What is the z-transform of y(n)? ~() = - (*)-(---) - (5) *(-1-1) Mark the correct...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
Solve these examples in detailed step wise
EXAMPLE 3.4.5 Determine the partial-fraction expansion of the proper function X(2) = 1- 1.52-1 +0.52-2 EXAMPLE 3.4.7 Determine the partial-fraction expansion of (1+z-1)(1 - 2-1)2 EXAMPLE 3.4.8 Determine the inverse z-transform of X (2) = 1-1.52-1 +0.52-? (a) ROC: Iz/ > 1 (b) ROC: Iz1 <0.5 (e) ROC: 0,5 < Iz <1 EXAMPLE 3.4.10 Determine the causal signal x(n) having the z-transform X(z) = (1 + 2-1) (1 - 2-1)2 EXAMPLE 3.5.2 A...
Problem 5. Determine the z-transform of the signal x[n] :=(-1)"nu[n]. You may use already known z-transforms, such as those listed in Table 5.1 (page 492) of the textbook, and properties of the z-transform. Moreover, notice that -1 = ejt. TABLE 5.1 Select (Unilateral) Z-Transform Pairs x[n] X[z] 8[n-k] ? 2-1 ոս[ո] (z - 1) z(z+1) (2-1)3 nºu[n] nu[n] z(z? + 4z +1) (2-1) Yºu[n] yn-u[n- 1] z-y 12 ny"u[n] (z-7) yz(z+y) (z-7)3 ny"u[n] n(n - 1)(n-2) (n-m+1) ym! lyl" cos...
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...
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...
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...
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
Question 1: (35 points: Consider the following sequences: x[n] = u[n] + 4" u[-n- 1] y[n] = x[n - 5) a) [10 points| Determine the Z-transform X(z) b) [10 points| Determine and draw the Region of Convergence (ROC) of x(n) c) [10 points] Determine the z-transform Y(z) d) [05 points) Determine the transfer function H(z)=Y(z)/X(z)
1. A linear time-invariant system hn is characterized by the following z transform function 3-42-1 1-3.5+1.5-2 (a) Calculate the poles and zeros manually. Plot the poles and zeros using Matlab. Does Matlab result agree with your calculation? (b) If the system is stable, specify the ROC of H(z) and determine hn (c) If the system is causal, specify the ROC of H(z) and determine hn
Problem 3 (30 points) An LTI system has an impulse response hin], whose z-transform equals 1-1 1. List all the poles and zeros of H(2). Sketch the pole-zero plot.. 2. If this system is causal, provide the ROC of H(2) and the expression of hin. case, is this system also stable? 3. If the ROC of H(z) does not exist, provide and the expression of hn.