Fundamentals of Signals and Systems
By Benoit Boulet

Appendix D: Tables of Transforms

Table D.1: Fourier Transform Pairs

Time domain x( t)

Frequency domain X( j ?)


1

















1

















Table D.2: Properties of the Fourier Transform

Time domain

Frequency domain






























Table D.3: Properties of the Fourier Series

Time domain

x(t), y(t) periodic of fundamental period T

Frequency domain








































Table D.4: Laplace Transform Pairs

Time domain x(t)

Laplace domain X( s)

ROC






1








































Table D.5: Properties of the Laplace Transform

Time domain

Laplace domain

ROC











































Table D.6: Proberties of the Unilateral Laplace Transform

Time domain x(t)

Laplace domain X(s)

ROC










































Table D.7: Discrete-Time Fourier Transform Pairs

Time domain x[ n]

Frequency domain

X( e j?) always periodic of period 2 ?




1





1



































Table D.8: Properties of the Discrete-Time Fourier Transform

Time domain

Frequency domain




































Table D.9: Properties of the Dicrete-Time Fourier Series

Time domain

x[n], y[n] periodic, fun period N, fund. freq.

Frequency domain







































Table D.10: z-Transform Pairs

Time domain x[ n]

z domain X( z)

ROC






1

































Table D.11: Properties of the z-Transform Pairs

Time domain

z domain

Copyright Career & Professional Group, a division of Thomson Learning, Inc. 2006 under license agreement with Books24x7
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