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.
A causal LTI system is described by the following 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 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)...
2. A discrete time LTI system is described by the difference equation (assume initial conditions are zero) y[n] + y[n – 1] = x[n] + 1/4x[n – 1] – 1/8x[n – 2] a) Find the transfer function of the system H(z). b) If you take the inverse of the transfer function (1/H(z)), is the system stable? Prove yes or no.
Problem 4. (20 points): Consider a causal LTI system that is described by the difference equation Find the impulse response sequence h[n] by computing the system function H(S2)
Consider an LTI system defined by the difference equationy[n] = -2x[n] + 4x[n-1] - 2x[n-2] (a) Determine the impulse response of this system. (b) Determine the frequency response of this system. Express your answer in the form H(ejw) = A(ejw)e-jwndwhere A(ejw) is a real function of w. Explicitly specify A(ejw) and the delay nd of this system
7. A causal LTI system has a transfer function given by H (z) = -1 (1 4 The input to the system is x[n] = (0.5)"u[n] + u[-n-1] ) Find the impulse response of the system b) Determine the difference equation that describes the system. c) Find the output y[n]. d) Is the system stable?
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a) What is the transfer function of the system? b) Sketch the impulse response of the system
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
can you please post the answer thanks FE yIn] x[n] -2 3. Given the causal LTI system with signal flow graph as shown (a) Determine the system function H(z) (5) (b) Determine the minimum multiply linear constant coefficient /O difference equation relating y[n] with x[n]. (10) EENG751 5/13/2019 FE yIn] x[n] -2 3. Given the causal LTI system with signal flow graph as shown (a) Determine the system function H(z) (5) (b) Determine the minimum multiply linear constant coefficient /O...