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SPFirst-L11 - Signal Processing First READING ASSIGNMENTS...

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8/22/2003 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 11 Linearity & Time-Invariance Convolution 8/22/2003 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS This Lecture: Chapter 5, Sections 5-5 and 5-6 Section 5-4 will be covered, but not “in depth” Other Reading: Recitation: Ch. 5, Sects 5-6, 5-7 & 5-8 CONVOLUTION Next Lecture: start Chapter 6 8/22/2003 © 2003, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES BLOCK DIAGRAM REPRESENTATION Components for Hardware Connect Simple Filters Together to Build More Complicated Systems LTI SYSTEMS GENERAL PROPERTIES of FILTERS L INEARITY T IME- I NVARIANCE ==> CONVOLUTION 8/22/2003 © 2003, JH McClellan & RW Schafer 5 IMPULSE RESPONSE, FIR case: same as CONVOLUTION GENERAL: GENERAL CLASS of SYSTEMS LINEAR and TIME-INVARIANT ALL LTI systems have h [ n ] & use convolution OVERVIEW ] [ ] [ ] [ n x n h n y = ] [ n h } { k b
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8/22/2003 © 2003, JH McClellan & RW Schafer 6 CONCENTRATE on the FILTER (DSP) DISCRETE-TIME SIGNALS FUNCTIONS of n , the “time index” INPUT x [ n ] OUTPUT y [ n ] DIGITAL FILTERING FILTER D-to-A A-to-D x(t) y(t) y[n] x[n] 8/22/2003 © 2003, JH McClellan & RW Schafer 7 BUILDING BLOCKS BUILD UP COMPLICATED FILTERS FROM SIMPLE MODULES Ex: FILTER MODULE MIGHT BE 3-pt FIR FILTER y[n] x[n] FILTER FILTER + + INPUT OUTPUT 8/22/2003 © 2003, JH McClellan & RW Schafer 8 GENERAL FIR FILTER FILTER COEFFICIENTS {b k } DEFINE THE FILTER
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