signal.lib
Class chebyshevPolynomial

java.lang.Object
  |
  +--signal.lib.chebyshevPolynomial

public final class chebyshevPolynomial

extends java.lang.Object

Implements methods associated with the Chebyshev Polynomials, Tk(x).

Constructor Summary

chebyshevPolynomial()

Method Summary

static void	chebyCoef(double[] u, double[] ak, int N) Given discrete function values u, the method returns the first N+1 discrete Chebyshev coefficients, ak
static double	chebySeries(double[] coef, double x) Evaluates the Chebyshev partial sum u += aN[k]*T(x,k) by Clenshaw's recurrence relation
static double	CJ(int m, int N) weights and normalizing factors, 1/Cj
static double	T(double x, double N) Returns the Chebyshev Polynomial of degree N
static double	Tp(double x, double N) Returns the derivative of the Chebyshev Polynomial of degree N
static double	xGL(int i, int N) Returns CGL points in the order order order -1,...,1
static double	xGLr(int i, int N) Returns CGL points in the order order 1,...,-1

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

chebyshevPolynomial

public chebyshevPolynomial()

Method Detail

xGLr

public static double xGLr(int i,
                          int N)

Returns CGL points in the order order 1,...,-1

xGL

public static double xGL(int i,
                         int N)

Returns CGL points in the order order order -1,...,1

CJ

public static double CJ(int m,
                        int N)

weights and normalizing factors, 1/Cj

T

public static double T(double x,
                       double N)

Returns the Chebyshev Polynomial of degree N

Tp

public static double Tp(double x,
                        double N)

Returns the derivative of the Chebyshev Polynomial of degree N

chebyCoef

public static final void chebyCoef(double[] u,
                                   double[] ak,
                                   int N)

Given discrete function values u, the method returns the first N+1 discrete Chebyshev coefficients, ak

chebySeries

public static double chebySeries(double[] coef,
                                 double x)

Evaluates the Chebyshev partial sum u += aN[k]*T(x,k) by Clenshaw's recurrence relation