I search to display a time-frequency signal with an original discrete temporal signal (sampling step = 0.001sec). I use Python and the library Scipy.signal. I use the function
cwt(data, wavelet, widths) to do a continuous wavelet transform, with the complex morlet wavelet (or gabor wavelet).
First step: Obtain a scale-translation signal. In doubt, I associate directly the array “widths” with the array of the possible different scales. Because, I don’t understand what is parameter width if it’s not scale. Perhaps, you will tell me “it’s the width of your current wavelet”! But, even if it is, I don’t know how linked width with scale…
My second problem is to find and display the equivalent with frequency. In literature, I find this formula: Fa = Fc / (s*delta), where Fa is the final frequency, Fc the center frequency of a wavelet in Hz, s the scale and delta the sampling period. So, ok for scale (if I find the link with the width) and delta (=0.001sec), but it’s more complicated with center frequency of the wavelet. In scipy documentation, I find that: “The fundamental frequency of this wavelet [morlet wavelet] in Hz is given by f = 2*s*w*r / M, where r is the sampling rate [s is here Scaling factor, windowed from -s*2*pi to +s*2*pi. Default is 1; w the width; and M the length of the wavelet].” I think it’s the center frequency, is it? Maybe the solution to my first problem is here also (scaling factor and scale..?)..?