Effect of Parameter Values on Morse Wavelet Shape
These plots show how different values of symmetry and time-bandwith affect the shape of a Morse wavelet. Longer time-bandwidths broaden the central portion of the wavelet and increase the rate of the long time decay. Increasing the symmetry broadens the wavelet envelope, but does not affect the long time decay. For symmetry values less than or equal to 3, the time decay increases as the time-bandwidth increases. For symmetry greater than or equal to 3, reducing the time-bandwidth makes the wavelet less symmetric. As both symmetry and time-bandwidth increase, the wavelet oscillates more in time and narrows in frequency. Very small time-bandwidth and large symmetry values produce undesired time-domain sidelobes and frequency-domain asymmetry.
In the time-domain plots in the left column, the red line is the real part and the blue line is the imaginary part. The contour plots in the right column show how the parameters affect the spread in time and frequency.