2025-L12su10

2025-L12su10 - 1 1 ECE2025 Summer 2010 Lecture 12 Digital...

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Unformatted text preview: 1 6/21/2010 1 ECE2025 Summer 2010 Lecture 12 Digital Filtering of Analog Signals (1st pass) Introduction to Z-Transforms 23 Jun 10 6/21/2010 3 ANNOUNCEMENTS ¡ HW #5 due June 28-29 ¡ June 23-24 ¡ Turn in Lab #4 ¡ Do Lab #5 ¡ 6/21/2010 4 READING ASSIGNMENTS ¡ This Lecture: ¡ Chapter 6, Sections 6-6, 6-7 & 6-8 ¡ Chapter 7 6/21/2010 5 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 2 6/21/2010 6 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 ] [ ] [ ] [ ] [ ∑ = − = M k k j j e k h e H ˆ ˆ ] [ ) ( ω ω L + + + + = − − − ω ω ω ω ˆ 3 ˆ 2 ˆ ˆ ] 3 [ ] 2 [ ] 1 [ ] [ ) ( j j j j e h e h e h h e H 6/21/2010 7 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 , , { = k b ω ˆ ω ˆ 6/21/2010 8 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 ˆ ˆ ] 2 [ ) ( ω ω δ ) ( ˆ ω j e H y [ n ] x [ n ] ω ˆ 2 j e − ω ˆ ω ˆ 6/21/2010 9 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 ˆ ˆ ] [ ) ( − = − = − = ∑ ] [ ] [ for ) ( and ] [ Find ˆ d j n n x n y e H n h − = ω ] [ ] [ d n n n h − = δ 3 6/21/2010...
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2025-L12su10 - 1 1 ECE2025 Summer 2010 Lecture 12 Digital...

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