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# hw3 - ECE130B Home Work 3 Due date by 5p.m at the home work...

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ECE130B January 20, 2010 Home Work 3 Due date : January 27, 2010 by 5p.m. at the home work box. Reading assignment . Chapter 3 of the text book. Exercise 1. Suppose you sample the continuous signal e 0 t at the rate of f s samples per second (with the first sample at t =0 ). i. Find all values of ω 0 for which the resulting discrete signal will be periodic. ii. Find all values of ω 0 for which the resulting discrete signal will have the fixed period N . Exercise 2. Suppose e j 2 π N kn is a discrete time signal with fixed values of N and k (so n is the discrete time variable) that was obtained by sampling a continuous signal of the form e 0 t at the rate f s samples per second. Find all possible values of ω 0 in terms of N , k and f s . Discrete time Fourier series . Let x [ n ] be a discrete periodic signal of period N . That is x [ n + N ] = x [ n ] for all values of n . The signal x [ n ] can be written as the sum of discrete harmionic periodic oscillators of period N via the formula x [ n ]= summationdisplay k =0 N - 1 a k e j 2 π N kn , (1) where the

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