Explain the z-transform of the following system transfer

Assignment Help Computer Engineering

Reference no: EM13141837

Discrete Time Systems
1. a) Find the z-transform of the following system transfer function assuming the input is a unit staircase (i.e. zero order held). The sampling rate is T=0.2.

P(s) = (s+2)/(s+1)(s+5)

b) Given the z-transform of a sequence, U(z) = Z{u},

U(z) = z/(z^2 - 0.8z + 0.6)

i. Find the first 4 terms of u by long division.
ii. Find the underlying signal u(t) assuming that T=1 and no aliasing has occured.

2. a) The system (P_s)(s) = 4/(s^2 + 2s + 3) is subject to a staricase input with T = 0.2 seconds. Calculate the Z domain transfer function (P_z)(z).

b) The system, (P_s)(s) = 1/(s + 2) is subject to a staircase input with T = 0.1 seconds. Calculate the w-domain transfer function (P_z)(w) and comment on the relationship between s- and w-doman transfer functions.

3. a) Given (P_s)(s) = 4/(s + 3), find the w domain description for T = 0.2 and comment on the similarity and difference between (P_s)(s) and (P_w)(w). Use 3 decimal place in your calculations.

bi) Calculate the z-transform of the signal, y)t_ = e^(0t)sin(5t) sampled at T = 1.0.

bii) By finding the inverse z-transform, show that aliasing has occurred and explain why.

c) Find the first 4 terms in the inverse z-transform of Y(z) = 2z/(z^2 + 0.5z + 0.3) by means of long division. Use the final value of the signal to confirm that your results make sense.

4. a) The system, (P_s)(s) = 3/(s^2 + s + 2.5) is subject to a staircase input with T=0.2. Calculate the Z doman transfer function (P_z)(z).

b) A sequence, y_B, has a Z transform,

Y(z) = (z^2 + z)/(z^3 + 2z^2 + 1.4z + 0.3)

Find the first 5 terms in the sequence (y_0 ... y_4) by long division.

c) By considering the initial and final value theorems in the Z domain, find equivalent initial and final value theorems in the W domain and confirm that they are similar to the S domain theorems.

5. Show that aliasing will occur if the signal y(t) = e^-t(sin)(2t) is sampled with T=0.2 by finding the z transform of the sampled sequence and then finding the inverse z transform.

c) If a system has the transfer function P(s) = 1/(s/(3+1)) and T = 0.2, find (P_z)(w).

d) Show that the unit step signal, u(t) = sigma(t)

6. ai) The system, (P_s)(s) = (4s + 7)/(s^2 + 3s + 2) is subject to a staircase input with T = 0.5. Calculate the z domain transfer function, (P_z)(z).

aii) Use the final value theorem to find the final value of the output if the input is a step. Does your answer make sense with respect to the final value of the step response of the continuos system?

b) Given (P_s)(s) = 2/(s + 3), find the w domain description for T = 0.2 and comment of the similarity and difference between (P_s)(s) and (P_w)(w).

c) Given (P_z)(z) = (2z^2 - 0.5z + 1)/(z^2 + 0.2z + 0.5) and u_o = 1, u_1 = 2, u_n = 0, n =/ 0, 1, initioal y = 0.

i) Calculate y_n for n=0, 1, 2, and 3 by writing the difference equation and substituition.
ii) Does the oscillating behaviour make sense in terms of the pole locations in the z plane?

7. a) Find the z-transform of the following system transfer function assuming the input is a unit staircase (i.e. zero order held). The sampling rate is T = 0.2.

P(s) = 3/(s^2 + s + 1)

b) A signal y(t) = e^(-0.t)sin*2pi(t) is sampled at a rate T = 0.5, Show that the z-transform of the sampled sequence is Y(z) = (ze^-0.25)(sin(pi))/(z + e^-0.5)^2 = 0. Make a sketch to explain what has happened.

c) Given P(s) = 1/(s+1), find (P_z)(w) for T = 0.1.

Reference no: EM13141837

Questions Cloud

Explain most computer memories are composed of a large : Most computer memories are composed of a large number different devices that are interconnected to form the whole memory array which is accessed using the address bus.

How a ruler can attain and retain power : Machiavelli's instruction on how a ruler can attain and retain power is often summed up in his statement, "the end justifies the means." Identify a current political leader who seems to follow Machiavelli's principles outlined in The Prince, and expl..

Distribution of partnership net income : Calculate the distribution of partnership net income (loss) for each independent situation below (for each situation, assume the average capital balance of P is $140,000 and of Q is $240,000).

What features are shared among these two : One of the most interesting concepts in animal evolution is the relationship between the phylum Echinoderms and the phylum Chordates. Humans belong to the phylum Chordata.

Explain the z-transform of the following system transfer : Discrete Time Systems, 1. a) Find the z-transform of the following system transfer function assuming the input is a unit staircase (i.e. zero order held). The sampling rate is T=0.2.

Prespective of a pro-euthanasia arguement : It should be from the prespective of a pro-euthanasia arguement and please include a counter arguement. The longer it is the better.

Statement about tax-exempt organizations : Which of the following is a not true statement about tax-exempt organizations?

Find probability-mean amount of electric bills is in range : Find the probability that the mean amount of electric bills for a random sample of 75 households selected from this city will be between $132 and $136. Round to 4 decimal places.

Analyze the short and long run effects : Suppose there is a surge in demand for olive oil after researchers discover that olive oil consumption reduces heart disease. Analyze the short and long run effects of this increased demand on you firm.

User Account

All Pages