ECE130A-HW02-F10

ECE130A-HW02-F10 - ECE 130A: Signal Analysis and Processing...

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ECE 130A: Signal Analysis and Processing Prof. Michael Liebling Fall 2010 TAs: Jingning Han, Hari Sivakumar Distribution: Monday, 4 October 2010 Homework Due: Tuesday, 12 October 2010, 5:00PM University of California, Santa Barbara Homework 2 Problem 1: Impulse Response (20 points) Calculate the following integrals: (a) R -∞ x ( t ) δ ( t )d t (b) R -∞ x ( t ) δ ( t - 4)d t (c) R -∞ x ( t ) δ ( τ )d τ (d) R -∞ x ( τ ) δ ( t - τ )d τ (e) R -∞ δ ( t - τ )d τ (f) R -∞ x ( τ ) δ ( τ )d τ (g) R -∞ exp(j2 πτ ) δ ( τ - 1)d τ (h) R -∞ x ( t )( δ ( τ - 1) - δ ( τ + 1))d τ Problem 2: Convolution (20 points) For each of the following pairs of waveforms, use the convolution integral to find the response y ( t ) of the LTI system with impulse response h ( t ) to the input x ( t ). Sketch your results. (a) x ( t ) = I [1,3] ( t ) = ( 1, 1 t 3 0 otherwise, and h ( t ) = ( ( t - 1) 3 , 1 t 2
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This note was uploaded on 12/06/2010 for the course ECE 130A taught by Professor Madhow during the Fall '07 term at UCSB.

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