0195136047.pdf

638 SIGNAL PROCESSING

A

t

(a) (b)

AD

−D/2 D/2 1/D 2/D 3/D

f

0

Amplitude

Figure 14.1.4Nonperiodic signal and its spectrum.(a)Single rectangular pulse.(b)Continuous amplitude

spectrum.

By lettingT →∞for the rectangular pulse train of Figure E14.1.4(a), so that all pulses

vanish except the one centered att= 0, we would obtain a single rectangular pulse, as shown in

Figure 14.1.4(a). Becausef = 1 /T→0 whenT →∞, intuitively, the amplitude lines will

merge to form a continuous plot, as shown in Figure 14.1.4(b). Spectral analysis of nonperiodic

signals involvesFourier transform theory, which goes beyond the scope of this text. Smooth

curves, such as one in Figure 14.1.4(b), suggest that the signal energy is spread over a continuous

frequency range, rather than being concentrated in discrete sinusoidal components. Note that the

amplitude atf=0 is equal to the net area DA of the nonperiodic signal.

When spectral peaks occur at or nearf=0, and their amplitude spectra become progressively

smaller as frequency increases, such waveforms are known aslow-pass signals,for which there

exists asignal bandwidth Wsuch that all significant frequency content falls within the range of

0 ≤f≤W. The concept of signal bandwidth plays a significant role in signal-processing and

communication systems. Table 14.1.1 lists the nominal bandwidths of a few selected signals.

The approximate reciprocal relationshipW∼= 1 /Dconveys the salient point that long pulses

have small bandwidths while short pulses have large bandwidths. This agrees qualitatively with

the rectangular pulse spectrum of Figure 14.1.4(b), although it ignores the components above

f= 1 /D. In order to preserve the square corners of the rectangular pulse shape, we would have

to takeW>> 1 /D.

Filtering, Distortion, and Equalization

Frequency response andfilterswere discussed in Section 3.4. Any undesired waveform alteration

produced by a frequency-selective network is known aslinear distortion.It is so designated to

distinguish it from the distortion caused by nonlinear elements. Let us now investigate filtering

and linear distortion from the point of view of spectral analysis.

TABLE 14.1.1Lowpass Signal Bandwidths of Selected Signals

Signal Type Bandwidth

Telephone-quality voice 3 kHz

Moderate-quality audio 5 kHz

High-fidelity audio 20 kHz

Television video 4 MHz