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SPFirst-L13 - Signal Processing First READING ASSIGNMENTS...

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10/6/2003 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 13 Digital Filtering of Analog Signals 10/6/2003 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS This Lecture: Chapter 6, Sections 6-6, 6-7 & 6-8 Other Reading: Recitation: Chapter 6 FREQUENCY RESPONSE EXAMPLES Next Lecture: Chapter 7 10/6/2003 © 2003, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES Two Domains: Time & Frequency Track the spectrum of x[n] thru an FIR Filter: Sinusoid-IN gives Sinusoid-OUT UNIFICATION : How does Frequency Response affect x(t) to produce y(t) ? D-to-A A-to-D x(t) y(t) y [ n ] x [ n ] ) ( ˆ ω j e H FIR ω ˆ ω ˆ 10/6/2003 © 2003, JH McClellan & RW Schafer 5 TIME & FREQUENCY FIR DIFFERENCE EQUATION is the TIME-DOMAIN = = = = M k M k k k n x k h k n x b n y 0 0 ] [ ] [ ] [ ] [ = = M k k j j e k h e H 0 ˆ ˆ ] [ ) ( ω ω " + + + + = ω ω ω ω ˆ 3 ˆ 2 ˆ ˆ ] 3 [ ] 2 [ ] 1 [ ] 0 [ ) ( j j j j e h e h e h h e H
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10/6/2003 © 2003, JH McClellan & RW Schafer 6 Ex: DELAY by 2 SYSTEM y [ n ] x [ n ] ) ( ˆ ω j e H y [ n ] x [ n ] ] [ n h ] 2 [ ] [ for ) ( and ] [ Find ˆ = n x n y e H n h j ω ] 2 [ ] [ = n n h δ } 1 , 0 , 0 { = k b ω ˆ ω ˆ 10/6/2003 © 2003, JH McClellan & RW Schafer 7 DELAY by 2 SYSTEM k = 2 ONLY y [ n ] x [ n ] ] 2 [ n δ ] 2 [ ] [ for ) ( and ] [ Find ˆ = n x n y e H n h j ω = = M k k j j e k e H 0 ˆ ˆ ] 2 [ ) ( ω ω δ ) ( ˆ ω j e H y [ n ] x [ n ] ω ˆ 2 j e ω ˆ ω ˆ 10/6/2003 © 2003, JH McClellan & RW Schafer 8 GENERAL DELAY PROPERTY ONLY ONE non-ZERO TERM for k at k = n d d n j M k k j d j e e n k e H ω ω ω δ ˆ 0 ˆ ˆ ] [ ) ( = = = ] [ ] [ for ) ( and ] [ Find ˆ d j n n x n y e H n h = ω ] [ ] [ d n n n h = δ 10/6/2003 © 2003, JH McClellan & RW Schafer 9 FREQ DOMAIN --> TIME ??
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