It is well known that a quadratic function defined on a finite field
of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear
(APN). For the even degree case there is no apparent relationship between the
values in the Fourier spectrum of a function and the APN property. In this
article we compute the Fourier spectrum of the quadrinomial family of APN
functions from . With this result, all known infinite families of APN functions
now have their Fourier spectra and hence their nonlinearities computed.