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Signals Systems - Reference Tables 1 Table of Fourier Transform Pairs Function, f(t) Fourier Transform, F(w) Definition of Inverse Fourier Transform Р ¥ ¥-

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Table of Fourier Transform Pairs of Energy Signals Function name Time Domain x(t) Frequency Domain X(ω) FT ( ) x t ( ) ( ) ( ) { } e j t X x t dt x t ω ω ∞ −

[PDF] Fourier Transform Table

Fourier Transform Table ( ) x t ( ) X f ( ) X ω ( )t δ 1 1 1 ( )f δ 2 ( ) πδ ω 0 ( ) t t δ − 0 2j ft e π − 0 j t e ω − 0 2j f t e π 0 ( ) f f δ − 0 2 ( ) πδ ω ω − 0

Fourier Transform Tables

Table A 4 collects several discrete time infinite duration transforms Remember that for these results a difference or sum in the frequency domain is interpreted 

A Tables of Fourier Series and Transform Properties

Soliman, S S and Srinath, M D Continuous and Discrete Signals and Systems, New York, Prentice-Hall, 1990 22 Tetley, L

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Table of Discrete-Time Fourier Transform Pairs: Discrete-Time Fourier Transform : X(Ω) = ∞ ∑ n=−∞ x[n]e −jΩn Inverse Discrete-Time Fourier Transform 

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DTFT Table Time Signal DTFT ∞

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7 mar 2015 · IV-AProperties of the discrete-time Fourier transform 9 IV- BDiscrete-time Fourier transform table 10

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DTFT Table

Time Signal DTFT

n,1 k k)2(2 ,2,1,0,11,2,3...,,1 ]sgn[n j e12 ][nu kj ke)2(11 ][n ,1 ,3,2,1],[qqn ,3,2,1, qe jq

1||],[anua

n 1||, 11 aae j , re o jn o e al real ,)2(2 o ko k otherwiseqqqn npq ,0,1,0,1,,1,,1

2/sinsin

21
q n BB sinc kB kp)2( 2 cos( ) o n koo kk)2()2( cos( ) o n koj oj keke)2()2( sin( ) o n koo kkj)2()2( sin( ) o n koj oj kekej)2()2(

DTFT Properties

Property Name Property

Linearity ][][nbvnax )()(bVaX

Time Shift

integerany ],[ qqnx integerany ),(qXe jq

Time Scaling 0),(aatx 0),/(

1 aaX a

Time Reversal ][nx

real is ][ if )()( nxXX

Multiply by n ][nnx

)(Xddj

Multiply by Complex Exponential

real ],[ onj nxe o real ),( oo X

Multiply by Sine ][)sin(nxn

o )()(2 oo XXj

Multiply by Cosine ][)cos(nxn

o )()(21 oo XX

Summation

n i ix][ kj kXXe)2()0()(11

Convolution in Time ][*][nhnx )()(HX

Multiplication in Time ][][nwnx

dWX)()(21 (conv.)

Parseval's Theorem (General)

dVXnvnx n )()(21][][

Parseval's Theorem (Energy)

dXnxtxdXnx nn 2 22
2 )(21|][|real is )( if)( 21][

Using CTFT Table to find Inverse

of a DTFT X(): x[n] = ??

Form and look up )()()(

2 pX)()(t

Then get

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