digital control Task 1 Find the Z transform of the causal sequence {xx} where Xx =...
The pole -zero diagram in figure 1 corresponds to the Z-transform [X(z)] of a causal sequence (xIn]). Sketch the pole-zero diagram of Y(z), where y[n]-x-n5]. Also, determine the region of convergence for Y (z). 2. a. (15 Marks) rm z-plane Figure 1 b. Discuss any six applications of Multirate Digital Signal processing or explain the need of Multirate Signal Processing with suitable Example. (10 Marks)
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...
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of the filter, Y(z)= X(z)H(z), for the sequence (i 2* x(n)a. (Use the geometric series 1-c k 0 (ii By using partial fractions, determine the response of the filter, y(n), to the input x(п) %— а". (iii What is the response to the input data x(n) (1)"? [Note: the Z- transform of a sequence x(n) is defined as X(z) x(n)z. The n-0 inverse Z- transform...
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...
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 5: (20=10+5+5 points) Consider a causal system with the following transfer function (the z-transform) 2 +42-2 H2) = 1 - 52-1 +6 1-52-1 +62- 2 2 < 121 <3. (a) Find the inverse z-transform of H(2). (b) Find the difference equation with input-output relation for this system. (c) Draw the diagram of realization (in form II) for this system.
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...
Part 1 (Calculation): The Z-transform (ZT) converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. It is the equivalent of the Laplace transform for discrete systems. The one-sided ZT, used for causal signals and systems, is defined as follows: Consider the digital system (filter) described by the input/output difference equation and z-domain transfer function Hz: yn-0.88 yn-1=0.52 xn-0.4 xn-1 Hzz=Y(z)X(z)=0.52-0.4 z-11-0.88 z-1=0.52 z-0.4z-0.88 Assuming a unit step function input, i.e.,...
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