A header-only C++ template class implementing a mixed-radix FFT. It factorizes the transform length, precomputes twiddle factors, and provides a recursive transform method with specialized butterfly functions for radices 2,3,4,5 and a generic fallback. The class is self-contained, using only standard C++ headers (vector, complex, cmath), and can be dropped into any C++ project. It demonstrates clean template metaprogramming, efficient use of STL containers, and careful handling of complex arithmetic and twiddle generation. It also includes a real-valued transform helper (transform_real).

Implements an N-dimensional complex FFT by decomposing the problem into a sequence of 1D FFTs along each dimension. It uses a clever stride-based approach to transpose the matrix between stages, effectively performing the multi-dimensional transform with minimal copying. The implementation is self-contained within the file, relying only on the core kiss_fft_stride function. It demonstrates a clear understanding of memory layout and algorithmic decomposition, and could be reused as a generic multi-dimensional transform module.

Implements fast FIR filtering using overlap-save (overlap-scrap) convolution via FFT. It handles the allocation of FFT plans, frequency-domain multiplication, and proper handling of sample buffers with offset management to simulate continuous filtering. The code includes both a direct convolution fallback for comparison and a flush mechanism. It demonstrates advanced signal processing concepts and careful memory management, and is structured as a reusable state object (kiss_fastfir_cfg) that can be applied to streaming audio or data.