Page 465 - Schaum's Outline of Theory and Problems of Signals and Systems
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45 2 PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS TRANSFORMS [APP. B
Some Common Fourier Transform Pairs:
sin Wn 0 i IRIS w
(0<Wcn-1-X(fl)= W<ln,5T
n-n
B.7 DISCRETE FOURIER TRANSFORM
Definition:
x[n] =O outside the range 0 I I - 1
n
N
x[n] ~[k]
Properties of the DFT:
Linearity: a,x,[n] + a2x2[n] -a, X,[k] + a, X,[k]
Time shifting: x[n - no],, - w,knux[k]
Frequency shifting: ~;~"ux[n] - X[k - k,],,
