Page 308 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 308
CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 295
z-transform of u[n] does not include the unit circle. Note that the unit step sequence u[n] is not
absolutely summable. The Fourier transform of u[n] is given by (Prob. 6.28)
6.4 PROPERTIES OF THE FOURIER TRANSFORM
Basic properties of the Fourier transform are presented in the following. There are
many similarities to and several differences from the continuous-time case. Many of these
properties are also similar to those of the z-transform when the ROC of X( z) includes the
unit circle.
A. Periodicity:
As a consequence of Eq. (6.41), in the discrete-time case we have to consider values of R
(radians) only over the range 0 I R < 27r or -7r I R < 7r, while in the continuous-time
case we have to consider values of o (radians/second) over the entire range - m < o < m.
B. Linearity:
C. Time Shifting:
D. Frequency Shifting:
x*[n] -X*(-R)
where * denotes the complex conjugate.
F. Time Reversal:
