xsFFT is an extremely simple implementation of FFTs and complex numbers. The package includes C, C++, and Objective C code. Also includes a simple interpolation algorithm. All code is based on the Cooley-Tukey algorithm.
The impetus for this project was the relative complexity of other projects, such as fftw. This is meant to be a simple implementation that hides much of the complexity of declaring things such as plans (which indicate intent for fftw). xsFFT is meant to be fast, regardless, and ignores minute optimizations achieved by fftw. xsFFT is also human readable.
Find the code here