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Unformatted text preview: 8/22/2003 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 26 Review: Digital Filtering of Analog Signals 8/22/2003 2003, JH McClellan & RW Schafer 3 LECTURE OBJECTIVES Sampling Theorem Revisited GENERAL: in the FREQUENCY DOMAIN Fourier transform of sampled signal Reconstruction from samples Effective Frequency Response Important FT properties Convolution multiplication Frequency shifting 8/22/2003 2003, JH McClellan & RW Schafer 4 Sampling: Freq. Domain EXPECT FREQUENCY SHIFTING !!! = = = = k t jk k n s s e a nT t t p ) ( ) ( = = k t jk k s e a t p ) ( 8/22/2003 2003, JH McClellan & RW Schafer 5 FrequencyDomain Representation of Sampling X s ( j ) = 1 T s X ( j ( k = k s )) Typical bandlimited signal 8/22/2003 2003, JH McClellan & RW Schafer 6 Aliasing Distortion If s < 2 b , the copies of X ( j ) overlap, and we have aliasing distortion . Typical bandlimited signal 8/22/2003 2003, JH McClellan & RW Schafer 7 Reconstruction of x ( t ) x s ( t ) = x ( nT s ) ( t nT s ) n = X s ( j ) = 1 T s X ( j ( k = k s )) X r ( j ) = H r ( j ) X s ( j ) 8/22/2003 2003, JH McClellan & RW Schafer 8 Reconstruction: FrequencyDomain ) ( ) ( ) ( so overlap, not do ) ( of copies the , 2 If j X j H j X j X s r r b s = > H ( j ) 8/22/2003 2003, JH McClellan & RW Schafer 9 Ideal Reconstruction Filter h r...
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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.
 Spring '10
 Nayak

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