We propose FFTX, a new framework for building high-performance FFT-based applications on exascale machines. Complex node architectures lead to multiple levels of parallelism and demand efficient ways of data communication. The current FFTW interface falls short in maximizing performance in such scenarios. FFTX is designed to enable application developers to leverage expert-level, automatic optimizations while navigating a familiar interface. FFTX is backwards compatible to FFTW and extends the FFTW Interface into an embedded Domain Specific Language (DSL) expressed as a library interface. By means of a SPIRAL-based back end, this enables build-time source-to-source translation and advanced performance optimizations, such as cross-library calls optimizations, targeting of accelerators through offload-ing, and inlining of user-provided kernels. We demonstrate the use of FFTX with the prototypical example of 1D and 3D pruned convolutions and discuss future extensions.