4-SYSC5602a4-W09[1] - CARLETON UNIVERSITY Department of...

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CARLETON UNIVERSITY Department of Systems and Computer Engineering SYSC 5602 – Introduction to Digital Signal Processing Winter Semester, 2007 Assignment #4 As signed: 6–March–2007 Due: (in-class) 22–March–2007 PROBLEM 4.1: The magnitude-squared of the frequency response for a continuous-time filter is given as | H ( j Ω) | 2 = 625Ω 6 Ω 6 + 151Ω 4 + 15775Ω 2 + 15625 (a) Plot the pole-zero diagram of H ( s ) H ( - s ). (b) Determine the transfer function H ( s ) for a stable filter that will produce | H ( j Ω) | 2 . (c) From the pole-zero diagram for H ( s ), determine if this filter is a lowpass, highpass, band- pass, or bandstop. (d) Draw an estimate for the magnitude of the frequency response for H ( s ). (e) Is the impulse-invariance method for converting a continuous-time filter to a discrete-time filter appropriate to use for this filter given by H ( s )? Justify your answer. PROBLEM 4.2: Obtain the direct form I, direct form II, cascade, and parallel structures signal flow graphs for the following system. H ( z ) = 2(1 - z - 1 )(1 + 2 z - 1 + z - 2 ) (1 + 0 . 5 z - 1 )(1 - 0 . 9 z - 1 + 0 . 81 z - 2 ) PROBLEM 4.3: Design a digital highpass Butterworth filter using the bilinear transformation design procedure.
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