FFT Examples

include/spectral/fft.hpp provides complex FFT, inverse FFT, real-input FFT, inverse real FFT, and reusable plans.

Real Signal Spectrum

#include <numerics.hpp>
#include <cmath>
#include <numbers>
 
constexpr int N = 1024;
constexpr double fs = 1000.0;
constexpr double pi = std::numbers::pi;
 
num::Vector x(N);
for (int i = 0; i < N; ++i) {
    double t = static_cast<double>(i) / fs;
    x[i] = std::sin(2.0 * pi * 50.0 * t)
         + 0.5 * std::sin(2.0 * pi * 120.0 * t);
}
 
num::CVector X(N / 2 + 1);
num::spectral::rfft(x, X);

Frequency bin \(k\) corresponds to

\[ f_k = k f_s / N . \]

num::Series spectrum;
for (num::idx k = 0; k < X.size(); ++k) {
    spectrum.store(static_cast<double>(k) * fs / N, std::abs(X[k]));
}

Complex Round Trip

num::CVector x(N), X(N), y(N);
 
num::spectral::fft(x, X);
num::spectral::ifft(X, y);

The inverse routine returns the normalized inverse transform.

Reusable Plan

num::spectral::FFTPlan plan(N, true, num::spectral::default_fft_backend);
 
for (int sample = 0; sample < nsamples; ++sample) {
    load_sample(sample, x);
    plan.execute(x, X);
}

Explicit Backend

num::spectral::fft(x, X, num::spectral::FFTBackend::seq);
num::spectral::fft(x, X, num::spectral::FFTBackend::simd);
num::spectral::fft(x, X, num::spectral::FFTBackend::stdsimd);
num::spectral::fft(x, X, num::spectral::FFTBackend::fftw);

default_fft_backend selects FFTW3 when available, otherwise the best built-in backend.