Question

The resultant signal obtained after frequency convolution along with constant multiplier \(\frac{1}{2πj}\) of the signals whose Laplace transforms are given by, \(\frac{1}{s+2}\) and \(\frac{1}{s+1}\).

(a) e^-2t + e^-t

(b) e^-2t

(c) e^-3t

(d) e^-t

This question was posed to me in examination.

The origin of the question is Average Power and Energy of a Signal in division Fourier Series of Signals and Systems

Answer 1

The correct answer is (c) e^-3t

The explanation is: f3 (t) = f1 (t). f2 (t)

The Laplace transform of f3 (t) is \(\frac{1}{2πj}\) F1(s) * F2(s)

Then, F1(s) = \(\frac{1}{s+2}\)

∴ f1 (t) = e^-2t u(t)

F2(s) = \(\frac{1}{s+1}\)

∴ f2 (t) = e^-t  u(t)

∴ f3 (t) = e^-3t  (for all t>0).