EEN336: Signals & Systems Spring 2009 HW7: Due March 19

EEN336: Signals & Systems Spring 2009 HW7: Due March 19 2013 Problem 1: Determine the Fourier series coefficients of the following signals: 1. x1[n] = 2 + cos(n=3 + =6) + sin(=2) 2. x2[n] = S1k=??1 [(??1)k(n ?? 2k)] Problem 2: What time-domain signals have the following Fourier series/transform representations: 1. X1[k] = cos(k=3) + cos(k=2 + =3) 2. X2(!) = S2k=??2 (! ?? k=4) (j!j ) Problem 3: The FS representation of x[n] is given by X[k] = sin(k=3). Use Fourier series proper- ties without determining x[n] to determine the following DT signals: 1. v[n] = x[n + 1] x[n ?? 1] (*: convolution) 2. w[n] = sin(n=2) x[n]. Problem 4: Determine the Fourier transform methods to determine the response of the following systems for the given input: 1. h1[n] = sin(2n=5) n and x1[n] = sin(n=3 + =4) + cos(3n=4) 2. h2[n] = sin(n=3) cos(n=2) n and x2[n] = sin(n=3 + =4) + cos(3n=4) 3. h3[n] = (1=2)jnj and x3[n] = (??1)n 1
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