Question

The Fourier transform of u (t) is B (jω) and the Laplace transform of u (t) is A(s). Which of the following is correct?

(a) B(jω) = A(s)

(b) A(s) = \(\frac{1}{s}\) but B(jω) ≠ \(\frac{1}{jω}\)

(c) A(s) ≠ \(\frac{1}{s}\) but B(jω) ≠ \(\frac{1}{jω}\)

(d) A(s) ≠ \(\frac{1}{s}\) but B(jω) = \(\frac{1}{jω}\)

This question was posed to me in exam.

The doubt is from Exponential Fourier Series and Fourier Transforms topic in portion Fourier Series of Signals and Systems

Answer 1

Right answer is (b) A(s) = \(\frac{1}{s}\) but B(jω) ≠ \(\frac{1}{jω}\)

To explain: Laplace transform of u (t) is given by u (t) –> A(s) = \(\frac{1}{s}\)

Fourier transform of u (t) is given by, u (t) = B (jω) = (\(\frac{1}{jω}\)) + π δ (ω)

Therefore A(s) = \(\frac{1}{s}\) but B(jω) ≠ \(\frac{1}{jω}\) is satisfied.