CWT

The Continuous Wavelet Transform (CWT) is a time-frequency analysis tool that decomposes a signal into wavelets. Unlike the Fourier transform, wavelets are localized in both time and frequency.

This implementation uses the specified wavelet function and widths to produce a 2D matrix of coefficients.

Excel Usage

=CWT(data, widths, wavelet_type)

• data (list[list], required): The input signal data.
• widths (list[list], required): Sequence of widths to use for the transform.
• wavelet_type (str, optional, default: “ricker”): The wavelet function to use.

Returns (list[list]): A 2D matrix of transform coefficients (widths as rows, data as columns).

Example 1: Ricker CWT

Inputs:

data							widths			wavelet_type
1	2	3	4	3	2	1	1	2	3	ricker

Excel formula:

=CWT({1,2,3,4,3,2,1}, {1,2,3}, "ricker")

Expected output:

Result
-0.497416	0.0948513	1.03926	1.90658	1.03926	0.0948513	-0.497416
0.4296	2.10362	3.77763	4.39092	3.77763	2.10362	0.4296
2.01115	3.57677	4.91964	5.42039	4.91964	3.57677	2.01115

Python Code

Show Code

import numpy as np
from scipy.signal import cwt as scipy_cwt
from scipy.signal import ricker, morlet2

def cwt(data, widths, wavelet_type='ricker'):
    """
    Perform a Continuous Wavelet Transform (CWT).

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

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

    Args:
        data (list[list]): The input signal data.
        widths (list[list]): Sequence of widths to use for the transform.
        wavelet_type (str, optional): The wavelet function to use. Valid options: Ricker, Morlet 2. Default is 'ricker'.

    Returns:
        list[list]: A 2D matrix of transform coefficients (widths as rows, data as columns).
    """
    try:
        def to_1d(v):
            if isinstance(v, list):
                return np.array([float(x) for row in v for x in row])
            return np.array([float(v)])

        data_arr = to_1d(data)
        widths_arr = to_1d(widths)

        # Map wavelet_type string to function
        wavelet_map = {
            'ricker': ricker,
            'morlet2': morlet2
        }
        wav_func = wavelet_map.get(wavelet_type, ricker)

        # Determine if output should be complex
        out_dtype = np.float64
        if wavelet_type == 'morlet2':
            out_dtype = np.complex128

        result = scipy_cwt(data_arr, wav_func, widths_arr, dtype=out_dtype)

        if wavelet_type == 'morlet2':
            return np.abs(result).tolist()

        return result.tolist()
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

data *

The input signal data.

widths *

Sequence of widths to use for the transform.

wavelet_type Optional Ricker Morlet 2

The wavelet function to use.