Why do I see horizontal lines in the results of a continuous wavelet in the Wavelet Toolbox 2.0 (R12) and above?

I have created an ideal sinusoidal signal. I then use the CWT function with a Morlet wavelet. The resulting plot has horizontal lines in it which I would not expect.

t = 1:1000;

S = sin(2*pi*t*1645.28/32768);

scale_exp = [2:-0.005:1];  

scales = 10.^scale_exp;

c = cwt(S,scales,'morl', 'plot') ;

colorbar

Answer 1

[MathWorks Support Team]

The behavior is normal in the sense that the CWT is not really a pure continuous analysis; it is considered an "over complete" analysis. The computation is a discretization of the function and not a real continuous computation using integrals. The CWT function only works with integer values of scales. This means that even if you generate a vector of non-integer scales, the CWT function changes the non integer scales to the closest integer value.

The unexpected horizontal lines can be the result of both the discretization of the function and the use of non-integer values for scales.