morlet1d

Compute the 1D Morlet Wavelet in frequency

Syntax

[out] = morlet1d(k,k_0,sigma)

Description

This function computes the 1D Morlet wavelet in frequency. That is, the wavelet given by

  PSIHAT (k) = exp( - sigma^2 * (k - k0).^2 / 2 )

where PSIHAT is the Fourier transform of PSI. This wavelet depends of two parameters: k0 and sigma. It is not truly admissible but for sigma*K_0>5.5, it is considered numerically admissible. This function is used by the cwt1d routine which compute continuous wavelet transform in 1D.

Input Data

k

[REAL VECTOR]: The frequency line. You can use the yawtb function 'vect' to create it (see example below).

k_0, sigma

[REAL SCALARS]: The wavelet parameters.

Output Data

out

[REAL MATRIX]: The wavelet in frequency.

Example(s)

>> step = 2*pi/128;
>> freqs = -pi : step : (pi-step);
>> wav = morlet1d(freqs,6,1);
>> plot(abs(wav));

Note that the two first lines are implemented by the yawtb 'vect' function:

>> freqs = vect(-pi,pi,128,'open');

References

See Also

cwt1d cwt1d_yashow cwt1dt cwt1dt_yashow meshgrid vect

Location

continuous/1d/wave_defs/morlet1d.m