s08_ps09_spring04

# s08_ps09_spring04 - Unied Engineering II Spring 2004...

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Unified Engineering II Spring 2004 Problem S8 (Signals and Systems) This problem shows why a radar system sends out a chirp, which has a broad range of frquencies in the signal, and not a short sinusoidal pulse, which is at a single frequency. To see why a sinusoidal pulse doesn’t work well, let’s try a radar signal u ( t ) = sin(2 πt ) , 3 t 0 0 , otherwise The matched filter for this pulse has impulse response g ( t ) = u ( t ) = sin( 2 πt ) , 0 t 3 0 , otherwise The radar sends out a signal, u ( t ), that reﬂects off the aircraft and returns to the radar system. The time it takes the signal to return is twice the distance to the aircraft, divided by the speed of light. The received signal is u ( t T ), where T is the round trip travel time of the signal. For the purposes of this problem, we can ignore the time delay, T , and just look at how the matched filter response to u ( t ). 1. Find the convolution y ( t ) = g ( t ) u ( t ) You will find it helpful to use the ﬂip and slide method to set up the integral. The integral can be evaluated relatively easily
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