The (mathcal{Z})-transform of a discrete-time filter (h(k)) at a (1 mathrm{~Hz}) sample rate is [H(z)=frac{1+(1 / 2)

Question:

The $\mathcal{Z}$-transform of a discrete-time filter $h(k)$ at a $1 \mathrm{~Hz}$ sample rate is

\[H(z)=\frac{1+(1 / 2) z^{-1}}{\left[1-(1 / 2) z^{-1}ight]\left[1+(1 / 2) z^{-1}ight]}\]

(a) Let $u(k)$ and $y(k)$ be the discrete input and output of this filter. Find a difference equation relating $u(k)$ and $y(k)$.

(b) Find the natural frequency and the damping coefficient of the filter's poles.

(c) Is the filter stable?

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

Step by Step Answer:

Related Book For book-img-for-question

Design And Analysis Of Control Systems Driving The Fourth Industrial Revolution

ISBN: 9781032718804

2nd Edition

Authors: Arthur G O Mutambara

See More Books

Question Posted: Mar 15, 2024 10:00 PM

See More Questions

answer all questions as instructed below. make sure you have attended all questions .Comparative Architectures (a) Describe the organisation of a two-level branch predictor that makes use of a global...
Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
8. A 12-tur square wire loop of 1-m length carrying a current of 1-A in the counter clockwise direction as shown in the figure. A magnetic field of magnitude 3000 G is directed into the board. Find,...
What is the reason for ice being less dense than water?
How can alignment between IT and enterprise strategy be applied to tools for data mining?
The Home Depot A
Assume the same set of facts for Stacy Company as in Problem 10-2 except that the market rate of interest of January 1, 2010, is 8% and the proceeds from the bond issuance equal $10,803. Required 1....
On February 12, 2021, Diego Inc. issued 330,000 of its common shares in exchange for equipment for which the cash price was known to be $790,000. The articles of incorporation authorized the issue of...
Use the $\mathcal{Z}$-transform to solve the difference equation \[y(k)-3 y(k-1)+2 y(k-2)=2 u(k-1)-2 u(k-2)\] where \[\begin{aligned}u(k) & =k, \quad k \geq 0 \\& =0, \quad k <0 \\y(k) & =0, \quad...
(a) Transform \[G(z)=\frac{(z+0.3)(z-0.3)}{(z-0.1)(z-0.5+0.5 i)(z-0.5-0.5 i)}\] into a continuous-time equivalent system by means of $\mathrm{ZOH}$ method of sampling intervals ranging from...
Albeit by rule of thumb, take a team of people with whom you associate closely and evaluate their behaviour characteristics Where is the team strong? Where is the team weak? Do you believe it is...
If the dose rate from a sample of Ga-67 is 0.052 mSv per hour at a distance of 1.1 m, then what would be dose rate at 3.5 m ?
A 1.6x10^9 p/s point source of Po210-Be source of 4.5 MeV is stored behind a X cm of paraffin, the dose equivalent rate is not to exceed 0.10 mSvh-1h at a distance of 1m. What is the X cm needed to...
X 10 Let A = -9 y 7 4 Z 210 If the kernel of A contains the vector what are x, y, and z? -2
8-22. E.O.Q., Carrying cost = Storing cost + Interest. Following data are available with respect to a certain material. Annual requirement.......... Cost to place an order.. Annual interest rate. _...
A new company started production. Job 1 was completed, and Job 2 remains in production. Here is the information from the job cost sheets from their first and only jobs so far: Job 1 Hours Total Cost...
An employer became aware that a union organizing campaign was underway in one of its plants. A union supporter was called in to a meeting with plant managers. At the end of the meeting, when the...
6. (Potential Energy and Conservation of Energy) What should be the spring constant k of a spring designed to bring a 1200-kg car to rest from a speed of 95 km/h so that the occupants undergo a...
What is a popular tool used to identify and express the functional requirements of a system?
Why do many new systems analysts fail to effectively analyze problems? What can they do to become more effective?
What is the trigger for communicating the project plan, and who is the audience? Why is communicating the project plan important?
Production numbers for 2 shifts are shown. The shift supervisor of Shift 2 insists to the production manager that her operators are more productive than the ones on Shift 1. Using a confidence level...
In a class, the scores that students got are as shown. What are the 25, 50, 75 and 100th percentiles for the data? 84 84 98 80 89 83 85 56 85 84 84 74 84 81 83 80 45 86 67 79 81 78 76 85 83 77 86 83...
Number of points made by Teams A and B are shown. Which statement is true based on running the F-Test Two-Sample for Variances in the Data Analysis pack in Excel? Use a confidence level of 10% to...

The (mathcal{Z})-transform of a discrete-time filter (h(k)) at a (1 mathrm{~Hz}) sample rate is [H(z)=frac{1+(1 / 2)

Question:

Step by Step Answer:

Design And Analysis Of Control Systems Driving The Fourth Industrial Revolution

Students also viewed these Computer science questions