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The output of a discrete-time system is related to the input by Y(n) x(n is 1...
1.3. Assume a discrete-time system with input u(k) and output y(k). The system has a constant...
1.3. Assume a discrete-time system with input u(k) and output y(k). The system has a constant input disturbance d. Find the augmented state-space model with input Au(k) and output y(k) for the plant model given as below: Im(k +1) = AmIm (k) + Bmu(k) + Bad; y(k) = Cmlm (k) (1.82) [10.5 0 ] [ 0.51 where Am = 0.1 -0.1; Bm = 1 ; Cm = [101]; Ba= 100 0.8 -0.6 1. Calculate the plant transfer function that relates...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) -----------------...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) ------------------------------------------------------------------------------------------------------------------------- Q2) The random process X(t) is called a white Gaussian noise process if X(t) is a stationary Gaussian random process with zero mean, and flat power spectral density, Let X(t) be a white Gaussian noise process that is input to...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n]...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
(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...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]....
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
Consider the discrete-time system with input x[n] and output y[n] described by : y[n]=x[n]u[2-n] Which of the...
Consider the discrete-time system with input x[n] and output y[n] described by : y[n]=x[n]u[2-n] Which of the following properties does this system possess? Justify your answer in each case. Do not use Laplace transforms a) Memoryless b)Time-invariant c) Linear d)Casual e) Stable
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
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...
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.
1.3. Assume a discrete-time system with input u(k) and output y(k). The system has a constant input disturbance d. Find the augmented state-space model with input Au(k) and output y(k) for the plant model given as below: Im(k +1) = AmIm (k) + Bmu(k) + Bad; y(k) = Cmlm (k) (1.82) [10.5 0 ] [ 0.51 where Am = 0.1 -0.1; Bm = 1 ; Cm = [101]; Ba= 100 0.8 -0.6 1. Calculate the plant transfer function that relates...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
(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...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
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...
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