(i) 2u(t) with u(t) (2M | May 2015)

(ii) e-2t u(t) with e-5tu(t) (4M | May 2015)

(iii) tu(t) with e-5tu(t) (4M | May 2015)

Subject : Signals & Systems

Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT).

Difficulty: Medium

(i) 2u(t) with u(t)

Let x(t) = 2u(t) and h(t) = u(t)

The output is given by the convolution as

$y(t) =\int_{-∞}^∞ x(τ) h(t- τ) \, dτ $ $y(t) =\int_{-∞}^∞ 2 u(τ) h(t- τ) \, dτ $

u(τ) = 1 for τ ≥ 0

u(t - τ) = 1 for …