Struct FourierSeries 

pub struct FourierSeries;

Discrete Fourier Transform and spectral utilities.

Provides Cooley-Tukey radix-2 FFT (in-place), IFFT, power spectrum estimation, and circular convolution via the convolution theorem.

Implementations

impl FourierSeries

pub fn fft(data: &[f64]) -> Vec<(f64, f64)>

Compute the FFT of data (length must be a power of 2).

Returns a vector of complex coefficients X[k] where X[k] = Σ x[n] * exp(-2πi kn/N).

pub fn ifft(spectrum: &[(f64, f64)]) -> Vec<f64>

Compute the inverse FFT.

Input is a slice of (re, im) pairs; output is the real part of the inverse transform (discards imaginary part which should be ~0 for real signals).

pub fn power_spectrum(data: &[f64]) -> Vec<f64>

Compute the one-sided power spectrum of data.

Returns |X[k]|^2 / N for k = 0, …, N/2.

pub fn convolve(a: &[f64], b: &[f64]) -> Vec<f64>

Circular convolution of a and b via the convolution theorem.

Both inputs must have the same length (a power of 2). Returns the circular convolution a * b.

pub fn frequencies(n: usize, fs: f64) -> Vec<f64>

Compute the DFT frequency bins for sample rate fs and n points.

Returns n/2 + 1 non-negative frequencies in Hz.

pub fn eval_series(coeffs: &[(f64, f64)], x: f64) -> f64

Evaluate the truncated Fourier series at points x using n_terms terms.

Coefficients (a_k, b_k) are the cosine and sine amplitudes. Returns sum_{k=0}^{n_terms-1} a_k cos(k x) + b_k sin(k x).