2025-L13 - ECE-2025 Fall-2008 Lecture 13 Digital Filtering...

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Unformatted text preview: ECE-2025 Fall-2008 Lecture 13 Digital Filtering of Analog Signals 6-Oct-08 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 2 Info: Lab, HW, etc. ¡ HW #7 due this week ¡ Lab #7 will start on Wed after break ¡ Filtering images ¡ Course Objective Students will be able to: Understand mathematical descriptions of signal processing algorithms and express those algorithms as computer implementations (MATLAB) 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 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 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 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 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 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 ] [ ] [ ] [ ] [ ∑ = − = 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 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 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 , , { = k b ω ˆ ω ˆ 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 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 ˆ ˆ ] 2 [ ) ( ω ω δ ) ( ˆ ω j e H y [ n ] x [ n ] ω ˆ 2 j e − ω ˆ ω ˆ 09/30/2008 ECE-2025 Fall-08 jMc-BHJ 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 ˆ ˆ ] [ ) ( − = − = − = ∑ ] [ ]...
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This note was uploaded on 09/17/2009 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Tech.

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2025-L13 - ECE-2025 Fall-2008 Lecture 13 Digital Filtering...

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