What is the partial fraction expansion of this Z-Transform? What is the pole zero plot look like?

Give me the proof of time shifting property of Z transform.

Problem 4: By using the inversion integral method, obtain the inverse z transform of: 1+ 6z-2 +z-3 X(z) : (1 – z-1)(1 – 0.2z-1)

Calculate the next z transform using the properties of the z transform.

Design a one-stage Butterworth RC low-pass filter with a cutoff frequency of 100 Hz at-3 dB if the source and load impedances are 50 0. Calculate the expected dynamic error and attenuation at 192 Hz in the realized filter. KNOWN f= 100 Hz k = 1 FIND C and &

Question 2 (a) Determine the z-transform, including the ROC in z-plane and a sketch of the pole-zero-plot, for sequence: *[„]= a"u[n] (b) ) For the z-transform H(z) = 1/ (1 – 4z)( 1 /4 – v3/2z + z²) 2 Determine possible regions of convergence. In each case comment stability and causality of the system whose transfer function is H(z). What is the output of the stable system to the input x(n) = 2cos(nt/2)? (c) A causal discrete-time signal x(n) has the Fourier transform X(e"). Write its z-transform in terms of the Fourier transform of the discrete-time signal, i.e., write the z-transform value based on its values on the unit circle.

Engineering Analysis Z-Transform - Properties .W 4: Determine the z transforms of the sequences (a) {(-}'}

What will be the z transform of the DT Dirac delta function? Show detailed calculation

3. Find the inverse z-transform of each of the following z-transforms. Determine the poles and zeros of each z-transform. a) X(z) = b) X(z) = c) X(z) = d) X(z) = 1-z-1 1-42-2 1-z-1 1-42-2 |z|>2 |z| 3 1 (1-32-1)2 12>2