Complex Number Utilities

Helper functions for complex number arithmetic.

Complex Type

type Complex = [number, number]; // [real, imaginary]

Arithmetic Operations

complexAdd()

function complexAdd(a: Complex, b: Complex): Complex;

complexSub()

function complexSub(a: Complex, b: Complex): Complex;

complexMul()

function complexMul(a: Complex, b: Complex): Complex;

complexScale()

function complexScale(a: Complex, scale: number): Complex;

complexConj()

function complexConj(a: Complex): Complex;

Returns the complex conjugate.

complexMagnitude()

function complexMagnitude(a: Complex): number;

Returns the magnitude (absolute value).

Twiddle Factors

twiddleFactor()

function twiddleFactor(k: number, n: number): Complex;

Computes e^(-2πi·k/n).

twiddleFactorInverse()

function twiddleFactorInverse(k: number, n: number): Complex;

Computes e^(2πi·k/n).

Data Conversion

interleavedToComplex()

function interleavedToComplex(data: Float32Array): Complex[];

Converts [Re, Im, Re, Im, ...] to [[Re, Im], ...].

complexToInterleaved()

function complexToInterleaved(data: Complex[]): Float32Array;

Converts [[Re, Im], ...] to [Re, Im, Re, Im, ...].

Utilities

complexApproxEqual()

function complexApproxEqual(
  a: Complex,
  b: Complex,
  tolerance?: number
): boolean;

Compares two complex numbers with tolerance.

naiveDFT()

function naiveDFT(data: Float32Array): Float32Array;

Computes DFT using the naive O(N²) algorithm. Useful for verification.

naiveIDFT()

function naiveIDFT(data: Float32Array): Float32Array;

Computes inverse DFT using the naive algorithm.

Example

import {
  complexMul,
  complexMagnitude,
  twiddleFactor,
} from 'webgpu-fft';

const a: Complex = [3, 4];
const b: Complex = [1, 2];

const product = complexMul(a, b);  // [-5, 10]
const mag = complexMagnitude(a);    // 5

const twiddle = twiddleFactor(1, 8); // [0.707, -0.707]