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Discrete-time Signals 35
Rectangular Pulse
Even Part
x(n)
1
0.8
0.6
0.4
0.2
0
−10 −5 0 5 10
n
xe(n)
1
0.8
0.6
0.4
0.2
0
−10 −5 0 5 10
n
0.6
Odd Part
xe(n)
0.4
0.2
0
−0.2
−0.4
FIGURE 2.4 Even-odd decomposition in Example 2.4
−10 −5 0 5 10
n
The sequence and its support are supplied in x and n arrays, respectively.
It first checks if the given sequence is real and determines the support
of the even and odd components in m array. It then implements (2.5)
with special attention to the MATLAB indexing operation. The resulting
components are stored in xe and xo arrays.
□ EXAMPLE 2.4 Let x(n) =u(n) − u(n − 10). Decompose x(n) into even and odd components.
Solution
The sequence x(n), which is nonzero over 0 ≤ n ≤ 9, is called a rectangular
pulse. Wewill use MATLAB to determine and plot its even and odd parts.
>> n = [0:10]; x = stepseq(0,0,10)-stepseq(10,0,10);
>> [xe,xo,m] = evenodd(x,n);
>> subplot(2,2,1); stem(n,x); title(’Rectangular pulse’)
>> xlabel(’n’); ylabel(’x(n)’); axis([-10,10,0,1.2])
>> subplot(2,2,2); stem(m,xe); title(’Even Part’)
>> xlabel(’n’); ylabel(’xe(n)’); axis([-10,10,0,1.2])
>> subplot(2,2,4); stem(m,xo); title(’Odd Part’)
>> xlabel(’n’); ylabel(’xe(n)’); axis([-10,10,-0.6,0.6])
The plots shown in Figure 2.4 clearly demonstrate the decomposition.
□
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