P9.1 When F(),what ROC corresponds to causal f(n)? P9.4 Find f(n) when F(z) - 4 (ROc...
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...
Q1-20 points) a) Find the transform of the following signals and plot the ROC. 1 x(n)=(-0,357u(n-4)+(0.25?u(n+2) IL- x(n)=-cu-n-1) b) Find the Inverse Z-transform of: z(2-1.5) for (2-0.33)(2-0.5) ROC: z>0.5
Consider the Z-Transform: H(z)= 2-2) a. Find the difference equation for this H() b. Find and sketch the Inverse Z-Transform h(n) for (i) causal andii) mixed cases. Specify which case of ROC corresponds to a stable system.
Problem 4: (a) and (b): Find the z-transform including the ROC for each of the following waveforms: [n] 3(금)"u[n] Xa | 지 = (c) Find the z-transfor by m of the impulse response hn] of an LTI system, when h[n] is given h[n] = 5(을)"u[n]. (d) and (e): Using z-transforms, find the responses (yan] and yb[n]) of the system described in part (c) to the inputs (an andn] described in parts (a) and (b
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.
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...
Question 1 Given a causal LTI system y[k] 0.5yk 1]f[k], with f[k] as input and y[k] as the output. (1) Find the transfer function H(z) and specify its ROC (2) Assume that f[k] -(H u[k] is the input to the LTI system. Use the Z transform's time- convolution property and the inverse Z transform to find the output y[k
Find Z tranform and ROC; Sketch pole zero x[n]=(2/3)^n u[-n-1]+(-(1/3))^n u[n]
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...
digital control Task 1 Find the Z transform of the causal sequence {xx} where Xx = (-1)". 2 Find the Z transform of the causal sequence {xx} where Xx = 4k - 2ak. 3 Find the Z transform of the causal sequences: (a) {k - 3} (b) {3k+2} 4 Find the inverse Z transformation of z? (2-3) F(z) = (22 - 22 + 1)(z - 2)