Page 184 - Fundamentals of Radar Signal Processing
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In fact, many phase modulated pulses are designed to have a spectrum that is
approximately constant magnitude (but with complicated phase characteristics)
over some desired bandwidth β, where β is much larger than the simple pulse
bandwidth of approximately 1/τ. Thus, an idealized model of the spectrum of the
ideal received phase-modulated radar pulse after translation to baseband is
(3.2)
where Φ(F) is some phase function. Figure 3.4 shows an example, the
magnitude spectrum of a linear frequency-modulated or “chirp” waveform with
a time-bandwidth product of 100; this waveform is studied in Chap. 4. On the
normalized frequency scale shown, the spectrum is approximately rectangular
with support f ∈(– 0.5, + 0.5), corresponding to ±β/2 Hz. This case offers a
relatively unambiguous definition of the bandwidth of the pulse (namely, β Hz),
making application of the Nyquist criterion to range sampling straightforward.
FIGURE 3.4 Magnitude of the Fourier transform of a linear FM “chirp”
waveform having a time-bandwidth product of 100.
3.1.2 Multiple Pulses: Slow Time and the CPI
The radar transmits not just a single pulse, but a periodic series of pulses. In
some cases (e.g., a rotating weather or surveillance radar), the pulse series may
be continuously ongoing, but in many cases it is organized into groups of M
