Question

The general solution of natural response is of the form of _________

(a) yh (n)= c1 λ1^n+c^2λ^2^n+⋯+cNλN^n

(b) yh (n)= c1 λ1^n+c^2λ^2^n+⋯+cNλN^n

(c) yh (n)= c1 λ1^2+c2λ2^2+⋯+cNλN^2

(d) yh(n)= c1 λ1^n-c^2λ^2^n+⋯+cNλN^n

The question was asked at a job interview.

The above asked question is from Discrete-Time Systems in the Time-Domain topic in section Signals and Systems Basics of Signals and Systems

Answer 1

The correct answer is (a) yh (n)= c1 λ1^n+c^2λ^2^n+⋯+cNλN^n

The best explanation: The general solution of natural response is of the form:

 yh (n)= c1 λ1^n+c^2λ^2^n+⋯+cNλN^n

The form will vary if the roots are repeating or complex.