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We found transfer function H(z) by z transform
After taking inverse of H(z), we found system stable as every pole lies inside unit circle. So it's a stable system.
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2. A discrete time LTI system is described by the difference equation (assume initial conditions are...
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.
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)...
A causal LTI system is described by the following difference equation:
A causal LTI system is described by the following difference equation: y(n) – Ay(n-1) - 2A2y(n − 2) = x(n) – 2x(n-1) + x(n–2), where A is a real constant. Determine the z-domain transfer function, H(z), of the system in terms of A.
Consider a discrete-time system described by the following difference equation. y(n) = y(n−1)−.24y(n−2) + 2x(n−1)−1.6x(n−2) Find...
Consider a discrete-time system described by the following difference equation. y(n) = y(n−1)−.24y(n−2) + 2x(n−1)−1.6x(n−2) Find the transfer function H(z). Find the zero-state response to the causal exponential input x(k) = .8nµ(n). This means that given H(z), we can calculate Y(z) and subsequently the output, y(n) with all initial conditions presumed to be zero. Hence the term, zero-state.
[2 Marks] 18. If (z) and u[n]-cos(2n)지지 the correct value of V(z) will be (2z-1) js 2 2zei5-1 2ze-15-1 2 2zel5-12ze-15-1 19. Determine the Z-transform of x[n]. [2 Marks each] n] sinl0n)u[n]0.3"...
[2 Marks] 18. If (z) and u[n]-cos(2n)지지 the correct value of V(z) will be (2z-1) js 2 2zei5-1 2ze-15-1 2 2zel5-12ze-15-1 19. Determine the Z-transform of x[n]. [2 Marks each] n] sinl0n)u[n]0.3" n] 0.5" cos (10n)u[n] In]-(0.3) u[/n] The transfer function of a discrete time system is H(z)- 20. 1+2z3z Use the inverse Z-transform to determine the system difference equation [4 Marks] 21. An LTI system is described by the following input/output difference equation: yln] 0.12yln x[n] (assume zero initial...
2. (a) For each sample of a discrete time signal x[n] as input, a system S...
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the...
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the pole-zero plot for this system. How many possible (ROCs) are there for H(z). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to (b) Which ROC (or ROCs) correspond to a stable system? Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to the output...
A discrete-time LTI system has the system function H(z) given below:
A discrete-time LTI system has the system function \(H(z)\) given below:$$ H(z)=\frac{z^{2}}{z^{2}-\frac{1}{4}} $$(a) Sketch the pole-zero plot for this system. How many possible regions of convergence (ROCs) are there for \(H(z)\). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to.(b) Which ROC (or ROCs) correspond to a stable system? Why?(c) Which ROC (or ROCs) correspond to a causal system? Why?(d) Write a difference equation that relates the input to the output of...
discrete time signals and systems causal LTI system has the block diagram: (a) find a difference...
discrete time signals and systems
causal LTI system has the block diagram:
(a) find a difference equation relating y[n] and x[n]
(b) determine if the system is stable
// هبه ۸[u] [u]x
[2 Marks] 18. If (z) and u[n]-cos(2n)지지 the correct value of V(z) will be (2z-1) js 2 2zei5-1 2ze-15-1 2 2zel5-12ze-15-1 19. Determine the Z-transform of x[n]. [2 Marks each] n] sinl0n)u[n]0.3" n] 0.5" cos (10n)u[n] In]-(0.3) u[/n] The transfer function of a discrete time system is H(z)- 20. 1+2z3z Use the inverse Z-transform to determine the system difference equation [4 Marks] 21. An LTI system is described by the following input/output difference equation: yln] 0.12yln x[n] (assume zero initial...
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the pole-zero plot for this system. How many possible (ROCs) are there for H(z). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to (b) Which ROC (or ROCs) correspond to a stable system? Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to the output...
A discrete-time LTI system has the system function \(H(z)\) given below:$$ H(z)=\frac{z^{2}}{z^{2}-\frac{1}{4}} $$(a) Sketch the pole-zero plot for this system. How many possible regions of convergence (ROCs) are there for \(H(z)\). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to.(b) Which ROC (or ROCs) correspond to a stable system? Why?(c) Which ROC (or ROCs) correspond to a causal system? Why?(d) Write a difference equation that relates the input to the output of...
discrete time signals and systems
causal LTI system has the block diagram:
(a) find a difference equation relating y[n] and x[n]
(b) determine if the system is stable
// هبه ۸[u] [u]x
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