Page 251 - Fundamentals of Radar Signal Processing

(i.e., sample the same range bin for each pulse). The filter output for pulse m is

sampled at t = t + mT, giving y (t + mT) = s (0) again.
p
l
m
l
If the sample taken at time tl after pulse transmission is associated with
range bin l, the M samples so obtained form a discrete constant-valued sequence
y[l, m] = sp(0), 0 ≤ m ≤ M – 1. The discrete-time causal matched filter in the
slow-time (m) dimension for such a sequence is h[m] = αy*[M – 1 – m]; with α
= 1/s (0), h[m] = 1 for 0 ≤ m ≤ M – 1. The output of this discrete-time matched
p
filter is

(4.62)

The peak output will occur when the two functions in the summand completely
overlap, which requires m = M – 1; then

(4.63)

Equation (4.63) indicates that in pulse-by-pulse processing, matched filtering of
the slow-time sequence from a given range bin reduces to coherently integrating

the slow-time samples in each range bin, and the resulting peak output is
identical to that obtained with a whole-waveform continuous matched filter of
Eq. (4.55). Figure 4.14 illustrates the row of slow-time samples that are
integrated (after matched filtering of the single pulse in fast time) to complete
the matched filtering process for the pulse burst. This operation is performed

independently for each range bin.