NuGet

Library can be also downloaded from nuget

Features And Algorithms

This library uses numerical calculator library so can handle same functions at input.

Mathematical formula used in this library is normal variant of Fourier Transform (not the Fast Fourier Transform).

Example

Take function f(x)=exp(x/20)*(sin(1/2*x)+cos(3*x)+1/5*sin(4*x)*cos(40*x))

Graph of this function shows it's not smooth:

Alter

You can use Fourier Transform to reduce noise and improve function smoothness. Fourier Transform (abscissa from 0 to 6, 256 samples) of this function look like this:

Alter

You can clearly see two groups of noisy frequencies. Lets reset all values less then 10 to 0 (reduce noise) and then invert the transformation. Our function now look like this:

Alter

Usage

Note: PointC is class similar to Point that additionally contains imaginary element. It comes with NumericalCalculatorCommon.dll which is inside this library compressed archive.

string function = "exp(x/20)*(sin(1/2*x)+cos(3*x)+1/5*sin(4*x)*cos(40*x))";
int sampling = 256;
double abscissaFrom = 0d;
double abscissaTo = 6d;
double cutoff = 10d;

List<PointC> pointsFT = new List<PointC>();
List<PointC> denoisedFunctionPoints = new List<PointC>();

//Computing FT
FourierTransform ft = new FourierTransform();
pointsFT = ft.Compute(function, sampling, abscissaFrom, abscissaTo);

//Cutoff
for (int i = 0; i < pointsFT.Count; i++)
{
    PointC pc = pointsFT[i];

    if (Math.Abs(pc.Y.Real) < cutoff)
        pc.Y = 0;

    pointsFT[i] = pc;
}

//Inverse FT
denoisedFunctionPoints = ft.ComputeInverse(pointsFT, sampling, abscissaFrom, abscissaTo);

Example application

Alter

Download: here

Disadvantages

Current version of Fourier Transform can't transform list of function value points - only function formula.

License

MIT License

Source code

Can be found on GitHub