MORLET2

The Morlet wavelet is a complex sinusoid modulated by a Gaussian envelope. It provides an excellent balance between time and frequency localization and is widely used in continuous wavelet transforms.

This version (morlet2) is designed for direct use with the CWT function.

Excel Usage

=MORLET2(m_points, s_width, w_omega)

m_points (int, required): Length of the wavelet (number of points).
s_width (float, required): Width parameter of the wavelet.
w_omega (float, optional, default: 5): Omega0 (central frequency parameter).

Returns (list[list]): A 1D array of the complex Morlet wavelet (interleaved real and imaginary).

Example 1: Basic Morlet2

Inputs:

m_points	s_width	w_omega
24	4	2

Excel formula:

=MORLET2(24, 4, 2)

Expected output:

Result
0.00518711	0.00613401	0.00084149	-0.0175205	-0.0531354	-0.099706	-0.134882	-0.125295	-0.0456509	0.0974124	0.256137	0.361056	0.361056	0.256137	0.0974124	-0.0456509	-0.125295	-0.134882	-0.099706	-0.0531354	-0.0175205	0.00084149	0.00613401	0.00518711
0.00306145	0.0102887	0.022363	0.0351516	0.0370115	0.0108514	-0.055695	-0.155194	-0.25201	-0.293169	-0.238617	-0.0921926	0.0921926	0.238617	0.293169	0.25201	0.155194	0.055695	-0.0108514	-0.0370115	-0.0351516	-0.022363	-0.0102887	-0.00306145

Python Code

Show Code

import numpy as np
from scipy.signal import morlet2 as scipy_morlet2

def morlet2(m_points, s_width, w_omega=5):
    """
    Generate a complex Morlet wavelet for a given length and width.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.morlet2.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        m_points (int): Length of the wavelet (number of points).
        s_width (float): Width parameter of the wavelet.
        w_omega (float, optional): Omega0 (central frequency parameter). Default is 5.

    Returns:
        list[list]: A 1D array of the complex Morlet wavelet (interleaved real and imaginary).
    """
    try:
        result = scipy_morlet2(int(m_points), float(s_width), w=float(w_omega))
        # Return interleaved real and imag
        return [result.real.tolist(), result.imag.tolist()]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m_points *

Length of the wavelet (number of points).

s_width *

Width parameter of the wavelet.

w_omega

Omega0 (central frequency parameter).