Continuous-time filters - Continuous and Discrete Time Signals and Systems - page 320

CHAPTER

7

Continuous-time filters

A common requirement in signal processing is to modify the frequency contents
of a continuous-time (CT) signal in a predefined manner. In communication sys-
tems, for example, noise and interference from the neighboring channels cor-
rupt the information-bearing signal transmitted via a communication channel,
such as a telephone line. By exploiting the differences between the frequency
characteristics of the transmitted signal and the channel noise, a linear time-
invariant system (LTI) system can be designed to compensate for the distortion
introduced during the transmission. Such an LTI system is referred to as a
frequency-selective filter, which processes the received signal to eliminate the
high-frequency components introduced by the channel interference and noise
from the low-frequency components constituting the information-bearing sig-
nal. The range of frequencies eliminated from the CT signal applied at the input
of the filter is referred to as the stop band of the filter, while the range of fre-
quencies that is left relatively unaffected by the filter constitute the pass band
of the filter.
Graphic equalizers used in stereo sound systems provide another application
for the continuous-time (CT) filters. A graphic equalizer consists of a combina-
tion of CT filters, each tuned to a different band of frequencies. By selectively
amplifying or attenuating the frequencies within the operational bands of the
constituent filters, a graphic equalizer maintains sound consistency within dis-
similar acoustic environments and spaces. The operation of a graphic equalizer
is somewhat different from that of a frequency-selective filter used in our earlier
example of the communication system since it amplifies or attenuates selected
frequency components of the input signal. A frequency-selective filter, on the
other hand, attempts to eliminate the frequency components completely within
the stop band of the filter.
This chapter focuses on the design of CT filters. We are particularly interested
in the frequency-selective filters that are categorized in four different categories
(lowpass, highpass, bandpass, and bandstop) in Section 7.1. Practical approxi-
mations to the frequency characteristics of the ideal frequency-selective filters
are presented in Section 7.2, where acceptable levels of distortion is tolerated

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