Page 466 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 466
APP. B] PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS TRANSFORMS 453
Conjugation: x*[n] H X*[- k Imod ,
Time reversal: x[ - n],,, , X[ - k I,,, ,
w
Duality: X[n] - Nx[-k],,,
Circular convolution: x,[n] @x2[n] -X,[k]X,[k]
1
Multiplication: x,[n]x2[n] o -X,[k] @ X2[k]
N
Real sequence: x[n] = xe[n] + xo[n] - X[k] = A[k] + jB[k]
x[-klmo,, =X*[kl
Even component: xe[n] t, Re(X[k 1) = A[k ]
Odd component: xo[n] - Im{ X[k]) = jB[k ]
j
Parseval S Relation:
Note
B.8 FOURIER SERIES
Complex hkponential Fourier Series:
Trigonometric Fourier Series:
a0 m
~(t) - + x (ak cos kwOt + bk sin k~,t)
=
k=l
2
x(t) sin kw,tdt
Harmonic Form Fourier Series:
