Page 182 - Fundamentals of Radar Signal Processing

FIGURE 3.2 Organization of received data: (a) vector of fast-time samples for
one pulse, (b) matrix of fast-time/slow-time samples for one CPI.

How rapidly should one sample the echo from a single received pulse, i.e.,
what should the spacing of the range bins be? The Nyquist theorem states that
the sampling rate F should equal or exceed the bandwidth of the received signal
s
(see App. B). In Chap. 2 it was shown that the received signal in the range
dimension can be modeled as the convolution of the range reflectivity function
and the modulation function x(t) of the transmitted waveform. The spectrum of
the received signal is thus the product of the spectra of the range reflectivity
function and the modulation function. This means that the bandwidth of the
received fast-time signal will be limited by the bandwidth of the transmitted
pulse. Therefore, the Nyquist rate in fast time is simply the bandwidth of the

transmitted pulse.
As shown in App. B, the spectrum of the simple complex exponential pulse
of frequency F Hz is a sinc function in the frequency domain centered at F Hz.
0
0
This spectrum is not strictly bandlimited; however, the 3-dB bandwidth β is
3
0.89/τ Hz, both the Rayleigh bandwidth β and 4 dB bandwidth β are 1/τ Hz,
4
r
and the null-to-null bandwidth β is 2/τ Hz. These approximate bandwidth
nn
measures are shown in Fig. 3.3 with F = 0 for convenience.
0