Page 320 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 320
CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 307
5. Time Reversal:
6. Duality:
7. Circular Convolution:
where
The convolution sum in Eq. (6.108) is known as the circular conuolution of x,[n] and
4nI.
8. Multiplication:
where
9. Additional Properties:
When x[n] is real, let
where x,[n] and xo[n] are the even and odd components of x[n], respectively. Let
x[n] - X[k] =A[k] + jB[k] = IX[k]leie[kl
Then x[ -kIm~d~ =X*[kl (6.1 10)
xe[n] w R~{X [k]) = A[k] (6.111a)
xo[n] -j Im{X[k]) = jB[k] (6.111b)
From Eq. (6.110) we have
10. Parseval's Relation:
Equation (6.113) is known as Parseual's identity (or Parseual's theorem) for the DFT.
