![3) Given the system function of a discrete time filter 1-2z-1 10.4z-1 with R. 0. C: Iz| > 0.4 The unit sample response h[n] is a) h[n] =-58m] 6(0.4)u[n] b) h[n]- -56[n] 60-0.4)ufn] c) h[n] = (-0.4n)2[n]-2 (-0.4n-1)u[n-1] d) h[n] = (-0.4)u[n]-2(-0.4)-111[n-1] e) b and c f) b and d g) a and d h) a and c i) none of the above hint: use Partial Fraction Expansion](http://img.homeworklib.com/questions/a660c8a0-cfca-11ea-a858-7767f1414cf2.png?x-oss-process=image/resize,w_560)
Homework Answers
3) Answer :-
The unit sample response h[n] is option d
Explanation :-
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3) Given the system function of a discrete time filter 1-2z-1 10.4z-1 with R. 0. C:...
A discrete time LTI filter at rest is given by its system function H(z), 1+z-1 H2)...
A discrete time LTI filter at rest is given by its system function H(z), 1+z-1 H2) = 1-0 8-1 R.O.C [z] > 0.8 (Hint: Use the z-transform and Partial Fraction Expansion to fill in the blanks.) The steady state unit-step response of the above filter is: Yuss [n] = — u[n]
The transfer function of a system is given by H(z)= Z/((z^2-0.8z+ 0.15)). To such a system...
The transfer function of a system is given by H(z)= Z/((z^2-0.8z+ 0.15)). To such a system we apply an input of the type x[n]=e^(-0.4n) "for n"≥0 . Find the response of the system in n domain using MATLAB for obtaining the partial fraction expansion and then manually inverting the output using z-transform tables.
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
a. b. c. d. An IIR filter has the difference equation: y'n Select the correct transfer function for this system...
a.
b.
c.
d.
An IIR filter has the difference equation: y'n Select the correct transfer function for this system from the selections below. 2+1.2 No transfer function exists for this system. H(0.5+1.2Y(2)21 2+0.5 H(2)220.5z +1.2 An IIR filter has the transfer function: H(z) 22 +0.92-0.14 Select the correct impulse response for this system from the selections below hn 2(0.2)n-1un - 1] - 2(0.7)n-uln - 1 -hin] = 2(-0.2)"u[n]-2(-0.7)"u[n] hin] = 2(-0.2)"-iuln-11-2(-0.7)"-1 u[n-1] No impulse response exists for this system....
Solve these examples in detailed step wise EXAMPLE 3.4.5 Determine the partial-fraction expansion of the proper...
Solve these examples in detailed step wise
EXAMPLE 3.4.5 Determine the partial-fraction expansion of the proper function X(2) = 1- 1.52-1 +0.52-2 EXAMPLE 3.4.7 Determine the partial-fraction expansion of (1+z-1)(1 - 2-1)2 EXAMPLE 3.4.8 Determine the inverse z-transform of X (2) = 1-1.52-1 +0.52-? (a) ROC: Iz/ > 1 (b) ROC: Iz1 <0.5 (e) ROC: 0,5 < Iz <1 EXAMPLE 3.4.10 Determine the causal signal x(n) having the z-transform X(z) = (1 + 2-1) (1 - 2-1)2 EXAMPLE 3.5.2 A...
A causal discrete-time LTI system is described by the equation
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
need asap 1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as...
need asap
1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as following h(t) 6u(t) where u(t) is unit step function. The output(Y (s)) is expressed as the product of input (R(s)) and transfer function Y(s) = R(s)H(s) The Laplace transform is defined as LTI system R(H) Y (s) Figure 1: LTI system in s-plane (a) (5 points) Find the tranisfer function(H(s)) of the LITI system. (b) (5 points) Find the Laplace transform of the input(r(t)....
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of...
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of the filter, Y(z)= X(z)H(z), for the sequence (i 2* x(n)a. (Use the geometric series 1-c k 0 (ii By using partial fractions, determine the response of the filter, y(n), to the input x(п) %— а". (iii What is the response to the input data x(n) (1)"? [Note: the Z- transform of a sequence x(n) is defined as X(z) x(n)z. The n-0 inverse Z- transform...
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.
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polyno...
Please do part C only, thank you.
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polynomials, ratios of polynomials, partial fraction expansions and transfer functions: see, for example, the commands roots, poly, conv, residue, zpk and tf (a) Use MATLAB to gener ate the continuous-time transfer function H5+15)( +26(s+72) s(s +56)2(s2 +5s +30) H(s) displaying the result in two forms: as (i) the given ratio of factors and (ii) a ratio of two polynomials. (b) Use...
A discrete time LTI filter at rest is given by its system function H(z), 1+z-1 H2) = 1-0 8-1 R.O.C [z] > 0.8 (Hint: Use the z-transform and Partial Fraction Expansion to fill in the blanks.) The steady state unit-step response of the above filter is: Yuss [n] = — u[n]
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
a.
b.
c.
d.
An IIR filter has the difference equation: y'n Select the correct transfer function for this system from the selections below. 2+1.2 No transfer function exists for this system. H(0.5+1.2Y(2)21 2+0.5 H(2)220.5z +1.2 An IIR filter has the transfer function: H(z) 22 +0.92-0.14 Select the correct impulse response for this system from the selections below hn 2(0.2)n-1un - 1] - 2(0.7)n-uln - 1 -hin] = 2(-0.2)"u[n]-2(-0.7)"u[n] hin] = 2(-0.2)"-iuln-11-2(-0.7)"-1 u[n-1] No impulse response exists for this system....
Solve these examples in detailed step wise
EXAMPLE 3.4.5 Determine the partial-fraction expansion of the proper function X(2) = 1- 1.52-1 +0.52-2 EXAMPLE 3.4.7 Determine the partial-fraction expansion of (1+z-1)(1 - 2-1)2 EXAMPLE 3.4.8 Determine the inverse z-transform of X (2) = 1-1.52-1 +0.52-? (a) ROC: Iz/ > 1 (b) ROC: Iz1 <0.5 (e) ROC: 0,5 < Iz <1 EXAMPLE 3.4.10 Determine the causal signal x(n) having the z-transform X(z) = (1 + 2-1) (1 - 2-1)2 EXAMPLE 3.5.2 A...
need asap
1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as following h(t) 6u(t) where u(t) is unit step function. The output(Y (s)) is expressed as the product of input (R(s)) and transfer function Y(s) = R(s)H(s) The Laplace transform is defined as LTI system R(H) Y (s) Figure 1: LTI system in s-plane (a) (5 points) Find the tranisfer function(H(s)) of the LITI system. (b) (5 points) Find the Laplace transform of the input(r(t)....
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of the filter, Y(z)= X(z)H(z), for the sequence (i 2* x(n)a. (Use the geometric series 1-c k 0 (ii By using partial fractions, determine the response of the filter, y(n), to the input x(п) %— а". (iii What is the response to the input data x(n) (1)"? [Note: the Z- transform of a sequence x(n) is defined as X(z) x(n)z. The n-0 inverse Z- transform...
Please do part C only, thank you.
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polynomials, ratios of polynomials, partial fraction expansions and transfer functions: see, for example, the commands roots, poly, conv, residue, zpk and tf (a) Use MATLAB to gener ate the continuous-time transfer function H5+15)( +26(s+72) s(s +56)2(s2 +5s +30) H(s) displaying the result in two forms: as (i) the given ratio of factors and (ii) a ratio of two polynomials. (b) Use...
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