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ece431FTtable

# ece431FTtable - Fourier Transform X f = Inversion Formula...

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FourierTransform X ( f ) = integraldisplay - x ( t ) e - j 2 π ft dt InversionFormula x ( t ) = integraldisplay - X ( f ) e j 2 π ft df x ( t ) X ( f ) I [ - T , T ] ( t ) 2 T sinc ( 2 Tf ) 2 f c sinc ( 2 f c t ) I [ - f c , f c ] ( f ) ( 1 -| t | / T ) I [ - T , T ] ( t ) T sinc 2 ( Tf ) f c sinc 2 ( f c t ) ( 1 -| f | / f c ) I [ - f c , f c ] ( f ) e - λ t u ( t ) 1 λ + j 2 π f e - λ | t | 2 λ λ 2 +( 2 π f ) 2 λ λ 2 + t 2 π e - 2 πλ | f | e - ( t / σ ) 2 / 2 2 π σ e - σ 2 ( 2 π f ) 2 / 2 Note . Theindicatorfunction I [ a , b ] ( t ) : = 1for a t b and I [ a , b ] ( t ) : = 0otherwise. In particular, u ( t ) : = I [ 0 , ) ( t ) istheunitstepfunction.Also,sinc ( t ) : = [ sin ( π t )] / ( π t ) for t negationslash = 0 andsinc ( 0 ) : = 1. Series Formulas N - 1 k
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