32
D. Rocchesso: Sound Processing
of the frequency response is depicted in fig. 10. We see that the specifications are
0
1
2
3
-80
-60
-40
-20
0
frequency [rad/sample]
magnitude [dB]
Figure 10: Magnitude of the frequency response of the length-11 filter
met. However, the response is not monotonically decreasing. This is due to the
fact that the specifications are quite demanding, thus impeding the satisfaction
of (21). In fact, the coefficients turn out to be a
0
= 0.369 and a
1
= 0.262, and
the zeros are not real but complex conjugate, as shown in the pole-zero plot of
fig. 11. The impulse response of the 10-th order FIR filter is obtained from its
-1
0
1
-1
-0.5
0
0.5
1
Re
Im
Figure 11: Pole-zero plot for the length-3 FIR filter
frequency response by solving in [a
0
a
1
. . . a
10
] the matrix equation
[a
0
a
1
. . . a
10
]
1
e
-j
. . .
e
-j10
= H
11
() ,
(23)
which is all contained in the lines
k = [0:10]'; kernelw = exp(-i*k*w);
aa = H11 / kernelw;