Question

6. Consider a causal linear system whose (zero-state) response to an input signal, f(t) = e...

6. Consider a causal linear system whose (zero-state) response to an input signal, f(t) = e −3tu(t), is y(t) = (−e −t + 4e −2t − 3e −3t )u(t). (

a) Find the transfer function H(s) of the system.

(b) Write the differential equation that describes the system.

(c) Plot the pole-zero diagram of system. Is the system stable?

(d) Plot the frequency response of the system, |H(w)|.

(e) Whats the systems zero-state response to another input signal, f1(t) = 2e −5tu(t)?

PLEASE make sure to answer d and e.

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

Homework Answers

Answer #1

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...
The two components of a linear system response are zero-input response and zero-state response. Explain the...
The two components of a linear system response are zero-input response and zero-state response. Explain the meaning of each of these components.What is the practical significance of zero-input response?
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 an LTI system whose frequency response is undesirable; the distorting system function is given as:...
Consider an LTI system whose frequency response is undesirable; the distorting system function is given as: Hdz=(1-0.8ej0.4πz-1)(1-0.8e-j0.4πz-1)(1-1.5ej0.6πz-1)(1-1.5e-j0.6πz-1) Assume the distorting function is both causal and stable. Design and examine compensation system Hc(z) such that when a signal sn is transmitted through this communication channel then perfect compensation is achieved i.e. scn=sn. b)   Determine the impulse response h[n] by using the inverse Z transform. Hz=log1+az-1+2Z-5,             z>a c) For what value of a will be the impulse response both stable and causal?...
Prove mathematically that if a sinusoidal input is applied to a linear stable system then the...
Prove mathematically that if a sinusoidal input is applied to a linear stable system then the steady-state response is a scaled and phase-shifted version of the input. Hints: 1. Assume a generic stable closed-loop transfer function. 2. Assume a generic sinusoidal input signal i.e. say ?(?) = ? sin(??) 3. Find c(t) and show mathematically that statement in the problem is satisfied.
Consider a causal LTI system described by the difference equation: y[n] = 0.5 y[n-1] + x[n]...
Consider a causal LTI system described by the difference equation: y[n] = 0.5 y[n-1] + x[n] – x[n-1] (a) Determine the system function H(z) and plot a pole-zero pattern in the complex z-plane. (b) Find the system response using partial fraction expansion when the input is x[n] = 2u[n]. Plot the result.
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!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT