Answered: calculate impulse response for- i)…

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...

See similar textbooks

Related questions

Question

calculate impulse response for-

i) y_m(k)=y(k)+n(k)

and

ii) y(k+1)=y(k)+w(k)

Expert Solution

Step 1

Given two difference equations as follows:

i) y_m(k)=y(k)+n(k)

and

ii) y(k+1)=y(k)+w(k)

we need to obtain impulse response for the two system of equations.

Step 2

Finding the impulse response for the first difference equation:

As you have not mentioned whether the system of equation is in continuous time domain or discrete time domain, we have considered it in discrete time domain.

First let us Z-transform the system of equation given in discrete time domain.

$y_{m} (k) = y (k) + n (k) δ (k - m) y (k) = y (k) + n (k), {(as y}_{m} (k) {represents m}^{t h} term of y (k)) δ (k - m) y (k) = y (k) + n (k) \overset{Z}{\leftrightarrow} Z^{- m} Y (k) = Y (k) + N (k)$

Thus, the Z transform of the difference equation is :

$Z^{- m} Y (z) = Y (z) + N (z) Y (z) (Z^{- m} - 1) = N (z) \frac{Y (z)}{N (z)} = \frac{1}{(Z^{- m} - 1)} Now for impulse response input n (k) = δ (k) \overset{Z}{\leftrightarrow} N (z) = 1 S o, Y (z) = \frac{1}{(Z^{- m} - 1)} N (z) = \frac{1}{(Z^{- m} - 1)} = - \frac{1}{1 - Z^{- m}} N o w, Y (z) \overset{Z^{- 1}}{\leftrightarrow} y (k) = - u (\frac{k}{m})$

Thus, the impulse response for the first difference equation is $- u (\frac{k}{m})$ .

Step by step

Solved in 3 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions