SPFirst-L12

SPFirst-L12 - 2/25/2005 2003, JH McClellan & RW...

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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 ) ( ) ( ) ( 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 ] 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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SPFirst-L12 - 2/25/2005 2003, JH McClellan & RW...

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