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32 Chapter 2 DISCRETE-TIME SIGNALS AND SYSTEMS
2
Real Part
1
Imaginary Part
1
0
0
−1
−2
−1
−3
−10 −5 0 5 10
n
3
Magnitude Part
−2
−10 −5 0 5 10
n
200
Phase Part
2
100
0
1
−100
0
−10 −5 0 5 10
n
−200
−10 −5 0 5 10
n
FIGURE 2.3 Complex-valued sequence plots in Example 2.3
Solution
MATLAB script:
>> n = [-10:1:10]; alpha = -0.1+0.3j;
>> x = exp(alpha*n);
>> subplot(2,2,1); stem(n,real(x));title(’real part’);xlabel(’n’)
>> subplot(2,2,2); stem(n,imag(x));title(’imaginary part’);xlabel(’n’)
>> subplot(2,2,3); stem(n,abs(x));title(’magnitude part’);xlabel(’n’)
>> subplot(2,2,4); stem(n,(180/pi)*angle(x));title(’phase part’);xlabel(’n’)
The plot of the sequence is shown in Figure 2.3.
□
2.1.3 DISCRETE-TIME SINUSOIDS
In the last section we introduced the discrete-time sinusoidal sequence
x(n) =A cos(ω 0 n + θ 0 ), for all n as one of the basic signals. This signal
is very important in signal theory as a basis for Fourier transform and
in system theory as a basis for steady-state analysis. It can be conveniently
related to the continuous-time sinusoid x a (t) =A cos(Ω 0 t + θ 0 )
using an operation called sampling (Chapter 3), in which continuous-time
sinusoidal values at equally spaced points t = nT s are assigned to x(n).
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