Question

An LTI discrete-time system has the impulse response h[n] = (1.2)^n * u[-n]. Find the system response to a unit step input x[n] = u[n].

Please explain the shifting im having a hard time grasping the concept (especially for the U[-n+k] shift

Note:u[n] is the unit step function

Answer #1

An LTI system has an impulse answer of h[n] = a^(n)H[n], H[n] is
the Heaviside step function. Obtain the output y[n] from the system
when the input is x[n]=H[n]. 2. Consider the discrete system
defined by> y[n] - ay[n-1] =x[n] Find the output when the input
is x[n] = Kb^(n)H[n], and y[-1]=y_(-1)\ Find the output when the
input is x[n] = K ẟ [n], and y[-1]=a Find the impulse response when
the system is initially at rest. Find the Heaviside...

The signal x[n] is the input of an LTI system with impulse
function of h[n]. x[n] = (0.4)^n u[n] and h[n] = (0.2)^n u[n].
(a) What is the DTFT of the output of the LTI system?
(b) What are the Energy density spectrums of the input and
output signals?
(c) What would be the inverse DTFT: X(w) =
1/(1-0.25e^-j(w-2))
(d) How would part (c) differ for the DTFT: X(w) =
1/(1-0.25e^-j(w-2)) + 1/(1-0.25e^-j(w+2))

The impulse response of an LTI system is h[n] = 3u[n+2]. a) Is
this system BIBO stable? Justify. b) Is the system causal?
Justify.

CHAPTER 13: DISCRETE-TIME SIGNAL (TEXTBOOK SIGNALS AND SYSTEM BY
MAHMOOD NAHVI
11. In an LTI system, x(n) is the input and h(n) is the
unit-sample response. Find and sketch the
output y(n) for the following cases:
i) x(n) = 0.3nu(n) and h(n) = 0.4nu(n)
ii) x(n) = 0.5nu(n) and h(n) = 0.6nu(n)
iii) x(n) = 0.5|n|u(n) and h(n) = 0.6nu(n)

A linear time invariant system has an impulse response given by
ℎ[?] = 2(−0.5) ? ?[?] − 3(0.5) 2? ?[?] where u[n] is the unit step
function.
a) Find the z-domain transfer function ?(?).
b) Draw pole-zero plot of the system and indicate the region of
convergence.
c) Is the system stable? Explain.
d) Is the system causal? Explain.
e) Find the unit step response ?[?] of the system, that is, the
response to the unit step input.
f) Provide...

For the LTI system described by the following system functions,
determine (i) the impulse response (ii) the difference equation
representation (iii) the pole-zero plot, and (iv) the steady state
output y(n) if the input is x[n] = 3cos(πn/3)u[n].
a. H(z) = (z+1)/(z-0.5), causal system (Hint: you need to
express H(z) in z-1 to find the difference equation )
b. H(z) = (1 + z-1+ z-2)/(1-1.7z-1+0.6z-2), stable system
c. Is the system given in (a) stable? Is the system given in...

2. Consider the following impulse responses h[n] of linear
time-invariant (LTI) systems. In each case,
(i) provide the transfer function H(z) (ZT of h[n]) and its
ROCh,
(ii) sketch the ROCh in the z-plane,
(iii) mark the pole and zero locations of H(z) (on the same plot
in the z-plane), and (iv) discuss whether or not the LTI system is
stable.
(a) h1[n] = (0.4)^n u[n] + (2 - 3j)^n u(n -2)
(b) h2[n] = (0.2)^(n+2) u[n] + (2 -...

a) If the transfer function of a system is H(z) = 2+z^(-2), what
is its impulse response?
b) If the transfer function of a system is 2z/(z-0.5) and it is
valid for when |z| > 0.5, what is its impulse response?
c) If the transfer function of a system is 1/(z-2), what is its
impulse response?
d) x[n] = (-4)^n U[n]. (U[n] is the unit step function). What is
its z-transform and the region of convergence of its
z-transform?
e)...

Given an input signal x[n], and the impulse response h[n],
compute the output signal.
x[n] = a^n *
u[1-n] for
|a| > 1
h[n] = u[2-n]

A continuous-time system with impulse response
h(t)=8(u(t-1)-u(t-9))
is excited by the signal
x(t)=3(u(t-3)-u(t-7))
and the system response is y(t).
Find the value of y(10).

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