Time Domain Representation of Continuous and Discrete Signals
95
P.1.13 Plot the functions indicated as follows over the range −3 ≤ t ≤ 3:
f 1 (t) = t
3
f 2 (t) = 3 + t
3
f 3 (t) = 2t
3
+ t
5
+ 3
f 4 (t) = tan(2t)
f 5 (t) = sin(2t)
and verify that all the preceding functions present odd symmetry, that is, f(t) = −f(t).
P.1.14 Plot the functions indicated as follows for the range −3 ≤ t ≤ 3:
f 1 (t) = t
2
f 2 (t) = 3 + t
2
f 3 (t) = 2t
4
+ t
6
+ 3
f 4 (t) = cos(2t)
f 5 (t) = |t|
and verify that all the preceding functions present even symmetry, that is, f(t) = f(−t).
P.1.15 Write a MATLAB function fi le that analyzes a given arbitrary function f(t) over the
range −3 ≤ t ≤ 3, and returns a message indicating if f(t) presents even or odd symmetry. Repeat the preceding problem over any given range.
P.1.16 Given the functions shown in Figure 1.79, sketch by hand for each function its even
and odd parts.
f 1 (t )
f 4 (t )
f 2 (t)
f 3 (t )
f 5 (t )
f 7 (t )
f 6 (t )
t
t
t
t
−1
0
−1
+1
−1
1
2
2
0
0
2
−2
2
t
t
t
1
3
3
2
1
0
−1 0
3
−1
0
3
1
1
2
1
2
FIGURE 1.79
Plots of P.1.16.
CRC_47760_CH001.indd 95
CRC_47760_CH001.indd 95
7/25/2008 4:16:30 PM
7/25/2008 4:16:30 PM