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Transforms

🌊 FFT / DFT​

Xk=∑n=0N−1xn e−i2πkn/NX_k = \sum_{n=0}^{N-1} x_n \, e^{-i 2\pi k n / N}

Func<double, double> f = t => Math.Exp(-t * t / 0.02);
var freq = f.FastFourierTransform(-0.5, 0.5, 100)
             .ToFrequencyResolution(100);

// DFT from real or complex samples
var dft = samples.DiscreteFourierTransform();

Inverse FFT / DFT

var timeDomain = freqDomain.InverseFastFourierTransform();
var timeDomain2 = freqDomain.InverseDiscreteFourierTransform();

🔄 Laplace Transform​

F(s)=∫0∞f(t) e−st dtF(s) = \int_0^\infty f(t)\,e^{-st}\,dt

double result = f.LaplaceTransform(2.0);
double inverse = F.InverseLaplaceTransform(1.0);

🔉 Low-Pass Filter​

var filtered = input.LowPassFilter(output, alpha: 0.25);