This function computes the real continuous wavelet coefficient for each given scale presented in the Scale vector and each position b from 1 to n, where n is the size of the input signal.
Let x(t) be the input signal and ψ be the chosen wavelet function, the continuous wavelet coefficient of x(t) at scale a and position b is:
The computation is implemented with a NAG function: nag_cwt_real(). It does not compute the coefficients with the definition of CWT. Instead, the integrals of the scaled, shifted wavelet function are approximated and the convolution is then computed.
For a given wavelet, you can map a scale and convert to pseudo-frequency by ways below:
In this formula:
The is the frequency contributes most to the variability of the wavelet, and it can be derived from maximizing the FFT of the wavelet modulus.