Question
Suppose the impulse responses of ℎ?[?] is given as: ℎ1 = 0.7?−1?[? − 1] (a) Is...
Suppose the impulse responses of ℎ?[?] is given as:
ℎ1 = 0.7?−1?[? − 1]
(a) Is ℎ?[?] stable? Justify your answer.
(b) If it is required that ℎ[?] = 0.7??[?], find ℎ?[?].
(c) Based on your answer in (b), if ?[?] = ?[? − 1] + 2?[? − 2] +
3?[? − 3].
Find ?[?] and write it in terms of ℎ?[?].
(d) If ?[?] = ?[?] + ?[? − 1] − 2?[? − 2] is the input to this
system, and the
output ?[?] = ?[? − 1], find the appropriate ℎ?[?].
Homework Answers
Answer #1
The given impulse response:
Stability:
(a) An LTI system is stable if the impulse response h(n) is absolutely summable i.e.
The overall impulse response from part (b)
For stability:
The system h(n) is stable.
(b)
From equation (1)
(c)
?[?] = ?[? − 1] + 2?[? − 2] + 3?[? − 3]
Then y[n] is:
Y[n] in terms of h1[n]:
Not the answer you're looking for?
Similar Questions
(d) A test on unknown LTI system is conducted by given an impulse as the input....
(d) A test on unknown LTI system is conducted by given an
impulse as the input. The output impulse response from this test is
given by:
ℎ[?]=[?[?−1]−?[?−4]]?[?]
A signal ?[?]=4?[?−1]+14[?[?]−?[?−3]] will be the new input to that
system. Find the new output if the input-output relationship for a
system given as ?[?]=ℎ[?]∗?[?].
[10 marks]
A linear time invariant system has an impulse response given by ℎ[?] = 2(−0.5) ? ?[?]...
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)...
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...
Consider a system defined by the input-output relationship given below: y(t) = x(t)x(t-2) a) Is the...
Consider a system defined by the input-output relationship given
below:
y(t) = x(t)x(t-2)
a) Is the system memoryless? Why?
b) Is the system stable? Why?
c) Is the system causal? Why?
d) Is the system invertible? Show why?
e) Find the impulse response of the system.
PLEASE ANSWER ALL QUESTIONS!
1. What is the impulse? Give the definition and formula. 2. Calculate the impulse required to...
1. What is the impulse? Give the definition and
formula.
2. Calculate the impulse required to stop each moving
ball described below.
mA = 4.55 kgvA = 1.5 m/smB = 0.7
kgvB = 9 m/smC = 1.05 kgvC = 4.5
m/smD = 0.84 kgvD = 6.75 m/s
The impulse for ball 'A', ImpA = Units Select
an answer kg m s m/s N*s N/s no units required .
The impulse for ball 'B', ImpB = Units Select
an answer s kg N*s m...
Find two possible impulse responses for the system below. Please explain briefly why there may be...
Find two possible impulse responses for the system below. Please
explain briefly why there may be two answers.
y[n-1] + (1/3)y[n-2] = x[n]
Using the following code: % Ex 6.4 First-order step and impulse response for two time constants...
Using the following code:
% Ex 6.4 First-order step and impulse response for two time
constants
%
clear all; close all;
t = 0:.1:100; % Time vector
subplot(1,2,1);
x = 250*exp(-0.05*t);
plot(t,x,'k');
xlabel('Time (hrs)','FontSize',14); ylabel('P_A
(mmHg)','FontSize',14);
title('Impulse Response','FontSize',14);
subplot(1,2,2);
x = 20*(1-exp(-0.05*t));
plot(t,x,'k');
xlabel('Time (hrs)','FontSize',14); ylabel('P_A
(mmHg)','FontSize',14);
title('Step Response','FontSize',14);
ANSWER:
The response of a 1st order linear body fluid balance
system to step function (L m (t) = 1/s,
Eqn. 6.9/p226) and impulse function (L d (t) = 1,...
An LTI system has an impulse answer of h[n] = a^(n)H[n], H[n] is the Heaviside step...
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...
1. Consider the functions ?(?) = √? + 1 , ?(?) = 2? 4−? , and...
1. Consider the functions ?(?) = √? + 1 , ?(?) = 2? 4−? , and
?(?) = ? 2 − 5
(a) Find ?(0), ?(0), ?(0)
(b) (??)(?)
(c) (? ∘ ?)(?)
(d) Find the domain of (? ∘ ?)(?)
(e) Find and simplify ?(?+ℎ)−?(?) ℎ .
(f) Determine if ? is an even function, odd function or neither.
Show your work to justify your answer.
2. Sketch the piecewise function. ?(?) = { |? + 2|, ??? ?...
The signal x[n] is the input of an LTI system with impulse function of h[n]. x[n]...
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))
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 12 minutes ago
asked 14 minutes ago
asked 18 minutes ago
asked 21 minutes ago
asked 21 minutes ago
asked 48 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago