Question: Consider a linear time-invariant system with input x[n] and output y[n] for which y[n 1] 5/2 y[n] + y[n + 1] = x[n].

Consider a linear time-invariant system with input x[n] and output y[n] for which

y[n – 1] – 5/2 y[n] + y[n + 1] = x[n].

The system may or may not be stable or causal. By considering the pole-zero pattern associated with the preceding difference equation, determine three possible choice for the impulse response of the system. Show that each choice satisfies the difference equation. Indicate which choice corresponds to a stable system and which choice corresponds to a causal system.

Step by Step Solution

★★★★★

3.37 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Three regions of convergence ... View full answer

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)

30-E-T-E-D-S-P (207).docx

120 KBs Word File

Students Have Also Explored These Related Telecommunication Engineering Questions!

A discrete-time system with input x (n) and out put y (n) is described in the frequency domain by the relation y() = e-j2X() + dX()/d (a) Compute the response of the system to the input x(n) = (n)....

The following data for water may or may not be useful for this quiz: You have a metal block with a mass of 177.1 g, specific heat of 325 Jkg -1 k -1 , the thermal conductivity of 199.7 Wm -1 K -1 ,...

The following items may or may not be relevant to a company's bank reconciliation: 1. The company recorded a deposit as $540, but it correctly cleared the bank for $450. 2. A check recorded for...

Consider a stable linear time-invariant system with input x[n] and output y[n]. The input and output satisfy the difference equation, y[n 1] 10/3 y[n] + y[n + 1] = x[n]. (a) Plot the poles and...

Consider the causal LTI system whose input x [ n ] and output y [ n ] are related by the following difference equation: y [ n + 1 ] = 4 x [ n + 1 ] 7 1 2 y [ n ] 1 1 2 y [ n 1 ] Using frequency -...

Consider a LTI discrete-time system with input x[n] and output y[n]. It is known that the impulse response of the system is (a) Determine the magnitude and phase responses |H(e jÏ )|and H(e...

Q . 5 ( a ) Consider a discrete - time system with input, x [ n ] , and output, y [ n ] . The input - output relationship for this system is y [ n ] = x 2 [ n ] 2 ( ii ) Is the system time -...

=1&aicc_sid=57949760hrblock&packageld=com.knowbe4.courses.btb.uuid.5f812ded-eec3-4124-ad51-ba2b3578b41d&qs=%5e%5e%5etUsBO0Qwsi... X...

Operating expenses would include O interest expense. O income tax expense. O freight-out. O freight-out and interest.

( a ) Consider a discrete - time system with input, x [ n ] , and output, y [ n ] . The input - output relationship for this system is y [ n ] = 2 x [ n ] + 1 ( i ) Is the system linear? Justify your...

Show that every C' vector field on the sphere S? has at least one singularity.

On January 1, 2020, No. 1 Leasing Company leased equipment to Maria Corporation for a 5-year period ending December 31, 2024, at which time possession of the leased equipment will revert back to No....

\ table [ [ 1 1 . 0 0 % , A ? Calculate the Payback period.

A South American country has had a high rate of inflation. Recently, its exchange rate was 15 cruzados per dollar; that is, one dollar will buy 15 cruzados in the foreign exchange market. It is...

Sally Johnson loaned a friend $10,000 at 15% interest, compounded annually. She is to repay the loan .in five equal end-of-year payments. Sally estimates the inflation rate during this period is 12%....

Inflation is a reality for the general economy of the United States for the foreseeable future. Given this assumption, calculate the number of years it will take for the purchasing power of today's...

Kraft Enterprises owns the following assets at December 31, 2010. What amount should be reported ascash? Cash in bank-savings account Checking account balance Postdated checks Certificates of deposit...

Consider a plane composite wall that is composed of three materials (materials A, B, and C are arranged left to right) of thermal conductivities k A = 0.24 W/m K, k B = 0.13 W/m K, and k C = 0.50...

Twenty-five mL of a 0.388 M solution of Na 2 SO 4 is mixed with 35.3 mL of 0.229 M Na 2 SO 4 . What is the molarity of the resulting solution? Assume that the volumes are additive.

For the gearset and conditions of Prob. 155, find the power rating for AGMA bending strength.

In straight-bevel gearing, there are some analogs to Eqs. (1444) and (1445). If we have a pinion core with a hardness of (HB) 11 and we try equal power ratings, the transmitted load Wt can be made...

Refer to your solution to Probs. 151 and 152, which is to have a pinion core hardness of 300 Brinell. Use the relations from Prob. 157 to establish the hardness of the gear core and the case...

PLEASE ANSWER ALL QUESTIONS AND SHOW WORK! 1. Under Basel III, the combination of Core Tier 1 capital and the capital conservation buffer raises the Core Tier 1 capital ratio to 7% 7.5% 4.5% 6% None...

E. Now assume that the equipments residual value could be as low as $0 or as high as $400,000, but $200,000 is the expected value. Because the residual value is riskier than the other relevant cash...

10. You are planning to buy a new car 3 years from today. The car will cost $22,000. How much do you need to deposit today in an account paying 2.5% compounded annually to reach your goal? A....