PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Time Domain Representation of Continuous and Discrete Signals 93

1.5 Application Problems

P.1.1 Sketch by hand, over the range − 3 ≤ t ≤ 6 , the following analog functions:

a. ƒ 1 (t) = 5u(t − 2)

b. ƒ 2 (t) = 3u(t − 1) − 3u(t − 3)

c. ƒ 3 (t) = t[u(t − 1) − u(t − 2)]

d. ƒ 4 (t) = δ(t + 1) + 2 δ(t − 1) + u(t − 2)

e. ƒ 5 (t) = t[u(−t) * u(t + 3)]

f. ƒ 6 (t) = u(t + 1) − u(t) + 3 δ(t − 3)

P.1.2 Sketch by hand, over the range − 3 ≤ n ≤ 6 , the following discrete sequences:

a. ƒ 1 (n) = 3(n − 2)u(n)

b. ƒ 2 (n) = n u(n)

c. ƒ 3 (n) = (−n)2 u(n)

d. ƒ 4 (n) = − 3 δ(n + 2) + 2 δ(n) + u(n) + u(n − 1) + 2u(n − 1)

e. ƒ 5 (n) = 2 η[u(n) − u(n − 2)]

f. ƒ 6 (n) = n[u(n + 2). u(−n)]

1

0.5

−0.5

− 1

− 10 − 5

0

0510

1

0.5

−0.5

− 1

− 10 − 5

0

1

0.5

−0.5

− 1

0

0510 −^10 −^50510

1

0.5

−0.5

− 1

− 10 − 5

0

0510

[f(t)*Kaiser window] versus t

[f(t)*Boxcar window] versus t

[f(t)*Triang. window] versus t

[f(t)*Barlett. window] versus t

t t

t t

Amplitude

Amplitude Amplitude

Amplitude

FIGURE 1.78

Plots of the windowed function f(t) using the Kaiser, Tr i a ng u l a r, Boxcar, and Bartlett windows of Example 1.20.