Challenge_15-1

# Challenge_15-1 - ω/2 =(2(cos(5 ω ∠-5 ω Then H(e j ω =...

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Discrete-Time Signals and Systems Dr. Fred J. Taylor, Professor Lesson Title: FIR Frequency Response Lesson Number: 15 (Section 6-3 to 6-4) L Challenge Two N+1=11 order comb filters, having an impulse response h[k]={1,0,0,0,0,0,0,0,0,0,0,1} and frequency response H(e j ω )=2(cos( ω N/2)e -j ω N/2 , are cascaded. What is the frequency response H 0 (e j ω ) of the cascaded filter? Response Treat the 1 st impulse response as an input signal having a frequency response: H(e j ω ) = | H(e j ω )| H(e j ω ) = (2(cos(10 ω /2)) -10
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Unformatted text preview: ω /2 = (2(cos(5 ω )) ∠-5 ω Then H (e j ω ) = | H(e j ω )| 2 ∠ 2H(e j ω ) = 4 cos(5 ω ) 2 ∠-10 ω You could also have convolved the two impulse responses producing h 21 =h*h producing: h 21 = [1,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,1] which has a frequency response: H 21 (e j ω ) = 1+2 e-j10 ω + e-j20 ω = (1+ e-j10 ω ) 2 = ((e-j5 ω )( e j5 ω +e-j5 ω )) 2 = (2(e-j5 ω )( e j5 ω +e-j5 ω )/2) 2 = 4 cos(5 ω ) 2 ∠-10 ω (as before) 1...
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## This note was uploaded on 04/15/2010 for the course EEL 3135 taught by Professor ? during the Spring '08 term at University of Florida.

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