SPFirst-L21

# SPFirst-L21 - Signal Processing First READING ASSIGNMENTS...

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Signal Processing First Lecture 21 Frequency Response of Continuous-Time Systems 4/3/2006 © 2003-2006, JH McClellan & RW Schafer 3 READING ASSIGNMENTS ± This Lecture: ± Chapter 10, all ± Other Reading: ± Recitation: Ch. 10 all, start Ch 11 ± Next Lecture: Chapter 11 4/3/2006 © 2003-2006, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES ± Review of convolution ± THE THE operation for LTI LTI Systems ± Complex exponential input signals ± Frequency Response ± Cosine signals ± Real part of complex exponential ± Fourier Series thru H(j ω ) ± These are Analog Filters 4/3/2006 © 2003-2006, JH McClellan & RW Schafer 5 LTI Systems ± Convolution defines an LTI system ± Response to a complex exponential gives frequency response H(j ) y ( t ) = h ( t ) x ( t ) = h ( τ ) −∞ x ( t ) d

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4/3/2006 © 2003-2006, JH McClellan & RW Schafer 6 Thought Process #1 ± SUPERPOSITION (Linearity) ± Make x(t) a weighted sum of signals ± Then y(t) is also a sum—same weights But DIFFERENT OUTPUT SIGNALS usually ± Use SINUSOIDS “SINUSOID IN GIVES SINUSOID OUT” ± Make x(t) a weighted sum of sinusoids ± Then y(t) is also a sum of sinusoids ± Different Magnitudes and Phase ± LTI SYSTEMS : Sinusoidal Response 4/3/2006 © 2003-2006, JH McClellan & RW Schafer 7 Thought Process #2 ± SUPERPOSITION (Linearity) ± Make x(t) a weighted sum of signals ± Use SINUSOIDS ± Any x(t) = weighted sum of sinusoids ± HOW? HOW? Use FOURIER ANALYSIS INTEGRAL Use FOURIER ANALYSIS INTEGRAL ± To find the weights from x(t) To find the weights from x(t) ± LTI SYSTEMS : ±
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SPFirst-L21 - Signal Processing First READING ASSIGNMENTS...

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