We are finding the Fourier transform for the function e(-ax) * u(x), where u(x) = unit step function and
u(x) = 0 for x < 0 and
= 1 for x >= 0
We find the transform for the signal given, for x >= 0 part only.
Fourier transform of the signal f(x) is defined as:
The given function grows to infinity as x tends to -∞. So its Fourier transform is not possible to determine if the lower limit is -∞ for the span of x. So we take the real time for x >= 0 only. We can take x >= -A for a real value of A and find the transform.