Final_Tables

Final_Tables - Table of Fourier Transform Pairs Signal Name...

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Unformatted text preview: Table of Fourier Transform Pairs Signal Name Right-sided exponential Left-sided exponential Square pulse “sinc” function Impulse Shifted impulse Complex exponential General cosine Cosine Sine General periodic signal Impulse Train Time-Domain: x.t / e a t u.t / Frequency-Domain: X.j!/ 1 a C j! 1 b j! sin.!T =2/ !=2 Œu.! C !0 / 1 e j !t0 .a > 0/ .b > 0/ u.t T =2/ e bt u. t / Œu.t C T =2/ sin.!0 t / t ı.t / ı.t t0 / u.! !0 / e j!0 t A cos.!0 t C / cos.!0 t / sin.!0 t / 1 X kD 1 1 X nD 1 2 ı.! Ae j ı.! ı.! j ı.! 1 X !0 / j !0 / C Ae ı.! C !0 / !0 / C ı.! C !0 / !0 / C j ı.! C !0 / 2 ak ı.! ı.! k !0 / ak e ı.t j k!0 t nT / 2 T kD 1 1 X kD 1 2 k=T / Table of Fourier Transform Properties Property Name Linearity Conjugation Time-Reversal Scaling Delay Modulation Modulation Differentiation Convolution Multiplication Time-Domain x.t / ax1 .t / C bx2 .t / x .t / x. t / x.at / x.t td / Frequency-Domain X.j!/ aX1 .j!/ C bX2 .j!/ X . j !/ X. j !/ 1 X.j.!=a// jaj e j !td X.j!/ !0 // x.t /e j!0 t x.t / cos.!0 t / d k x.t / dt k x.t / h.t / x.t /p.t / 1 2 1 2 X.j.! X.j.! 1 !0 // C 2 X.j.! C !0 // .j!/k X.j!/ X.j!/H.j!/ X.j!/ P .j!/ Date: 1-May-2008 Table of z -Transform Pairs Signal Name Time-Domain: xŒn ıŒn ıŒn n0  z z -Domain: X.z/ 1 n0 Impulse Shifted impulse Right-sided exponential General cosine an uŒn r n cos.!0 n/uŒn O 1 1 1 az 1 1 r cos.!0 /z 1 O 2r cos.!0 /z 1 C r 2 z O 2 Table of z -Transform Properties Property Name Linearity Delay Convolution Time-Domain xŒn ax1 Œn C bx2 Œn xŒn nd  z -Domain X.z/ aX1 .z/ C bX2 .z/ z nd X.z/ xŒn hŒn X.z/H.z/ Date: 1-May-2008 ...
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This note was uploaded on 01/27/2011 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Tech.

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Final_Tables - Table of Fourier Transform Pairs Signal Name...

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