PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

24 Practical MATLAB® Applications for Engineers

ANALYTICAL Solution

The functions f(t − 1), f(t − 2), f(t + 1), and f(t + 2) are shown in Figure 1.22.

R.1.74 Given the continuous time signal f(t), then by multiplying the independent variable
t by − 1 , a reverse time function f(−t) is created. The same can be said about the
sequence f(n) and its discrete reverse time sequence f(–n).

R.1.75 For example, using the function defi ned in R.1.72, the reverse function f(−t) is
shown in Figure 1.23.

R.1.76 Given the function f(t), then by multiplying the independent variable t by a real
constant a, the function experiences the following changes:
a. If a > 1 , then f(t) is compressed in time by a factor of 1/a.
b. If a < 1 , then f(t) is expanded in time by a factor of a.

R.1.77 For example, using the function defi ned in R.1.72, sketch the plots for f(2t) and f(t/2).

− 2 − 1 0 1 2 3 4

− 2

− 1

0

1

f(t

−1)

t

− 2 − 1 0 1 2 3 4

− 2

− 1

0

1

f(t

−2)

t

− 4 − 3 − 2 − 1 0 1 2

− 2

− 1

0

1

f(t

+1)

t

− 6 − 5 − 4 − 3 − 2 − 1 0

− 2

− 1

0

1

f(t

+2)

t

FIGURE 1.22
Plots of f(t − 1), f(t − 2), f(t + 1), and f(t + 2) of R.1.73.

f(t)

1

− 1 1

− 2

− 3

t

FIGURE 1.21
Plot of f(t) of R.1.73.