2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the ...
Please solve the following with full steps. 2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
4- Let the step response of a linear, time-invariant, causal system be (-1).uln] ylnl.ynl-ler uln].. 15 3 3 12 a) Find the transfer function H(Z) of this system b) Find the impulse response of the system. Is this system stable? c) Find the difference equation representation of this system. 4- Let the step response of a linear, time-invariant, causal system be (-1).uln] ylnl.ynl-ler uln].. 15 3 3 12 a) Find the transfer function H(Z) of this system b) Find the...
Use the Z-transform to find the general solution (zero-input and zero-state) for the following linear recursive difference equation written in advanced form: y[n+2] +3y[n+1]+2y[n] = 2x[n+2] A. Use the Z-transform to find the zero-input solution with initial conditions: y[-2]=2, and y(-1)=3 B. Use the Z-transform to find the zero-state solution if the source function is given by, x[n]=3" u[n] C. Write the general solution to the linear recursive difference equation D. Use the Z-transform to find the transfer function (H(z))...
(a) Find the z-transform of (i) x[n] = a"u[n] +b"u[n] + cºul-n – 1], lal <151 < le|| (ii) x[n] = n*a"u[n] (iii) x[n] = en* [cos (în)]u[n] – en" (cos (ien)] u[n – 1] (b) 1. Find the inverse z-transform of 1-jz-1 X(2) = (1+{z-1)(1 – {z-1) 2. Determine the inverse z-transform of x[n] is causal X(x) = log(1 – 2z), by (a) using the power series log(1 – x) = - 95 121 <1; (b) first differentiating X(2)...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference equation for the system specified by H(z) b) Assuming the system is causal, determine the impulse response hln]. c) Is it possible to find an h[n] that is stable? If not, explain why. If it is possible, determine h[n] for this case.
?3: (a). Find the Z-Transform of h(t)-1 (?[n] + fin-1] + ?[n-21 + fin-31) (b). Find the unit impulse response corresponding to the following system (c)Plot the region of convergence and the Z transform for ln"un], where uin- 0 elscwhere and a is
uestion A causal, linear time-invariant system is excited with an input x (n) described as x(n) 3u(n) with the output y(n) of the system as follows: 7l n) -2"u(n) y(n)- a) Determine z-transform X(z) and Y (z) (4 marks) b) Determine the transfer function H(z). (3 marks) Based on (b), determine the impulse response h(n). Based on (b), sketch the z-plane for the transfer function of the system Based on (d), determine the stability of the system and discuss the...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...