Module convolution_fft 

FFT-based 1D linear convolution for OxiGDAL GPU.

Implements linear convolution via the FFT theorem:

Y = IFFT(FFT(signal) * FFT(kernel))

where * is pointwise complex multiplication. This is equivalent to direct convolution for finite-length sequences, and is efficient when both sequences are padded to the same power-of-two length.

Limitation

The underlying Fft1d kernel supports sizes up to 2048. For inputs where (signal.len() + kernel.len() - 1).next_power_of_two() > 2048 this module returns GpuError::InvalidKernelParams. Long signals require an Overlap-Save or Overlap-Add segmentation strategy (not implemented here).

Sign convention

Forward FFT: twiddle angle = -2π·k/N (no normalisation). Inverse FFT: twiddle angle = +2π·k/N, result divided by N.

Thread safety

FftConvolution holds an Arc<GpuContext> and is Send + Sync.

Structs

FftConvolution

GPU-accelerated FFT-based 1D linear convolution.

Constants

MAX_FFT_CONVOLUTION_SIZE

Maximum single-pass FFT size supported by FftConvolution.

Functions

complex_multiply

Pointwise complex multiplication: (ar + i·ai) × (br + i·bi).

convolve_reference

Pure-Rust reference linear convolution (direct O(N·M) algorithm).