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Problems
1. Consider a stationary radar transmitting a simple square pulse (modulation
only, not including the carrier term) of duration τ:
The receiver uses a causal matched filter with T = τ, so h(t) = x*(τ – t).
M
The pulse is transmitted with the leading edge being emitted at time t = 0.
An echo is received from a stationary target at a range of R meters. At what
time t peak will the peak output of the matched filter be observed? Show all
work.
2. Consider the same pulse and matched filter used in the previous problem.
Assume that now the target is at range R meters when the pulse hits it, but
is moving with a radial velocity toward the radar of kλ/2τ m/s, where k is
any integer (except k ≠ 0). The received signal (again, after the carrier is
removed) can be modeled as
where F is the Doppler shift in hertz. Find the output waveform of the
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causal matched filter. What is its value at t = 2R/c + τ seconds?
3. Suppose the ambiguity function of some waveform x(t) of duration τ = 1
