Determine the Nyquist rate for signal x(t)defined as
follows:
x(t)= 20,000sinc(20,000*pi*t)
Plot the spectrum of the sampled signal and check whether
aliasing error exists for the following values of the sampling rate
(ws): 40,000*pi, 20,000*pi,10,000*pi
energy and
power of signals.
(a) Plot
the signal x(t)
=
e−tu(t)
and determine its energy. What is the power of x(t)?
(b) How
does the energy of z(t)
=
e−∣t∣,
−∞
<
t
<
∞, compare to the energy
of z1(t)
=
e−tu(t)?
Carefully plot the two signals.
(c) Consider the
signaly(t)
=
sign[xi(t)]
=
1
xi(t)
≥
0
−1
xi(t)
< 0
for
−∞
<
t
<
∞,i
=
1,2. Find the
energy and the power of...
Given a sinusoidal signal:
x(t) = Asin(2πft)
Find Fourier Transform (FT) of the sinusoidal x(t) given above
and plot the spectrum with:
a. A = 2, f = 1000Hz
b. A = 2, f = 9000Hz
c. A = 5, f = 1000Hz
d. A = 10, f = 10000Hz
What's the Fourier transform of the following equations:
1) f(t)=1/(t^2+a^2) a is a constant
2) e^[-absolute value(t)/a]*cos(b*t) a and b are constants
Both the Fourier Series and the Discrete Fourier Transform are
calculated using summation. Explain the key differences in what the
inputs each of the Fourier Series and the DFT are AND the
requirements the inputs.
Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞<t<∞. 2
(a) Find all t that give x intercepts and y-intercepts, and plot
them.
(b) Find all t which give horizontal or vertical tangents, and
plot the corresponding points, with a short horizontal or vertical
segment to indicate the tangent line.
(c) Find the values of t for which x(t) is increasing and those
for which it is decreasing. Do the same for y.
(d) Determine what happens to x(t) and y(t) as t → ∞.
(e) Make...