The following difference equation is used to obtain recursively the ratio / c[n + 1] = (1

Question:

The following difference equation is used to obtain recursively the ratio α/β

c[n + 1] = (1 − β) c [n] + α n ≥ 0

with c[0] as an initial condition. Solve the difference equation, and find under what condition(s) the solution c[n] will converge to the desired answer of α/β as n tends to infinity.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Signals and Systems using MATLAB

ISBN: 978-0123948120

2nd edition

Authors: Luis Chaparro

See More Books

Question Posted: Dec 29, 2018 07:13 AM

See More Questions

Consider the Fibonacci sequence generated by the difference equation f[n] = f[n 1] + f[n 2], n 0 with initial conditions f[ 1] = 1, f[ 2] = 1. (a) Find the Z-transform of f[n], or F(z). Find the...
The transfer function of an RLC circuit is H(s) = Y(s)/X(s) = 2s/(s 2 +2s+1). (a) Obtain the ordinary differential equation with input x(t) and output y(t). Approximating the derivatives by...
Consider a discrete-time system represented by the difference equa-tion y[n] = 0.5y[n 1] + x[n] where x[n] is the input and y[n] the output. (a) An equivalent representation of the system is given by...
Toby dies on 2 March 2021, leaving an estate valued at 400,000. None of the transfers made on death are exempt from IHT. Calculate the IHT due on the estate if the total of the gross chargeable...
Given the following information about the clothing and hardware departments of Phillips Company, prepare a departmental expense allocation sheet showing expenses by department....
Surface albedo is defined as the ratio of solar energy directed upward from a surface over energy incident upon the surface. Surface albedo is a critical climatological parameter of sea ice. The...
Downloading apps to your cell phone. According to a study, nearly 40% of adult cell phone owners have downloaded an application (app) to their cell phone. The accompanying table gives the probability...
Information related to plant assets, natural resources, and intangibles at the end of 2012 for Lucy Company is as follows: buildings $1,100,000; accumulated depreciationbuildings $650,000; goodwill...
A project Nirrti is considering requires an initial cash outlay of $688,000 for equipment. She expects to spend an additional $71,000 in the first year to cover costs as the project will produce...
FeVer Beverages is a typical coffee shop that operates at Batangas. Recently, the general manager is facing a challenge about not meeting their target lead time of serving the hot coffee of 15...
A sinusoid x(t) = cos(t) is a band-limited signal with maximum frequency max = 1 (a) Using Fourier transform properties determine the maximum frequency of x 2 (t). What sampling period T s can be...
A discrete-time averager is represented by the input/output equation y[n] = (1/3)(x[n + 1] + x[n] + x[n 1]), where x[n] is the input and y[n] the output. (a) Determine whether this system is causal...
A base class can also be called a ____________. a. Child class b. Superclass c. Derived class d. Subclass
Verify the results of Eq. (14.48) for the properties of the chiral projection operators. Data from Eq. 14.48 P = P+ P+ + P = 1 P_P+ P+P = 0 Py" = y P
Prove that the estimating equations in (11.13) are unbiased under MCAR, but are generally biased without the stringent MCAR assumption. (x) [y - f (xt;)] = 0, i=1 (11.13)
Refer to Figure 11.5: Which is the most expensive subcontract for this project? How much were the costs for the general contractor's crews for item 4? Figure 11.5 Division 1 2 3 4 5 6 7 Work Gen'l...
a. Using observations on the change in consumption $D C_{t}=C_{t}-C_{t-1}$ and the change in income $D Y_{t}=$ $Y_{t}-Y_{t-1}$ from 1959Q3 to 2015Q4, obtained from the data file cons_inc,...
Water at $20^{\circ} \mathrm{C}$ flows by gravity from a large reservoir at a high elevation to a smaller one through a 35-m-long, 5-cm-diameter cast iron piping system that includes four standard...
Show that converges if p > 1 and diverges if p 1. 8 ,00 P x dx
Select the correct answer for each of the following questions. 1. On December 31, 20X3, Saxe Corporation was merged into Poe Corporation. In the business combination, Poe issued 200,000 shares of its...
In Section 7.5, one proposed solution that allowed mobile users to maintain their IP addresses as they moved among foreign networks was to have a foreign network advertise a highly specific route to...
Consider the following idealized LTE scenario. The downstream channel (see Figure 7.21) is slotted in time, across F frequencies. There are four nodes, A, B, C, and D, reachable from the base station...
True or false: Ethernet and 802.11 use the same frame structure.
Deacon Company is a merchandising company that is preparing a budget for the three - month period ended June 3 0 th . The following information is available Deacon Company Balance Sheet March 3 1...
Mango Company applies overhead based on direct labor costs. For the current year, Mango Company estimated total overhead costs to be $460,000, and direct labor costs to be $230,000. Actual overhead...
Which of the following do we expect to be the horizon growth rate for a company (long term growth rate- say 30-50 years)? A) Inflation B) Industry Average C) Zero D) Market Beta

The following difference equation is used to obtain recursively the ratio / c[n + 1] = (1

Question:

Step by Step Answer:

Recursively for cn as n then 1 1 or 0 2 ind...View the full answer

Signals and Systems using MATLAB

Students also viewed these Computer science questions