linear time-invariant continuous system and Matlab

1. A discrete-time system has the following unit-pulse response:
h[n] = 0.5^n - 0.25^n for n >= 0

Correspondingly, the following difference equation describes the behavior of the system:
y[n + 2] - 0.75y[n +1] + 0.125y[n] = 0.25x[n +1]

a. Use the MATLAB command conv to calculate the response of the system
to a unit step input, x[n]=u[n]. Consider 0 <= n <= 20 . Show what you type into the MATLAB command window. Also, submit a plot of the output. Be sure to label your axes.

2. A linear time-invariant continuous-time system has the impulse response below:
h(t) =[cos 2t + 4 sin 2t]u(t)

(a). Determine the transfer function H(s) of the system.
(b). Plot the system impulse response using MATLAB.
(c). The input, x(t) is defined as x(t)=((5/7)e^-t) - ((12/7)e^-8t), x >= 0. Find x(s).
(d). Compute the output response Y(s).
(e). Compute and plot y(t).

The solution is comprised of detailed explanation of application of Laplace transform to find the transfer function of the linear time-invariant continuous system in s-domain. It also shows the calculation of the impulse response of the system. Furthermore, it also elaborates on finding the system output in both s-domain and time domain with certain input. Finally, the application is verified in Matlab codes.

Please refer to attached. Please submit Matlab code along with plots and anwsers. Thanks.
A lineartime-invariantcontinuous-time system has the impulse response below:
h(t) =[cos 2t + 4 sin 2t]u(t)
(a) Determine the transfer function H(s) of the system.
(b) Plot the system impulse response using MATLAB.
(c) The input,

A lineartime-invariant discrete-time system has transfer function
h(z)=((z^2)-z-2)/((z^2) + 1.5z-1)
a. Use MATLAB to obtain the poles of the system. Is the system stable?
Explain.
b. Compute the step response. This should be done analytically, but you can
use MATLAB commands like conv and residue.
c. Plot the first seve

1. Is the lineartime-invariantcontinuous-time system with the impulse response h(t) = sin 2t for t ≥ 0 BIBO is stable? Explain.
2. Determine if the lineartime-invariantcontinuous-time system defined by:
is stable, marginally stable, unstable, or marginally unstable. Show work.
3. Compute the steady-state

(la_7.doc)
A lineartime-invariant discrete-time system has transfer function
H (z) = z² - z - 2
-----------
z² - 1.5z - 1
a. Use MATLAB to obtain the poles of the system. Is the system stable?
Explain.
b. Compute the step response using MATLAB commands like conv and residue.
c. Plot the f

See attached file for full description:
Activity 1:
Consider the discrete-time signal: x[n] = sin(2*pi*Mn/N), and assume N = 12. For M = 4, 5, and 10, plot x[n] on the interval 0 =< 0 < = 2n - 1. Use stem in Matlab to create your plots, and be sure to approximately label your axes.
Questions: What is the fundamental period

Please see the attachment for all the questions with proper symbols/notations.
1. Compute the Laplace transform of e^(-10t)cos(3)u(t) .
2. Compute the z-transform of the discrete time signal defined by:
x[n] = δ[n] + 5δ[n - 1]
3. Compute the inverse Laplace transform of X(s) = (s+2) / (s^2+7s+12) .
4.

Please solve the following numerical analysis problem:
Determine the flow Qt : R^2 into R^2 for the nonlinearsystem: x' =f(x) with
f(x) = [ -x1 ]
[ x1^2 + 2x2 ]
and show that the set S = { x E R^2l x2 = -x^2/4 } is invariant with respect to the flow {Qt}.
Plea