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Unformatted text preview: CARLETON UNIVERSITY Department of Systems and Computer Engineering SYSC 5602 Introduction to Digital Signal Processing Winter Semester, 2007 Assignment #4 Assigned: 6March2007 Due: (in-class) 22March2007 PROBLEM 4.1: The magnitude-squared of the frequency response for a continuous-time filter is given as | H ( j ) | 2 = 625 6 6 + 151 4 + 15775 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 ) | 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- . 9 z- 1 + 0 . 81 z- 2 ) PROBLEM 4.3: Design a digital highpass Butterworth filter using the bilinear transformation design procedure.Design a digital highpass Butterworth filter using the bilinear transformation design procedure....
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