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(a) For the discrete-time signal given by x[n] = (1/6)"u[n-2] (i) Using the Z-transform definition, find its Z-transform, X(z). (ii) Plot the pole/zero diagram, shading the ROC. 4.

(a) For the discrete-time signal given by x[n] = (1/6)"u[n-2] (i) Using the Z-transform definition, find its Z-transform, X(z). (ii) Plot the pole/zero diagram, shading the ROC. 4.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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4. (a) For the discrete-time signal given by x[n] = (1/6)*u[n-2] (i) Using the Z-transform definition, find its Z-transform, X(z). (ii) Plot the pole/zero diagram, shading the ROC. (b) For the two systems with impulse responses hi[n] = (0.5)" u[n] h2[n] = (2)ªu[n] Write down their transfer functions, H1(z) and H2(z). Don't forget to include the corresponding ROCS. and (i) If we connect H1(z) and H2(z) in cascade, the resulting cascade interconnection will have a combined transfer function calculated by (ii) H(z) = H1(z).H2(z),
Transcribed Image Text:4. (a) For the discrete-time signal given by x[n] = (1/6)*u[n-2] (i) Using the Z-transform definition, find its Z-transform, X(z). (ii) Plot the pole/zero diagram, shading the ROC. (b) For the two systems with impulse responses hi[n] = (0.5)" u[n] h2[n] = (2)ªu[n] Write down their transfer functions, H1(z) and H2(z). Don't forget to include the corresponding ROCS. and (i) If we connect H1(z) and H2(z) in cascade, the resulting cascade interconnection will have a combined transfer function calculated by (ii) H(z) = H1(z).H2(z),
Determine the transfer function interconnection of the two systems for the specific values of H1(z) and H2(z) given in part (b)(i) above. Find all the poles and zeros for the cascade system and indicate them on the pole-zero plot shading the ROC. for a cascade
Transcribed Image Text:Determine the transfer function interconnection of the two systems for the specific values of H1(z) and H2(z) given in part (b)(i) above. Find all the poles and zeros for the cascade system and indicate them on the pole-zero plot shading the ROC. for a cascade
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