FFTtä

FFTtä is a theoretical variant of the Fast Fourier Transform designed to optimize spectral analysis of time-domain signals, particularly in streaming or real-time contexts. It extends the classic FFT by incorporating adaptive tiling and memory-aware computation to reduce cache misses and memory bandwidth.

Algorithmic approach: FFTtä preserves the divide-and-conquer spirit of Cooley–Tukey but introduces tiling strategies that map the computation to cache lines more efficiently. It precomputes and reuses twiddle factors in tiles, and supports adaptive windowing to handle non-stationary signals. It can operate in real-valued and complex modes and accommodates mixed-radix implementations.

Variants and implementation: There are 1D FFTTä for one-dimensional signals and 2D FFTTä for images and spatial data. Implementations emphasize portability across CPUs, GPUs, and DSPs, with streaming APIs to process sliding windows and overlapping frames.

Performance and considerations: The asymptotic complexity remains O(N log N), but practical performance gains vary with hardware layout, cache size, and data alignment. Numerical precision and rounding error are similar to conventional FFTs; care is needed for large-scale transforms and real-to-complex reductions.

Applications: FFTtä is proposed for real-time audio analysis, communications monitoring, radar and sonar signal processing, and image analysis where low-latency spectral estimates are required.