Signals and Systems

SHORT QUESTIONS AND ANSWERS

 

Q1. Define the following:

(i) zero input response (ii) zero state response (iii) characteristic polynomial (iv) characteristic equation and (v) eigen values

Ans.:

(i) Zero Input Response (ZIR): The response which occurs even without input is known as zero input response and it is due to initial condition.

 

ZIR = Φ(k) x(0) = A^k x(0)

where           Φ(k) = A ^kis termed as the state transition matrix.

(ii) Zero State Response: The response which occurs when all initial conditions are zero is known as zero state response.

 

 

(iii) Characteristic Polynomial: The characteristic polynomial of the matrix A of order