Please solved it in time domain No z domain Consider the following discrete-time LTI system ?[?]...
Please solved it in time domain No z domain
Consider the following discrete-time LTI system ?[?] − 0.3?[? − 1] − 0.04?[? − 2] = ?[?] + 2?[? − 1] with the initial conditions ?[−1] = 3, and ?[−2] = 0, and the input ?[?] = 3??[?].
(a) Determine the total solution, analytically. (b) Determine the total solution using MATLAB. Compare the results between (a) and (b) by plotting the difference for 0 ≤ ? ≤ 20
(c) Determine the zero-input response, analytically.
(d) Determine the zero-input response using MATLAB. Compare the results between (c) and (d) by plotting the difference for 0 ≤ ? ≤ 20
(e) Determine the zero-state response, analytically.
(f) Determine the zero-state response using MATLAB. Compare the results between (e) and (f) by
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Please solved it in time domain No z domain
Consider the following discrete-time LTI system ?[?]...
Consider the following discrete-time LTI system ?[?] − 0.3?[? − 1] − 0.04?[? − 2] =...
Consider the following discrete-time LTI system ?[?] − 0.3?[? − 1] − 0.04?[? − 2] = ?[?] + 2?[? − 1] with the initial conditions ?[−1] = 3, and ?[−2] = 0, and the input ?[?] = 3??[?]. (a) Determine the total solution, analytically. (b) Determine the total solution using MATLAB. Compare the results between (a) and (b) by plotting the difference for 0 ≤ ? ≤ 20 (c) Determine the zero-input response, analytically. (d) Determine the zero-input response using...
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.
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
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...
BC:9.4 A LTI discrete time system has an impulse response h[n] = (−0.6)nu[n] + (0.95)nu[n −...
BC:9.4 A LTI discrete time system has an impulse response h[n] =
(−0.6)nu[n] + (0.95)nu[n − 1] Find the transfer function, Hˆ (e jωˆ
), in the normalized frequency domain. Use Matlab to plot the
magnitude and phase (in degrees) of Hˆ (e jωˆ ) in the range of −π
≤ ωˆ ≤ π. Attach your Matlab source code with the plots.
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.6)"u[n] + (0.95)"u[n-1] Find the transfer...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Deter...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1)...
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1) u[n]. Use Fourie transforms to determine the response of this system to the input x[n] = ml + un).
The following is known about a discrete-time LTI system with input rn] and output vin: (a)...
The following is known about a discrete-time LTI system with input rn] and output vin: (a) If x[n] = (-2)" for all n, then y[n] = 0 for all n. (b) If r/n] (1/2)"u[n] for all n, then y[n is of the form: where a is a constant (c) Determine the value of the constant a. (d) Determine the response vinl if the input lnl is n for all n.
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n)...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
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...
BC:9.4 A LTI discrete time system has an impulse response h[n] =
(−0.6)nu[n] + (0.95)nu[n − 1] Find the transfer function, Hˆ (e jωˆ
), in the normalized frequency domain. Use Matlab to plot the
magnitude and phase (in degrees) of Hˆ (e jωˆ ) in the range of −π
≤ ωˆ ≤ π. Attach your Matlab source code with the plots.
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.6)"u[n] + (0.95)"u[n-1] Find the transfer...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1) u[n]. Use Fourie transforms to determine the response of this system to the input x[n] = ml + un).
The following is known about a discrete-time LTI system with input rn] and output vin: (a) If x[n] = (-2)" for all n, then y[n] = 0 for all n. (b) If r/n] (1/2)"u[n] for all n, then y[n is of the form: where a is a constant (c) Determine the value of the constant a. (d) Determine the response vinl if the input lnl is n for all n.
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
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