PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Time Domain Representation of Continuous and Discrete Signals 25

ANALYTICAL Solution

The functions for f(2t) and f(t/2) are shown in Figure 1.24.

Note that the concepts and defi nitions presented for the case of continuous time

functions such as compression, expansion, time reversal, inversion, and time and

amplitude shifting are equally applicable for the case of discrete sequences by changing

the independent variable t to n.

R.1.78 Time signals (or sequences) encountered in real-world problems are in general real

functions of t (or n). But sometimes it is useful to work with complex signals or

sequences when performing systems analysis. Complex sequences can easily be

expressed in terms of their real and imaginary parts of f(t) or f(n) as illustrated in

the following expressions:

f n()
real f n[()] j imag f n^ [()]
a n() jb n(), for the discrete ccase

f(−t)

1

1

3

− 1

− 2

.5

0

t

FIGURE 1.23

Plot of f(−t) of the function defi ned in R.1.75.

FIGURE 1.24

Plots of f(2t) and f(t/2) of R.1.73.

1

−1.5

−. (^50) .5 1 t
.5
f(2t)
f(t/2)
− 2
1
.5
0 1 2
t
− 2
− 2
− 6