Digital Signal Processing Reference
In-Depth Information
40
Transition Band
20
Stopband
Passband
0
0
0.2
0.4
0.6
0.8
1
(a) Normalized Frequency
40
Transition Band
Transition Band
20
Passband
Stopband
Stopband
0
0
0.2
0.4
0.6
0.8
1
(b) Normalized Frequency
40
Stopband
20
Passband
Transition Band
0
0
0.2
0.4
0.6
0.8
1
(c) Normalized Frequency
Figure 4.22:
(a) Magnitude response of a simple lowpass filter made by summing adjacent cosine cor-
relators; (b) Same, but bandpass; (c) Same, but highpass. For purposes of discussion, a “passband” can be
defined as a range of frequencies over which the desired filter response is above a certain level, a “stopband”
can be defined as a range of frequencies over which the desired filter response is below a certain level or
near zero, and a “transition band” is a range of frequencies lying between a passband and a stopband.
flatness) in the passband, the maximum response in the stopband(s), the steepness of roll off or transition
from passband to stopband, and the phase response of the filter. The lack of adequate signal suppression in
the stopbands, is clearly shown in Figs. 4.21 and 4.22, as is the large amount of passband ripple. These and
the other deficiencies mentioned will be attacked using a variety of methods to effectively design excellent
filters meeting user-given design specifications. The description of these methods requires a number of
chapters, but with the brief look we have had at frequency-selective filtering using the fundamental idea
of correlation, the reader should have little difficulty understanding the principles of operation and design
of FIR filters when they are encountered in Volume III of the series.
4.10
SINUSOIDAL FIDELITY
We noted earlier that in saturation, the correlation sequence between a correlator and a periodic sinusoidal
excitation signal contains a steady-state or periodic response in saturation. Now let's consider Fig. 4.23,
