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JSci is a set of open source Java packages. The aim is to encapsulate scientific methods/principles in the most natural way possible. As such they should greatly aid the development of scientific based software. It offers: abstract math interfaces, linear algebra (support for various matrix and vector types), statistics (including probability distributions), wavelets, newtonian mechanics, chart/graph components (AWT and Swing), MathML DOM implementation, ... Note: some packages, like javax.comm, for the astro and instruments package aren't listed as dependencies (not available).
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package JSci.maths.wavelet;

import JSci.GlobalSettings;
import JSci.maths.*;
import JSci.maths.wavelet.*;
import JSci.maths.wavelet.splines.*;
import java.io.*;
import java.util.Arrays;

/****************************************
* This class use the linear spline as a general model for a signal.
* While this is a reasonnable design choice, this can certainly be overwritten
* if necessary.
* Basic operations on signal are supported.
* @author Daniel Lemire
*****************************************/
public class Signal extends LinearSpline implements NumericalConstants, Cloneable  {
	private Filter filterdual;
	final static double normalisation=1.0/SQRT2;
	private double[] param;
  /********************************************
  * Return a copy of this object
  *********************************************/
	public Object clone() {
    Signal s=(Signal) super.clone();
    if(filterdual!=null)
      s.filterdual=filterdual;
      //the previous line is unsafe?
    if(param!=null) {
      s.param=new double[param.length];
      System.arraycopy(s.param,0,param,0,param.length);
    }
    return(s);
	}
  /************************************
  * This method generates a copy of the
  * current object with a different data
  * content.
  **************************************/
  private Signal copy(double[] v) {
		if(filterdual!=null) {
			if(param!=null) {
				double[] p=new double[param.length];
                                System.arraycopy(param,0,p,0,p.length);
				return(new Signal(filterdual,v,p));
			} else {
				return(new Signal(filterdual,v));
			}
		} else {
			return(new Signal(v));
		}
  }
	/******************************
	*******************************/
	public Signal () {
  }

	/***********************************
	************************************/
	public Signal (double[] v) {
		super(v);
  	}

	/******************************
	*******************************/
	public Signal (Filter f,double[] v, double[] p) {
		super(v);
		filterdual=f;
                System.arraycopy(p,0,param,0,param.length);
	}

	/********************************
	*********************************/
	public Signal(Filter f) {
		filterdual=f;
	}

	/*********************************
	**********************************/
	public Signal (Filter f,double[] v) {
		super(v);
		filterdual=f;
	}


	/********************************************
  * Get the sampled values of the sample as
  * an array.
	*********************************************/
	public double[] getValues() {
		return(this.interpolate(0));
	}

	/*********************************
  * set the signal associated Filter
	**********************************/
	public void setFilter(Filter f) {
		filterdual=f;
	}

	/***********************************
  * Set the parameter of the Filter (if
  * it applies).
	************************************/
	public void setParameters(double[] p) {
		for(int k=0;k20) {
			throw new IllegalArgumentException("Too many iterations.");
		}
		if (J<0) {
			throw new IllegalArgumentException("Cannot have a negative number of iterations.");
		}
		double[] data=this.interpolate(0);
		double[][] fwt=new double[J+1][];
		for(int j=1;j<=J;j++) {
			fwt[j]=highpassProject(data);
			data=lowpassProject(data);
		}
		fwt[0]=data;
		FWTCoef t=new FWTCoef(fwt);
		return(t);
	}

	/********************************
	* The Fast Wavelet Transform
  * with Wavelet packets
  * @param J number of iterations
  * @param cout cost function
	*********************************/
	public FWTPacketCoef fwtPacket(int J, MappingND cout) {
		if (J>20) {
			throw new IllegalArgumentException("Too many iterations.");
		}
		if (J<0) {
			throw new IllegalArgumentException("Cannot have a negative number of iterations.");
		}
		double[] data=this.interpolate(0);
		double[][] fwt=new double[J+1][];
		double[] choix1,choix2;
		boolean[] choixStandard=new boolean[J];
		for(int j=0;jl)||(l<0)) {
			throw new IllegalArgumentException("This Kronecker doesn't exist.");
		}
		double[] v=new double[l];
		v[i]=a;
		return(v);
	}

	/***************************
  * Compute the L2 norm of the
  * signal
	****************************/
	public double norm() {
		double[] data=this.interpolate(0);
		return(ArrayMath.norm(data));
	}

	/***********************************
	* @author Don Cross
        * @author Daniel Lemire
	************************************/
    public Complex[] fft() {
		double[] data=this.interpolate(0);
		return(fft(data));
	}

        /**
        * Performs the Fourier transform.
        * Convenience method for {@link JSci.maths.FourierMath#transform(double[]) FourierMath.transform}.
        */
	public static Complex[] fft(double[] data) {
                return FourierMath.transform(data);
        }
        /**
        * Performs the Fourier transform.
        * Convenience method for {@link JSci.maths.FourierMath#transform(Complex[]) FourierMath.transform}.
        */
	public static Complex[] fft(Complex[] data) {
                return FourierMath.transform(data);
        }
  /*********************************
  * Return the absolute value of
  * the FFT
  **********************************/
	public double[] absFFT() {
		Complex[] fft=fft();
		double[] answer=new double[fft.length];
		for(int i=0;idata.length-2) {
			if (data.length<4) {
				throw new IllegalArgumentException ("Your signal is too short to be denoised : "+data.length+" < 4");
			}
			throw new IllegalArgumentException ("Since you signal has dimension "+data.length+", the parameter must be at most : "+(data.length-2));
		}
		Complex[] ff=Signal.fft(data);
		ff[k+1]=Complex.ZERO;
		ff[data.length-1-k]=Complex.ZERO;
		Complex[] tf=Signal.fftInverse(ff);
		for(int l=0;lGlobalSettings.ZERO_TOL) {
					throw new IllegalArgumentException("Complex values detected during synthesis. Please get in touch with Daniel Lemire at [email protected] to report this error.");
				}
		}
    super.setValues(data);
	}

  /**********************************************
  * Return the entropy of the signal
  ***********************************************/
  public double entropy () {
    return(EngineerMath.entropy(this.evaluate(0)));
  }

	/*****************************************
  * Apply the given array as a convolution
  * Filter and return a new Signal.
  * As one often want to compare the result
  * to the original signal, this method is
  * "safe", that is, it won't change the current
  * object.
  * @param f an array containing the coefficients
  *   of the convolution Filter
	******************************************/
	public Signal filter (double[] f) {
		double[] data=interpolate(0);
		if(data.length-(f.length-1)<=0) {
			throw new IllegalArgumentException("Your signal is too short for this Filter : "+data.length+", "+f.length);
		}
		double[] ans=new double[data.length-(f.length-1)];
		for(int k=0;k1)) {
      throw new IllegalArgumentException("The parameter p must be between 0 and 1: "+p);
    }
    double[] values=this.interpolate(0);
    double range=ArrayMath.max(values)-ArrayMath.min(values);
    double threshold=range*p;
    double[] med=(this.medianFilter(n)).interpolate(0);
    for(int k=n;kthreshold) {
        values[k]=med[k-n];
      }
    }
    return(copy(values));
  }
}