Note that the delta function in the expression above arises due to the following argument. Defining Δ Δ = ω ω f i − − ω ω the time derivative of sin 2 ⁡ ⁡ ( Δ Δ t / 2 ) / Δ Δ 2 is sin ⁡ ⁡ ( Δ Δ t ) / ( 2 Δ Δ ) , which behaves like a delta function at large t (for more information, please see Sinc function#Relationship to the Dirac delta distribution).