edu.mines.jtk.dsp

Class WarpFunction1

java.lang.Object

edu.mines.jtk.dsp.WarpFunction1

public abstract class WarpFunction1
extends java.lang.Object

Synthetic warping functions for 1-D sequences. The function u(x) describes the warping, in which a point x is displaced to a point y(x) = x+u(x).

Warping is the computation of the sequence g(y) = f(x(y)). Unwarping is the computation of the sequence f(x) = g(y(x)).

For warping, we need the function x(y) = y-u(x(y)) = y-uy(y). We compute the displacement uy(y) by iteration so that uy(y) = u(x(y)).

We also define a midpoint m(x) = (x+y(x))/2, and compute the displacement um(m) = u(x(m)) from u(x) by iteration so that um(m) = u(x(m)).

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	WarpFunction1(int n)

Method Summary

Methods

Modifier and Type	Method and Description
static WarpFunction1	constant(double u, int n) Returns a warping for a constant shift.
static WarpFunction1	constantPlusSinusoid(double c, double u, int n) Returns a constant-plus-sinusoidal warping.
static WarpFunction1	gaussian(double u, int n) Returns a derivative-of-Gaussian warping.
static WarpFunction1	sinusoid(double u, int n) Returns a sinusoidal warping.
abstract double	u(double x) Returns the shift u(x).
float[]	um() Returns an array[n] of shifts um(m) = u(x(m)).
double	um(double m) Returns the shift um(m) = u(x(m)).
float[]	unwarp(float[] g) Unwarps a sampled function.
float[]	ux() Returns an array[n] of shifts u(x).
double	ux(double x) Returns the shift u(x).
float[]	uy() Returns an array[n] of shifts uy(y) = u(x(y)).
double	uy(double y) Returns the shift uy(y) = u(x(y)).
float[]	warp(float[] f) Warps a sampled function.

Methods inherited from class java.lang.Object

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

Constructor Detail

WarpFunction1

protected WarpFunction1(int n)

Method Detail

constant

public static WarpFunction1 constant(double u,
                     int n)

Returns a warping for a constant shift.

Parameters:

u - shift.

n - number of samples.

gaussian

public static WarpFunction1 gaussian(double u,
                     int n)

Returns a derivative-of-Gaussian warping.

Parameters:

u - maximum shift.

n - number of samples.

sinusoid

public static WarpFunction1 sinusoid(double u,
                     int n)

Returns a sinusoidal warping.

Parameters:

u - maximum shift.

n - number of samples.

constantPlusSinusoid

public static WarpFunction1 constantPlusSinusoid(double c,
                                 double u,
                                 int n)

Returns a constant-plus-sinusoidal warping.

Parameters:

c - constant shift.

u - maximum sinusoidal shift.

n - number of samples.

u

public abstract double u(double x)

Returns the shift u(x).

Parameters:

x - the coordinate x.

Returns:

the shift.

ux

public double ux(double x)

Returns the shift u(x).

Parameters:

x - the coordinate x.

Returns:

the shift.

um

public double um(double m)

Returns the shift um(m) = u(x(m)).

Parameters:

m - the coordinate m.

Returns:

the shift.

uy

public double uy(double y)

Returns the shift uy(y) = u(x(y)).

Parameters:

y - the coordinate y.

Returns:

the shift.

ux

public float[] ux()

Returns an array[n] of shifts u(x).

Returns:

array of shifts.

um

public float[] um()

Returns an array[n] of shifts um(m) = u(x(m)).

Returns:

array of shifts.

uy

public float[] uy()

Returns an array[n] of shifts uy(y) = u(x(y)).

Returns:

array of shifts.

warp

public float[] warp(float[] f)

Warps a sampled function.

Parameters:

f - array of values f(x).

Returns:

array of values g(y) = f(y-u(x(y)).

unwarp

public float[] unwarp(float[] g)

Unwarps a sampled function.

Parameters:

g - array of values g(x).

Returns:

array of values f(x) = g(x+u(x)).