Question

A) Use direct integration to find the Fourier transform G(f) of signal ga​(t)=Π(t−1)−5exp(−2∣t+3∣)

(b) Use direct integration to find the Fourier transform of gb​(t)=δ(2t−1)+2e−tu(t−1)
(c) Use direct integration to find the inverse Fourier transform of Gc​(f)=δ(πf)−2δ(f−0.5)

Answer 1

To find the Fourier transforms and inverse Fourier transform of the given signals, use direct integration and evaluation of the integrals.

Step-by-step explanation:

1. To find the Fourier transform G(f) of signal ga(t), first write the expression for ga(t) in terms of unit step functions. Then, use direct integration to find the Fourier transform by evaluating the integral.
2. To find the Fourier transform of signal gb(t), again express gb(t) in terms of unit step functions and perform direct integration to find the Fourier transform.
3. To find the inverse Fourier transform of Gc(f), apply the inverse Fourier transform formula, using the given expression for Gc(f) and evaluating the integral.