viva_math/fft

Fast Fourier Transform over viva_math/complex.

Implements the recursive Cooley-Tukey radix-2 FFT. Inputs to fft and ifft must have power-of-two length; use pad_to_power_of_two when a signal needs zero-padding first.

Examples

import viva_math/complex
import viva_math/fft

fft.fft([
  complex.real(1.0),
  complex.zero(),
  complex.zero(),
  complex.zero(),
])
// -> [1+0i, 1+0i, 1+0i, 1+0i]

Values

fft

</>

pub fn fft(
  signal: List(complex.Complex),
) -> List(complex.Complex)

Forward FFT.

The signal length must be a power of two. Invalid lengths panic via fft_size, matching the total return type requested for this module.

fft_size

</>

pub fn fft_size(signal: List(complex.Complex)) -> Int

Return the signal length if it is a power of two.

Panics for empty or non-power-of-two inputs because the public API returns Int directly.

ifft

</>

pub fn ifft(
  spectrum: List(complex.Complex),
) -> List(complex.Complex)

Inverse FFT using IFFT(x) = conj(FFT(conj(x))) / N.

The spectrum length must be a power of two. The final result is normalized by N, so ifft(fft(signal)) recovers the original signal up to floating point round-off.

pad_to_power_of_two

</>

pub fn pad_to_power_of_two(
  signal: List(complex.Complex),
) -> List(complex.Complex)

Pad a signal with complex zeros up to the next power of two.

Already valid lengths are returned unchanged; an empty signal remains empty.