Question: Consider the difference equation representing a causal LTI system y[n] + (1/) y[n 1] = x[n 1]. (a) Find the impulse response of

Consider the difference equation representing a causal LTI system

y[n] + (1/α) y[n – 1] = x[n – 1].

(a) Find the impulse response of the system, h[n], as a function of the constant a.

(b) For what range of values of a will the system be stable?

Step by Step Solution

★★★★★

3.44 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a Taking the difference equation ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

30-E-T-E-D-S-P (20).docx

120 KBs Word File

Students Have Also Explored These Related Telecommunication Engineering Questions!

Q:

For what range of values of h will a sensitivity analysis on the effect of a change of h in the number of TV sets stocked in the College Park store be valid?

Q:

Find the impulse response of an ideal high pass filter with the frequency response function -2 fto p() %3D | 1- 2W

Q:

Consider the difference equation yn = -3yn-1 + 8, y0 = 1. (a) Generate y1, y2, y3 from the difference equation. (b) Solve the difference equation. (c) Use the solution in part (b) to obtain y4?

Q:

Exercise 6: An important group of investors wants to determine the profitability of establishing themselves in the country with the famous beverage brand Dr. Pepper in its two versions: blue and red....

Q:

The block diagram representation of the filter is given below: (a) find the system function H(z) of this filter. (b) find the difference equation between input and output signals, x(n) and y(n) (c)...

Q:

In the following situation, decide whether you would use a personal interview, telephone survey, or self-administered questionnaire. Give your reasons. A survey of the residents of a new subdivision...

Q:

A causal LTI system has the system function (a) Find the impulse response of the system, h[n]. (b) Find the output of this system, y[n], for the input x[n] = e j(?/2) n . 1+ 2z- +2? H(z) = (1 + 2-1)...

Q:

You have designed an IIR low-pass filter with an input-output relation given by the difference equation (i) y[n] = 0.5y[n 1] + x[n] + x[n 1] n 0 where x[n] is the input and y[n] the output. You...

Q:

Could I please have the worked solution for the following question: a) The transfer function of a linear time-invariant (LTI) causal digital system is given by: H(z)=z+0.6z Find the impulse response...

Q:

For the distribution of the sample means that you produced in Exercise 7 (truck odometers), a. Show that the mean of the distribution is equal to the population mean. b. Compute the standard...

Q:

The Johnson Robot Company's marketing manager's estimate that the demand curve for the company's robots in 2012 is P = 3,000 - 40Q where P is the price of a robot and Q is the number sold per month....

Q:

Hugo has $ 1 9 2 in an account. The interest rate is 1 2 % compounded annually. To the nearest cent, how much interest will he earn in 4 years? Use the formula B = p ( 1 + r ) t , where B is the...

Q:

Dynamic magneto conductivity tensor for free electrons a metal with a concentration n of free electrons of charge e is in a static magnetic field B. The electric current density in the xy plane is...

Q:

A 2.00-kg stone is sliding to the right on a frictionless horizontal surface at 5.00 m/s when it is suddenly struck by an object that exerts a large horizontal force on it for a short period of time....

Q:

One 110-kg football lineman is running to the right at 2.75 m/s while another 125-kg lineman is running directly toward him at 2.60 m/s. What are? (a) The magnitude and direction of the net momentum...

Q:

The Scampini Supplies Company recently purchased a new delivery truck. The new truck cost $22,500, and it is expected to generate net after-tax operating cash flows, including depreciation , of...

Q:

The presence of an unseen planet orbiting a distant star can sometimes be inferred from the motion of the star ab we see it. As the star and planet orbit the center of mass of the star-planet system,...

Q:

Sketch the equipotential lines surrounding the two conducting plates shown in Figure 19.28, given the top plate is positive and the bottom plate has an equal amount of negative charge. Be certain to...

Q:

Consider the system shown in figure(a) Determine its impulse response h(n).(b) Shown that h(n) is equal to the convolution of the following signals.h1(n) = ?(n) + ?(n - 1)h2(n) = (1/2)n u (n) x(n)...

Q:

Consider the sketch the convolution yi(n) and correlation ri(n) sequences for the following pairs of signals and comments on the resultobtained. (a) x{n) = {1, 2. 4) h:(n) (1.1. 1.1. 1) (b) x(n) {0....

Q:

The zero-state response of a causal LTI system to the input x(n) = {1, 3, 3, 1} is y(n)={1,4,6,4,1}. Determine its impulse response.

Q:

The malicious software that used to launch distributed denial of service ( DDoS ) attacks: Select one: a . logic bombs b . Trojan Horse c . Zombie d . b + c

Q:

Arnold Inc. is considering a proposal to manufacture high-end protein bars used as food supplements by body builders. The project requires use of an existing warehouse, which the firm acquired three...

Q:

If you paid $44 to a loan company for the use of $1, 233 for 88 days, what annual rate of interest did they charge? (Assume a 360-day year.) The annual rate of interest is %. (Round to three decimal...