Page 310 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 310
CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 297
Since X(t) is periodic with period To = 27r and the fundamental frequency oo = 27r/T0 = 1,
will
Eq. (6.53) indicates that the Fourier series coefficients of ~(t) be x[-k]. This duality
relationship is denoted by
~(t) Bc, =x[-k] (6.54)
where FS denotes the Fourier series and c, are its Fourier coefficients.
I. Differentiation in Frequency:
J. Differencing:
The sequence x[n] -x[n - 11 is called the firsf difference sequence. Equation (6.56) is
easily obtained from the linearity property (6.42) and the time-shifting property (6.43).
K. Accumulation:
Note that accumulation is the discrete-time counterpart of integration. The impulse term
on the right-hand side of Eq. (6.57) reflects the dc or average value that can result from
the accumulation.
L. Convolution:
As in the case of the z-transform, this convolution property plays an important role in the
study of discrete-time LTI systems.
M. Multiplication:
