• A unit step function is mathematically defined as,

  u (t) =1 for t ≥ 0

  =0 elsewhere

Using the definition of the Fourier transform we get,

But unit step function is present for t ≥ 0

We cannot substitute value of δ (t) directly in above equation because it is infinitely

large at t=0 .Hence we use the Shifting property of delta function.

Shifting property of delta function states that:

• A gate function is mathematically defined as,

rect (t/T) = A for –T/2 ≤ t ≤ T/2

= 0 elsewhere

Therefore the Fourier transform will be,