HW4 - h ( t ) = ± A- | t | -A ≤ t ≤ A otherwise where...

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EEE 203 – Signals and Systems Homework Assignment #4 Assigned: 20 March 2008 Due: 3 April 2008 Reading: Chapter 3, sections 3.1, 3.2, and 3.5. Work to hand in: 1. Define x 1 ( t ) = sinc 2 ( t ) and x 2 ( t ) = cos(Ω t ) x 1 ( t ). Find a value W such that Z -∞ x 1 ( t ) x 2 ( t ) dt = 0 for all | Ω | > W . 2. You wish to jam a suppressed-carrier AM radio transmission r ( t ) of bandwidth 1 . 82 × 10 4 π centered at frequencies ± 1 . 2 × 10 6 π . You have at your disposal a baseband jamming waveform n ( t ) of bandwidth 2000 π and a tunable oscillator the produces a cosive wave c Ω ( t ) = cos(Ω t ). Design a signal of the form j ( t ) = c Ω ( t ) n ( at ) with a > 0 to jam the transmission (i.e., find good values of a and Ω to use and explain why you chose them). 3. A continuous-time LTI system has impulse response
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Unformatted text preview: h ( t ) = ± A- | t | -A ≤ t ≤ A otherwise where A > 0. (a) Find the smallest value of A so that the signal x 1 ( t ) = cos(10 6 × 2 πt ) is attenuated to zero by the system. (b) Assume the value of A determined above. What is the system’s response to x 2 ( t ) = cos(10 6 × 2 π ( t-t ))? (c) What is the system’s response to x 3 ( t ) exp(10 5 × 2 πit )? 4. Calculate the following integrals. (a) Z 10 π π | e it 2 | 3 dt (b) Z ∞-∞ cos 2 ( t )sinc 2 (2 t ) dt (c) Z ∞-∞ e-iτ e i ( t-τ ) sinc( τ )sinc( t-τ ) dt...
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This note was uploaded on 09/29/2008 for the course EEE 203 taught by Professor Chakrabarti during the Spring '07 term at ASU.

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