If u(t) = < sin(5t),
cos(5t), t > and
v(t) = < t, cos(5t),
sin(5t) >, use the formula below to find the given
derivative.
d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t)
d/dt [ u(t) x v(t)] = ?
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
Based on fourier series
Q1: how to determine if a signal function x(t) is
periodic and ac. And what happens if there is x(t) = sint + cost +
sint? How would we know if ac/periodic?
Q2: What is fourier series and fourier
coefficients?
Q3: What is Fourier Trigonometric Series?
Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1.
Determine and plot the spectrum Fourier Transform of signal x(t) (
For plot : Use only interval n=-2 to n=2). 2. Based on the result
obtained in part one. Determine Complex Exponential Fourier Series,
and trigonometric Fourier Series. 3. Evaluate the energy spectral
density of the periodic signal x(t) in rang (n=-2 to n=2)
Starting with the Fourier transform pair
x ( t ) = u ( t + 1 ) - u ( t
- 1 ) ⇔ X ( Ω ) = 2
sin ( Ω ) / Ω
and using no integration indicate the properties of the Fourier
transform that will allow you to compute the Fourier transform of
the following signals
x 1 ( t ) = - u ( t + 2 ) + 2
u ( t ) - u ( t - 2...
A continuous signal contains the following two components:
x1(t) = 3 cos 20πt
x2(t) = 3 cos 50πt
(a) Find the minimum required sampling rate to avoid
aliasing.
(b) Draw the discrete time signals obtained after sampling, when
sampled with Fs = 100 Hz. Explain the disadvantage(s), if any, of
sampling beyond the Nyquist rate.
(c) Assume the sampling rate is Fs= 40 Hz, which components are
exposed to aliasing effects? Support your answer by showing
“Nyquist intervals” and the...
Consider the vector function given below.
r(t) =
2t, 3 cos(t), 3 sin(t)
(a) Find the unit tangent and unit normal vectors T(t) and
N(t).
T(t) =
N(t) =
(b) Use this formula to find the curvature.
κ(t) =