# First and Second Derivatives of a Periodic Function Using Discrete Fourier Transforms

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Consider the family of periodic functions , where . This Demonstration applies the discrete Fourier transform to compute the first and second derivatives of . (The derivative order 0 gives the original function.) The derivatives obtained analytically are shown in dashed red, while the numerical solutions are shown in blue. For a large number of sample points, there is close agreement between the two methods.

Contributed by: Housam Binous, Ahmed Bellagi, and Brian G. Higgins (September 2015)

Open content licensed under CC BY-NC-SA