ECE
ECE130A-F10-HW06

# ECE130A-F10-HW06 - 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, 8 November 2010 Electrical & Computer Engineering Dept. Homework Due: Tuesday, 16 November 2010 at 6:00 p.m. University of California, Santa Barbara Homework 6 Problem 1: Fourier Transforms (20 Points) (a) Compute the frequency response H (j ω ) of the impulse response h ( t ) (and sketch its magnitude) using the Fourier transform relationship X (j ω ) = Z -∞ x ( t )e - j ω t d t , when h ( t ) is given by h ( t ) = e - 2( t - 1) u ( t - 1). (b) Compute the response y ( t ) to the input signal x ( t ) = sin(2 π t - π /2). Problem 2: Fourier Transform Computation (25 Points) Determine and sketch the magnitude | X (j2 π f ) | of the Fourier transform for the following signals. State for each waveform whether it is a baseband or bandpass signal (the definitions are to be applied loosely, with most of the frequency content being in a band around DC for a baseband signal, and most of the frequency content being in a band away from DC for a bandpass signal): (a) x ( t ) = sinc(2 t )sinc(3 t ) (b) x ( t ) = cos(4 π t ) (c) x ( t ) = sinc(2
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