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?[?].

Engineering   Electrical-Engineering   
0 0
Add a commentTranscribed image text
Next >

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]:

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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]
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...
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,...
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))
2. Consider the following impulse responses h[n] of linear time-invariant (LTI) systems. In each case, (i)...
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 -...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT