For each of the following discrete systems described by either its transfer function or its unit...
b) The transfer function of a causal linear time-invariant (LTI) discrete-time system is given by: 1+0.6z1-0.5z1 i Does the system have a finite impulse response (FIR) or infinite 3 impulse response (IIR)? Explain why. ii Determine the impulse response h[n] of the above system iii) Suppose that the system above was designed using the bilinear transformation method with sampling period T-0.5 s. Determine its original analogue transfer function. b) The transfer function of a causal linear time-invariant (LTI) discrete-time system...
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.
Please show all the steps clearly. Find the system transfer function of a causal LSI system whose impulse response is given by 2. 0.5)"l sin[0.5(n- 2)]u[n - 2] and express the result in positive powers of z. 72-1 h[n] = Hint: The transfer function is just the z-transform of impulse response. However, we must first convert the power of -0.5 from (n - 1) to (n - 2) by suitable algebraic manipulation Find the system transfer function of a causal...
(1) When a polynomial for the numerator of a transfer function is represented by the vector [1 3 0j in Matlab, what is the polynomial (in )? Ss35 (2) What is the final value of a response which is given b1612 (o)- (0)-3(0)3 ()undefined (3) Determine the damping ratio of the system described by)235 )1(b) 2.5 (c)5 (d) 10 (e) 25 (f) something else (4) (True or alse) The system with the following characteristic equation is stable. (5) Marginally stable...
Please show the solution to the problem above 15. A discrete-time system has a transfer function (the z transform of its impulse response) H)Ifa unit sequence 24 . If a unit sequence and y[2]? + z + u[n] is applied as an excitation to this system, what are the numerical values of the responses y[O]. y
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u/n), where u/h) is the unit step and B is an arbitrary constant (B>0), Take y-1)-0. Answer with either causal or 'anticausal only QUESTION 2 For the following system: yn) -yn-1Va -x(n), for a 0.9, find y(10), assuming y(n) - o, for ns -1.Hint: find a closed form for yin) and use it to find the required output sample. (xin)-1 for n>-0) QUESTION 3 A filter has the...
Convert the following continuous time transfer function to discrete time transfer functions with sampling rates of 0.01 and 0.1. Write with an equation editor the two discrete transfer functions. Next apply a unity feedback to the continuous transfer function and the two discrete transfer functions. Based on the poles of the closed-loop continuous transfer function, is the system stable? Why? Plot the poles of the discrete transfer functions on the z-plane. Are the two systems stable and why?
Each of the following equations specifies an LTID system. Determine whether these systems are asymptotically stable, unstable, or marginally stable. 9.6-1 (a) yk 20.6y[k + 1] - 0.16y[k] = f k + 1 - 2flk] (b) (Е? (c) (E 1Ey{k] = (E + 2)fjk] (d) yk2y(k]0.96y(k - 2] 2flk - 1] +3f(k - 3] (e) (E2- 1)(E +E+1)уk] 3DEflk] +1)yk fk] Each of the following equations specifies an LTID system. Determine whether these systems are asymptotically stable, unstable, or marginally...
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
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?