6 0.8 1
frequency in π units
1
Impulse response
0.5
h(n)
0
−0.5
−1
0 25 50
n
FIGURE 7.33 Digital Hilbert transformer design plots in Example 7.20
window to minimize ripples near the band-edge frequencies. This function’s
syntax also has several forms including:
• h = fir2(N,f,m) designs an Nth-order (N = M−1) lowpass FIR filter
and returns the impulse response in vector h. The desired magnitude
response of the filter is supplied in vectors f and m, which must be
of the same length. The vector f contains normalized frequencies in
the range from 0 to 1, where 1 corresponds to π rad/sample. The first
value of f must be 0 and the last value 1. The vector m, contains the
samples of the desired magnitude response at the values specified in f.
The desired frequency response is then interpolated onto a dense, evenly
spaced grid of length 512. Thus, this syntax corresponds to the naive
design method.
• h = fir2(N,f,m,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.
• h = fir2(N,f,m,npt) or h = fir2(N,f,m,npt,window) specifies the
number of points, npt, for the grid onto which fir2 interpolates the
frequency response. The default npt value is 512.
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