A continuous signal contains the following two components: x1(t) = 3 cos 20πt x2(t) = 3...

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 aliased frequencies.

Expert Solution

We found sampling frequency of given signals.

If we use Fs = 100Hz, there is no disadvantage. It's always better to use more than twice of signal frequency to avoid aliasing.

We discussed if sampling frequency is less , then there is aliasing.

Fs= 40 Hz will only affect X2 signal as sampling frequency is less.

We discussed in the form of Nyquist intervals as there will be overlapping in X2 signal if we use Fs = 40 Hz coz it's taking more time to pass. As it's taking more time to pass, incoming signal will collide with current signal

Manojponduru answered 11 months ago

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that...

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that T is invertible. b)Find T inverse.

To better understand the polarization consider two components of the electric field: Ex(t) = 3 Cos...

To better understand the polarization consider two components of the electric field: Ex(t) = 3 Cos (w t) and Ey(t) = 4 Cos (w t-phi). Then determine the functional form of Ey(Ex) (that is find Ey as a function of Ex at any time t) for the following phase angles  = 0, 45, 90, -90, 180 degrees. State these functional forms (polarizations) and sketch them in (Ex, Ey) plane being as specific as you can with maxima and minima...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0 0 otherwise Find Cov(X2, X3)

. Given the following non-periodic signal: x(t) = 3 e-5t cos(12t) u(t) Find the Fourier...

. Given the following non-periodic signal: x(t) = 3 e-5t cos(12t) u(t) Find the Fourier transform expression X(ω) without using Table. Calculate the magnitude spectrum of X(ω) for ω = π/8, π/4, and π/2

Let T: R2 -> R2 be a linear transformation defined by T(x1 , x2) = (x1...

Let T: R2 -> R2 be a linear transformation defined by T(x1 , x2) = (x1 + 2x2 , 2x1 + 4x2) a. Find the standard matrix of T. b. Find the ker(T) and nullity (T). c. Is T one-to-one? Explain.

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t...

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)

Consider the following three consumption bundles (X1,X2)=(10,10) ; (X1,X2)=(15,10) ; (X1,X2)=(3000,8).

Answer each of the following statements True/False/Uncertain. Give a full explanation of your answer including graphs where appropriate. (When in doubt, always include a fully labeled graph.)A) Consider the following three consumption bundles (X1,X2)=(10,10) ; (X1,X2)=(15,10) ; (X1,X2)=(3000,8). Non-satiation implies that (15,10) is preferred to (10,10) but does not imply that (3000,8) is preferred to (10,10).B) It is not theoretically possible for two indifference curves to cross if the preference relations they are based on satisfy the assumptions of completeness,...

Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf f(x1, x2)...

Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf f(x1, x2) = 4x1(1-x2) , 0<x1<1 0<x2<1 0, otherwise (ii) For the same joint pdf, calculate E(X1X2) and E(X1 + X2) (iii) Calculate Var(X1X2)

Find the Fourier coefficients of the following signal. x(t) = 5 + 2sin(w0.t) + cos(2.w0.t) -...

Find the Fourier coefficients of the following signal. x(t) = 5 + 2sin(w0.t) + cos(2.w0.t) - 3sin(2.w0.t)

10) A continuous-time system is described by the following relation, y(t) = (cos 3t) x (t)...

10) A continuous-time system is described by the following relation, y(t) = (cos 3t) x (t) where y(t) is the output of the system and x(t) is the input to the system. D etermine by sufficient explanation whether the system is: a) Stable, b) Memoryless, c) Causal, d) Time invariant, e) Linear.

Question