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2025-L12

# 2025-L12 - ECE-2025 Spring-2004 Info Web-CT Lab HW Lab#6...

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ECE-2025 Spring-2004 Lecture 12 Frequency Response of FIR 20-Feb-04 2/19/2004 ECE-2025 Spring-04 jMc 2 Info: Web-CT, Lab, HW Lab #6: FIR Filtering of Images Interpolation for Digital Cameras Prob Set #6 due next week Quiz #2 on 5-March (Friday) Coverage: HW #4, #5, #6, and #7 Chapters 3(FourierSeries), 4, 5, and 6 Lecture 2/19/2004 ECE-2025 Spring-04 jMc 3 READING ASSIGNMENTS This Lecture: Chapter 6, Sections 6-1, 6-2, 6-3, 6-4, & 6-5 Other Reading: Recitation: Chapter 6 FREQUENCY RESPONSE EXAMPLES Next Lecture: Chap. 6, Sects. 6-6, 6-7 & 6-8 2/19/2004 ECE-2025 Spring-04 jMc 4 LECTURE OBJECTIVES SINUSOIDAL INPUT SIGNAL DETERMINE the FIR FILTER OUTPUT FREQUENCY RESPONSE of FIR PLOTTING vs. Frequency MAGNITUDE vs. Freq PHASE vs. Freq ) ( ˆ ˆ ˆ ) ( ) ( ω ω ω j e H j j j e e H e H = MAG PHASE

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2/19/2004 ECE-2025 Spring-04 jMc 5 DOMAINS: Time & Frequency Time-Domain: “n” = time x[n] discrete-time signal x(t) continuous-time signal Frequency Domain (sum of sinusoids) Spectrum vs. f (Hz) ANALOG vs. DIGITAL Spectrum vs. omega-hat Move back and forth QUICKLY 2/19/2004 ECE-2025 Spring-04 jMc 6 DIGITAL “FILTERING” CONCENTRATE on the SPECTRUM SPECTRUM SINUSOIDAL INPUT INPUT x[n] = SUM of SINUSOIDS Then, OUTPUT y[n] = SUM of SINUSOIDS FILTER D-to-A A-to-D x(t) y(t) y [ n ] x [ n ] ω ˆ ω ˆ 2/19/2004 ECE-2025 Spring-04 jMc 7 FILTERING EXAMPLE 7-point AVERAGER Removes cosine By making its amplitude (A) smaller
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2025-L12 - ECE-2025 Spring-2004 Info Web-CT Lab HW Lab#6...

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