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# HW11 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 310 Digital Signal Processing Problem Set 11 Fall 2003 Due: Wednesday, November 12, 2003 Problem 11.1 The system function H I ( z ) represents a type I FIR generalized linear-phase system with impulse response h I ( n ) = h I ( N - n ) (0 n N ) with N odd. This system is cascaded with a LSI system with impulse response g ( n ) = δ ( n ) - δ ( n - 1) to produce a third system with system function H ( z ) and impulse response h ( n ). Find the order of the ﬁlter H ( z ). Prove that the overall system is a generalized linear-phase system, and determine what type of linear phase system it is. Problem 11.2 A common method to design FIR ﬁlters is the windowing method whereby an ideal ﬁlter with inﬁnitely long impulse response h d ( n ) is approximated by an FIR ﬁlter according to h ( n ) = n h d ( n ) , 0 n N 0 , otherwise (1) The transfer function of the resulting FIR ﬁlter

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HW11 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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