Digital Signal Processing Reference
In-Depth Information
(b)
Find and compare the frequency spectra of the trapezoidal waveforms shown in
Figure P5.9.
f
(
t
)
2
1
0
1
2
3
4
5
t
(a)
g
(
t
)
2
1
0
0.5
1.0
1.5
2.0
2.5
t
(b)
Figure P5.9
5.10.
(a)
Use the time-derivative property to find the Fourier transform of the triangular
wave-form shown in Figure P5.10.
(b)
Use the time-derivative property to find the Fourier transform of the trapezoidal
signal shown in Figure P5.9(a)
f
(
t
)
A
a
a
t
(s)
Figure P5.10
5.11.
(a)
Consider a linear, time-invariant system with impulse response
0.5
sin(2t)
t
h(t) =
.
Find the system output if the input is
(b)
Find the system output if the input is changed to
y(t)
x(t) = cos(t) + sin(3t).
sinc(2pt)
5.12.
(a)
For the electrical network shown in Figure P5.12, complete the following:
(i)
Determine the frequency response function.
(ii)
Sketch the magnitude and phase frequency response.
(iii)
Find the impulse response function for this network.
(b)
Repeat Part (a) for the circuit of P5.12(b).
5.13.
Show that the time-scaling property of the Fourier transform, with
a
constant, is valid.
That is, show that
F(v/a)
ƒ a ƒ
f(at)
Î
f
"
.
