EE1003_SupplementaryNote1

# EE1003_SupplementaryNote1 - Supplementary Note#1 Let us rst...

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Supplementary Note #1 Let us frst recall the mathematical expression For the PAM signal’s spectrum From page 3 oF Chap. 2: V s ( f )= 1 2 V ( f ) z }| { 1 4 δ ( f - f m )+ 1 4 δ ( f + f m ) + X k =0 1 j (2 k +1) π V ( f (2 k +1) f 0 ) z }| { 1 2 δ ( f - (2 k f 0 - f m 1 2 δ ( f - (2 k f 0 + f m ) - 1 2 δ ( f +(2 k f 0 - f m ) - 1 2 δ ( f k f 0 + f m ) | {z } V ( f +(2 k +1) f 0 ) . To explain why the copies oF V ( f ) in the PAM signal’s spectrum V s ( f ) will be non- overlapping iF f 0 > 2 f m , let us Focus on the spectral components corresponding to the distorted copy oF V ( f ) centered at 0 Hz, i.e., 1 2 V ( f 1 4 δ ( f - f m 1 4 δ ( f + f m )( 1 ) and the distorted copy oF V ( f ) centered at f 0 , i.e., 1 V ( f - f 0 1 [ δ ( f - f 0 - f m δ ( f - f 0 + f m )] . (2) ±rom equation (1), the frst distorted copy oF V ( f ) consists oF 2 spectral lines, one centered at f m , the other, at - f m . Similarly, From equation (2), the second distorted copy oF

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## This note was uploaded on 11/30/2011 for the course EEE 1001 taught by Professor Phoon during the Spring '11 term at National University of Singapore.

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EE1003_SupplementaryNote1 - Supplementary Note#1 Let us rst...

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