sqdog2d

Compute the square of 2D Scaling difference of Gaussian Wavelet

Syntax

[out] = sqdog2d(kx,ky,alpha)

Description

This function computes the square of 2D Scaling difference of Gaussian Wavelet in frequency plane. This wavelet given by

  PSI(x,y)       = sdog2d(x,y,alpha).^2;
  PSIHAT (kx,ky) = (1/2) * exp( - K.^2/4 ) ...
           + 1/(2*alpha^2) * exp ( - alpha^2 * K.^2 / 4) ...
           - 2/(alpha^2 + 1) * exp ( - alpha^2 * K.^2 / ...
                                      (2*(alpha^2 + 1)) )

where: PSIHAT is the Fourier transform of PSI and K = (kx,ky). This wavelet depends of the alpha parmeter. 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.

order, sigma

[REAL SCALARS]: The wavelet parameters.

Output Data

out

[REAL MATRIX]: The wavelet in frequency plane.

Example(s)

>> step = 2*pi/128;
>> [kx,ky] = meshgrid( -pi : step : (pi-step) );
>> wav = sdog2d(kx,ky,6,1);
>> imagesc(wav);

References

See Also

cwt2d cwt2d_yashow meshgrid samcwt2d samcwt2d_yashow sarcwt2d

Location

continuous/2d/wave_defs/sqdog2d.m