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....
Sean Browne owns and manages a computer repair service, which had the following trial balance on December 31, 2016 (the end of its fiscal year). Summarized transactions for January 2017 were as...
In the case of the previous question, if the effect of the finite speed of sound were neglected, would $h$ be larger or smaller? What percentage error would be made? Previous question: One wants to...
1. What are Honest Teas competitive advantages? 2. Look at the list you generated. Which is most important to you as a consumer and why? 3. Given what you already know about Honest Teas business...
A 45-year-old man presents to the Emergency Department with a fever, widespread rash, and confusion. His only past history of note was Sydenham's chorea and a number of recent dental extractions....
Overall, Steve Edwards, vice president of Marketing at Ditten hoefer's Fine China, is very pleased with the success of his new line of Gem-Surface china plates. Gem-Surface plates are different from...
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...
Identify the major and minor products of the following reaction: CH2OH CH2CH3 CH3CCi_
Several plants reach their plateau well before the end of the observation period. How is the analysis affected if repeated values are removed from the end of each series?
Explain the purpose and the implementation of the Box-Tidwell method. Why must the unmodified REML criterion be avoided?
How can we be assured that the log transformation is really needed or substantially beneficial? (Chap. 19).
The R commands are designed to decompose the total sum of squares additively into components associated with certain subspaces, which are mutually orthogonal for this design. Explain how to compute...
For $y \in \mathbb{R}^{n}$, a decomposition of the total sum of squares \[ \|y\|^{2}=y^{\prime} y=y^{\prime} A_{1} y+\cdots+y^{\prime} A_{k} y \] is called orthogonal if each $A_{r}$ is an...
What is meant by chance variation?
Suppose the spot and six-month forward rates on the Norwegian krone are Kr 5.78 and Kr 5.86, respectively. The annual risk-free rate in the United States is 3.8 percent, and the annual risk-free rate...
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.
The Pallon Company manufactures a variety of handerated bed frames. The company's manufacturing activitiesor the current Sear follow:Manufacturing Activity Estimated Cost Cost Driver Used as...
A company's inventory records indicate the following data for the month of April: Date Activities Units Acquired at Cost Units Sold at Retail April 1 Beginning inventory 8 2 0 units @ $ 3 6 = $ 2 9 ,...
How do authors employ intertextual allusions to enrich the layers of meaning in their works and establish connections across disparate literary traditions?

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