![3. A digital filter is described by the difference equation where u[n] represents the unit step sequence. The initial conditions of the system are y[-1] = 0 and y[-2] = 1. (a) Draw a block diagram implementation of the above system. (b) Determine the output y[n] (c) Determine the zero-input solution. (d) Determine the zero-state solution. (e) Is the system stable? Justify your answer](http://img.homeworklib.com/questions/0eb1e7d0-00e8-11ec-92e8-0f15a9d51392.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
3. A digital filter is described by the difference equation where u[n] represents the unit step...
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
Problem 3: Consider an IIR filter described by the difference equation (a) What is the system...
Problem 3: Consider an IIR filter described by the difference equation (a) What is the system function H(a) of this fiter? [5 points) (b) Determine the zeros and poles of the system and sketch the zero-pole plot in z-plane. 5 points (c) Plot the block diagram of this IIR filter. [10 points (d) Given the input zfn-cos(mn/3) + 2δ[n] + 5in-11, determine the output yln. 15 points
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0...
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0.9)-10:491 -ones (1,50) s- conv(u,h) 2. Plot h and u using stem function for 50 samples only stem(10:491, s(1:50) 1. Given a system described by the following difference equation: yIn] 1143yn 1 0.4128y[n -2 0.0675x[n0.1349xn 0.675x[n-2] Determine the output y in response to zero input and the initial conditionsy-11 and yl-2] 2 for 50 samples using the following commands: a -,-1.143,...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the giv...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y +...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5)...
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5) Write an expression for the frequency response of the system, H(e/). b. (5) Sketch the magnitude response of the system as a function of frequency over Nyquist interval. (5) Determine the output when the input is xln] 5+2cos(0.5 sequence e. (5) Determine the output when the input is the unit-step sequence uln.
Digital Signal Processing QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Der...
Digital Signal Processing
QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Derive an expression for the output sequence yin], in terms of the input b) sequence, xla], and delayed input and output sequences 10 151 e) Find the unit sample response for the filter (first three terms only)
QUESTION SIX A digital filter system has a transfer...
please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) +...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
1. For a stable and causal filter described by the following difference equation: yIn] = 1.3y[n-1] + 0.4y[n-2] + 2x[...
1. For a stable and causal filter described by the following difference equation: yIn] = 1.3y[n-1] + 0.4y[n-2] + 2x[n] - 1.3x[n-1]. For a sinusoidal input elnnu[n], Determine (a) the steady state response, (b) the transient response, (c) the 60 dB time constant.
1. For a stable and causal filter described by the following difference equation: yIn] = 1.3y[n-1] + 0.4y[n-2] + 2x[n] - 1.3x[n-1]. For a sinusoidal input elnnu[n], Determine (a) the steady state response, (b) the transient response,...
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for inpu...
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
Problem 3: Consider an IIR filter described by the difference equation (a) What is the system function H(a) of this fiter? [5 points) (b) Determine the zeros and poles of the system and sketch the zero-pole plot in z-plane. 5 points (c) Plot the block diagram of this IIR filter. [10 points (d) Given the input zfn-cos(mn/3) + 2δ[n] + 5in-11, determine the output yln. 15 points
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0.9)-10:491 -ones (1,50) s- conv(u,h) 2. Plot h and u using stem function for 50 samples only stem(10:491, s(1:50) 1. Given a system described by the following difference equation: yIn] 1143yn 1 0.4128y[n -2 0.0675x[n0.1349xn 0.675x[n-2] Determine the output y in response to zero input and the initial conditionsy-11 and yl-2] 2 for 50 samples using the following commands: a -,-1.143,...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5) Write an expression for the frequency response of the system, H(e/). b. (5) Sketch the magnitude response of the system as a function of frequency over Nyquist interval. (5) Determine the output when the input is xln] 5+2cos(0.5 sequence e. (5) Determine the output when the input is the unit-step sequence uln.
Digital Signal Processing
QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Derive an expression for the output sequence yin], in terms of the input b) sequence, xla], and delayed input and output sequences 10 151 e) Find the unit sample response for the filter (first three terms only)
QUESTION SIX A digital filter system has a transfer...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
1. For a stable and causal filter described by the following difference equation: yIn] = 1.3y[n-1] + 0.4y[n-2] + 2x[n] - 1.3x[n-1]. For a sinusoidal input elnnu[n], Determine (a) the steady state response, (b) the transient response, (c) the 60 dB time constant.
1. For a stable and causal filter described by the following difference equation: yIn] = 1.3y[n-1] + 0.4y[n-2] + 2x[n] - 1.3x[n-1]. For a sinusoidal input elnnu[n], Determine (a) the steady state response, (b) the transient response,...
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
Most questions answered within 3 hours.
-
Given a standardized normal distribution (with μ = 0 and a σ =
1), what is...
asked 35 minutes ago -
Given the following information:
acetic acid
CH3COOH
Ka = 1.8×10-5
triethylamine
(C2H5)3N
Kb = 5.2×10-4
(1)...
asked 21 minutes ago -
Potassium permanganate(KMNO4)is has a solubility of 6.4 g/ 100 g
of water at 20ºC, and 250...
asked 18 minutes ago -
51.
As the marginal propensity to expend rises, the multiplier:
decreases.
is impossible to determine.
increases....
asked 25 minutes ago -
The Baldwin Company currently has the following balances on their
balance sheet:
Total
Liabilities
$69,309
Common...
asked 28 minutes ago -
A quiet town in Kansas has 10 people, all of whom have the same
preferences. There...
asked 33 minutes ago -
Summarize what an organization needs from a leader.
a. Analyze what might happen to an organization...
asked 36 minutes ago -
How would one critically evaluate an organizations marketing
strategies from the viewpoint of its consumers, as...
asked 35 minutes ago -
Company XYZ know that replacement times for the quartz time
pieces it produces are normally distributed...
asked 50 minutes ago -
A) Write the acid-base reaction that occurs between Na2HPO4 and
NaOH
B) Write the possible reactions...
asked 1 hour ago -
What advantages does the Natural Law Theory have in comparison
with the Divine Command Theory? Explain...
asked 1 hour ago -
A diver comes off a board with arms straight up and legs
straight down, giving her...
asked 1 hour ago