SPFirst-L12

SPFirst-L12 - © 2003 JH McClellan& RW Schafer 1 Signal...

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Unformatted text preview: 2/25/2005 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 12 Frequency Response of FIR Filters 2/25/2005 © 2003, JH McClellan & RW Schafer 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 2/25/2005 © 2003, JH McClellan & RW Schafer 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 2/25/2005 © 2003, JH McClellan & RW Schafer 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 2/25/2005 © 2003, JH McClellan & RW Schafer 8 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 2/25/2005 © 2003, JH McClellan & RW Schafer 9 FILTERING EXAMPLE ¡ 7-point AVERAGER ¡ Removes cosine ¡ By making its amplitude (A) smaller ¡ 3-point AVERAGER ¡ Changes A slightly ( ) ∑ = − = 6 7 1 7 ] [ ] [ k k n x n y ( ) ∑ = − = 2 3 1 3 ] [ ] [ k k n x n y 2/25/2005 © 2003, JH McClellan & RW Schafer 10 3-pt AVG EXAMPLE USE PAST VALUES 40 for ) 4 / 8 / 2 cos( ) 02...
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This note was uploaded on 03/03/2010 for the course EE 48976 taught by Professor Nayak during the Spring '10 term at USC.

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SPFirst-L12 - © 2003 JH McClellan& RW Schafer 1 Signal...

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