Application of Fresnel Integral Approximations

Given these Fresnel integrals just obtained, we may apply the approximations given in the Fresnel integral review in section 2, provided that the conditions specified therein are met. We will first discuss the large limits approximation while assuming a rectangle window. We then explore the effect of the Hann window on the validity of the large limits approximation, and make the discovery that the Hann window in effect converts the large limits approximation into the infinite limits approximation via liftering.