2025-L12 - DCONVDEMO ECE-2025 Spring-2009 Lecture 12...

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ECE-2025 Spring-2009 Lecture 12 Frequency Response of FIR 20-Feb-09 DCONVDEMO 2/19/2009 ECE-2025 Spring-09 jMc 2 Lecture EADING ASSIGNMENTS READING ASSIGNMENTS ± This Lecture: ± Chapter 6, Sections 6-1, 6-2, 6-3, 6-4, & 6-5 ± ther Reading: Other Reading: ± Recitation: Chapter 6 ± REQUENCY RESPONSE EXAMPLES FREQUENCY RESPONSE EXAMPLES ± Next Lecture: Chap. 6, Sects. 6-6, 6-7 & 6-8 2/19/2009 ECE-2025 Spring-04 jMc 3 ECTURE OBJECTIVES LECTURE OBJECTIVES ± SINUSOIDAL INPUT SIGNAL ± DETERMINE the FIR FILTER OUTPUT ± REQUENCY RESPONSE f FIR AG FREQUENCY RESPONSE of FIR ± PLOTTING vs. Frequency ± AGNITUDE vs Freq MAG PHASE MAGNITUDE vs. Freq ± PHASE vs. Freq ) ( ˆ ˆ ˆ ) ( ) ( ω j e H j j j e e H e H = 2/19/2009 ECE-2025 Spring-04 jMc 4
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OMAINS: Time & Frequency DOMAINS: Time & Frequency ime omain: “n”=t ime ± 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 2/19/2009 ECE-2025 Spring-04 jMc 5 IGITAL “FILTERING” DIGITAL “FILTERING” FILTER D-to-A A-to-D x(t) y(t) y [ n ] x [ n ] ONCENTRATE on the PECTRUM ω ˆ ˆ ± CONCENTRATE on the SPECTRUM ± SINUSOIDAL INPUT ± INPUT x[n] = SUM of SINUSOIDS ± Then, OUTPUT y[n] = SUM of SINUSOIDS 2/19/2009 ECE-2025 Spring-04 jMc 6 ILTERING EXAMPLE FILTERING EXAMPLE ± 7-point AVERAGER () = 6 7 1 7 ] [ ] [ k n x n y ± Removes cosine ± By making its amplitude (A) smaller = 0 k ± 3-point AVERAGER 2 p ± Changes A slightly ( ) = = 0 3 1 3 ] [ ] [ k k n x n y 2/19/2009 ECE-2025 Spring-04 jMc 7
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2025-L12 - DCONVDEMO ECE-2025 Spring-2009 Lecture 12...

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