cauchy2d

Compute the 2D Cauchy Wavelet in frequency plane

Syntax

[out] = cauchy2d(kx,ky,delta,sigma,l,m)

Description

This function computes the 2D Cauchy wavelet in frequency plane. That is, the wavelet given by:

                  _
                 |(E(delta-pi/2) . K)^l 
                 |           * (E(-delta+pi/2) . K)^m 
                 |           * exp( - 0.5 * sigma * |K-K_0|^2 )  
PSIHAT(kx,ky) = <                      INSIDE C(-delta,delta)
                 |  
                 |0                    OUTSIDE C
                 `-       
where: E(alpha) = (cos(alpha), sin(alpha))
       K        = (kx, ky)                  
       K_0      = (l+m)^0.5 * (sigma - 1)/sigma * (1,0)
       C(-delta,delta) = the cone supported by E(delta)
                         and E(-delta)

The wavelet parameters are thus:

• delta : the aperture of the cone;
• sigma : the frequency spread of the wavelet;
• l,m : its vanishing moments.

This function is used by the cwt2d routine which compute continuous wavelet transform in 2D.

Input Data

kx, ky

[REAL MATRICES]: The frequency plane. Use meshgrid to create it.

delta

[REAL SCALAR]: The aperture of the cone (in gradiant)

sigma

[REAL SCALAR]: The frequency spread of the wavelet

l,m

[INTEGERS]: The vanishing moments

Output Data

out

[REAL MATRIX]: The wavelet in frequency plane.

Example(s)

>> step = 2*pi/128;
>> [kx,ky] = meshgrid( -pi : step : (pi-step) );
>> wav = cauchy2d(kx,ky,pi/6,1,4,4);
>> imagesc(wav);

References

See Also

cauchy2d cwt2d dergauss2d dog2d esmex2d gauss2d gaussx2d gaussz2d meshgrid mexican2d morlet2d samcwt2d sarcwt2d sdog2d sqdog2d

Location

continuous/2d/wave_defs/cauchy2d.m