2.40. The discrete-time system shown in Fig. 2-29 consists of two unit delayelements and two scalar multipliers. Write a difference equation thatrelates the output y[n] and the input x[n].x[n]UnitUnityln -2) delayyln - 1]delayFig. 2-29In Fig. 2-29 the output of the first (from the right) unit delay element isy[n - 1] and the output of the second (from the right) unit delay elementis yln - 2). Thus, from Fig. 2-29 we see thatyln] = a,yln - 1] + a,yln – 2] + x[n](2.144)oryln] - a,yln - 1]- a,yln - 2] n](2.145)which is the required second-order linear difference equation.Note that, in general, the order of a discrete-time LTI system consist-ing of the interconnection of unit delay elements and scalar multipliers isequal to the number of unit delay elements in the system.

A linear constant coefficient difference equation serves as a way to express just this relationship…

2.40. The discrete-time system shown in Fig. 2-29 consists of two unit delay elements and two scalar multipliers. Write a difference equation that relates the output y[n] and the input x[n]. Unit Unit yln - 21 delay yln-1] delay Fig. 2-29 In Fig. 2-29 the output of the first (from the right) unit delay element is y[n - 1] and the output of the second (from the right) unit delay element is y[n - 2). Thus, from Fig. 2-29 we see that yln] a,yln-11 + a,yln- 21 +x[n] (2.144) or yln] - a,yln- 1]-a,yln- 2] n] (2.145) which is the required second-order linear difference equation. Note that, in general, the order of a discrete-time LTI system consist- ing of the interconnection of unit delay elements and scalar multipliers is equal to the number of unit delay elements in the system.

2.40. The discrete-time system shown in Fig. 2-29 consists of two unit delay elements and two scalar multipliers. Write a difference equation that relates the output y[n] and the input x[n]. Unit Unit yln - 21 delay yln-1] delay Fig. 2-29 In Fig. 2-29 the output of the first (from the right) unit delay element is y[n - 1] and the output of the second (from the right) unit delay element is y[n - 2). Thus, from Fig. 2-29 we see that yln] a,yln-11 + a,yln- 21 +x[n] (2.144) or yln] - a,yln- 1]-a,yln- 2] n] (2.145) which is the required second-order linear difference equation. Note that, in general, the order of a discrete-time LTI system consist- ing of the interconnection of unit delay elements and scalar multipliers is equal to the number of unit delay elements in the system.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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