ece642-1-3

ece642-1-3 - ECE 642 - COMMUNICATION SYSTEMS I Lecture 1,...

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1 I. Review of Time-Frequency Relations © 2002 by Jacob Klapper ECE 642 - COMMUNICATION SYSTEMS I Lecture 1, Part 3 Review of Time-Frequency Relations Professor Jacob Klapper Department of Electrical and Computer Engineering New Jersey Institute of Technology I. Review of Time-Frequency Relations © 2002 by Jacob Klapper Fourier Series A periodic x(t) can be written as a possibly infinite sum of harmonic phasors. (1-1) where C n = complex constant depending on n 0 jn ω t x(t)= C e n n=- I. Review of Time-Frequency Relations © 2002 by Jacob Klapper Fourier Series (cont’d) Equivalently, 00 n1 0 x(t)=A A cosn t n Bs i n n t n = = (1-2) where A 0 , A n , B n = real constants
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2 I. Review of Time-Frequency Relations © 2002 by Jacob Klapper Exercise Can you sketch the frequency domain from (1-1) or (1-2) ? What provides the amplitude and phase ? One –sided or two-sided spectra ? Note: Frequency domain is discrete in f I. Review of Time-Frequency Relations © 2002 by Jacob Klapper Example 63 66 33 1.5 1.5 25 0 21 0 0 0 0 2 100 23 tt x(t) cos( ) ) j( ) ) ee j () j ππ π⋅ =+ + + +− + + +⋅ I.
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This note was uploaded on 09/14/2011 for the course ECE 642 taught by Professor Jacob during the Spring '11 term at NJIT.

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ece642-1-3 - ECE 642 - COMMUNICATION SYSTEMS I Lecture 1,...

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