Question

A signal e^-at sin (ωt) is the input to a real linear time-invariant system. Given K and ∅ are constants, the output of the system will be of the form Ke^-bt sin (vt + ∅). The correct statement among the following is __________

(a) b need not be equal to a but v must be equal to ω

(b) v need not be equal to ω but b must be equal to a

(c) b must be equal to a and v must be equal to ω

(d) b need not be equal to a and v need not be equal to ω

This question was addressed to me by my college professor while I was bunking the class.

My question comes from Fourier Series and LTI Systems in section Fourier Series of Signals and Systems

Answer 1

Correct option is (a) b need not be equal to a but v must be equal to ω

Easy explanation: For a system with input e^-at sin (ωt) and output Ke^-bt sin (v t + ∅), frequency (v) to output must be equal to input frequency (ω) while b will depend on system parameters and need not be equal to a.