Page 233 - Fundamentals of Radar Signal Processing
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The result is
(4.19)
This result is illustrated in Fig. 4.3. The matched filter output is a triangle
function of duration 2τ seconds with its peak at t = T as expected. The peak
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value is ατ; since the energy of the unit amplitude pulse is just τ, the peak value
equals αE as predicted.
FIGURE 4.3 Matched filter output for a simple pulse.
The noise power at the output of the matched filter is
(4.20)
The SNR is therefore
(4.21)
consistent with Eq. (4.13). Note that the gain α has no effect on the SNR.
4.2.3 All-Range Matched Filtering
The matched filter was designed to maximize the output SNR at a particular time
instant T . This raises several questions. How should T be chosen, and how
M
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can the range of a target be related to the resulting output? What happens if the
