Page 169 - Fundamentals of Radar Signal Processing

so that the amplitude of the spectrum of the received pulse, and therefore of the
pulse itself, is proportional to the amplitude of the spectrum of the angle

averaged range profile, evaluated at the transmitted frequency. Since it is the
complex spectrum that appears in Eq. (2.124), both the amplitude and phase of
the returned pulse are affected by the amplitude and phase of the reflectivity
spectral sample. Equation (2.130) shows that a narrowband radar pulse can be
interpreted as measuring a frequency sample of the spectrum of the angle-

averaged reflectivity range variation.
Another case of interest occurs when x(t) is a wideband pulse of
bandwidth β Hz. For some waveforms such as the linear frequency-modulated
pulse, the magnitude of the spectrum X(F) is approximately a rectangle as shown
i n Fig. 2.31. The spectrum of the receiver waveform is then
approximately that of the angle-averaged range profile over the bandwidth of the
pulse, modified by the phase of the pulse spectrum:

FIGURE 2.31 Pictorial interpretation of Eq. (2.131) illustrating the spectral
windowing effect of a wideband radar pulse.

(2.131)

In other words, the pulse spectrum acts as a window selecting a portion of the
spectrum of the angle-averaged reflectivity. This result will be useful in
understanding the use of linear FM and other modulated waveforms to achieve
fine range resolution in Chap. 4.

2.9 Summary
An understanding of the nature of the signals of interest is prerequisite to the
design of successful signal processing systems. This chapter reviews the most