Find a closed-form of the z-transform of x[n]= -(0.6)^-n, for n = -999 to -1
Find a closed-form of the z-transform of x[n]= -(0.6)^-n, for n = -999 to -1
2+z-1 1. The Z-transform of a signal x[n] is given as X(z) = }</21 < a) Find the signal x[n] [7] b) Draw the pole – zero plot of the z-transform .[3] c) Is x[n] causal or not? Justify your answer [2]
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the Inverse Z-transform of given function. a) R(Z) =- (1-e") (-(z-e-ar) 3 +282+8-1 b) F (Z) = (2-2)2(2+2) Find the Z-Transform of X2 [x] = X1 [n + 3] u [n] 3- Solve the difference equation 3 4 With initial conditions y-1] 1 and yl-2] 3 4- Let the step response of a linear, time-invariant, causal system be 72 3) ulnl 15 3 a) Find the...
(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)...
3. (20%) The Z-Transform of x[n] is X(2), 72(152 – 3) WA(Z-0.25) (7z – 1) Find a. the signal x[n]. b. If y[n] = x[n], n=1..-5, y[n] = 0 elsewhere. Find the Z-transform Y(2).
3. The signal x[n] =-(b)”u[-n – 1]+ (0.5)”u[n], a) find the z-transform X(z) [5] b) plot the ROC. [3] С
(a) Find the z-transform of (i) x[n] = a"u[n] + B^u[n] + cºul-n – 1], lal< 161 < le| (ii) x[n] = n-au[n (iii) x[n] = {** [cos (Tan)]u[n] -em* [cos (fin)]u[n – 1]
solve the fibinacci recursion formula to a closed form usung the inverse z-transform Z --U Fix is furtf 6 F-1 = f -z = 1 fica fkul + F 1 U = Z CU U 42
For x[n]-(0.3). 1. a. (2 pts) Find the z-transform, X(z b. (3 pts) Sketch the pole-zero plot. c. (3 pts) Find the region of convergence of the transform. Sketch it in the z-plane. d. (3 pts) Use your answer in part a to write down the DTFT of x,[n]=(0.3)"u[n]. Why is it necessary to multiply by the unit step function to get the DTFT?
Using the z-Transform Tables, find the inverse z-Transform of the following function, this is, find y[n] find the inverse z-Transform of the following function, this is, find y[n] z Y(z) = 2 + 1.5z + + 0.25 z z+1 (2-1)2 (2+0.5)
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...