Hello Itai,
In MATLAB, you can use the cwtft function with the'morl' wavelet and the'scales' input parameter set to a vector of scales at which to compute the transform to differentiate a signal using a Gaussian Continuous Wavelet Transform (CWT).
Here is an example code snippet:
% Define input signal
t = linspace(0, 1, 1000);
x = sin(2*pi*10*t) + randn(size(t));
% Compute CWT using Morlet wavelet and scales from 1 to 100
scales = 1:100;
cwt = cwtft(x, 'wavelet', 'morl', 'scales', scales);
% Compute differentiation of CWT coefficients
dcwt = diff(abs(cwt.cfs), 1, 2);
% Find maxima and minima of differentiated coefficients
maxima = findpeaks(dcwt);
minima = findpeaks(-dcwt);
In this example, the input signal x is first defined as a noisy sinusoid. Then, using the'morl' wavelet and scales between 1 and 100, we compute the CWT of x. The cwt structure contains the derived CWT coefficients.
The differentiation of the CWT coefficients is then calculated using the diff function. The dcwt variable holds the differentiated coefficients that are produced.
The findpeaks function is then used to determine the maximum and minimum values of the differentiated coefficients. In order to locate the negative peaks, we use -dcwt for the minima.
It should be noted that the code in the preceding sentence presupposes that the input signal x has been integrated over time to determine the vertical acceleration. To identify ICs and FCs according to the procedure you supplied, the generated signal can be subjected to the CWT differentiation and peak detection procedures.
Hope this resolves your issue.
