hw1_501_Au08

# hw1_501_Au08 - ECE-501 Homework#1 Introduction to Analog...

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ECE-501 Introduction to Analog and Digital Communications Winter 2008 Homework #1 Sep 24, 2008 HOMEWORK ASSIGNMENT #1 Due Wednesday Oct. 1, 2008 (in class) Reading: 1. Visit the course web page. 2. Text, Ch. 1. 3. Text, Ch. 2.1-2.5 (the subsection on Time-Bandwidth Product is optional). 4. 2.6-2.7 (the sections on Paley-Wiener Criterion, pulse response of ideal LPFs, and Approximation of Ideal LPFs are optional). Problems: 1. (Haykin 2.2) [Note: the solution given in the book is incorrect!] 2. Say that w ( t ) is a real-valued signal. Prove that its Fourier transform magnitude is symmetric around f = 0, i.e., that | W ( f ) | = | W ( - f ) | . 3. (Haykin 2.6) 4. (Haykin 2.9) 5. Lowpass ﬁlters (a) Find the inverse Fourier transform, h ( t ), of the ideal lowpass ﬁlter, H ( f ) given by H ( f ) = ± 1 , | f | ≤ B 0 , else (b) Prove that the ideal linear-phase LPF has a delayed sinc impulse response: G ( f ) = ± e - j 2 πft o | f | ≤ B 0 | f | > B F ←→ g ( t ) = 2 B sinc(2 B ( t - t o )) ( Hint:

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## This note was uploaded on 10/25/2009 for the course ECE 501 taught by Professor Schniter,p during the Spring '08 term at Ohio State.

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hw1_501_Au08 - ECE-501 Homework#1 Introduction to Analog...

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