Continuous Wavelet Transforms ◾ 99
e last wavelet in our list is the generalized Morse wavelet (GMW)
[8,23]. ese are designed to maximize the eigenvalues of a particular
joint time-frequency localization operator [24] and are controlled by two
parameters, β and γ. For a valid wavelet, we must have β > 0 and γ > 0.
Here, α
β,γ
is a normalization constant, and H(ω) is the Heaviside or unit
step function. Varying these two parameters enables these wavelets to
have a broad range of characteristics while remaining exactly analytic.
e GMWs are in fact a “superfamily” of wavelets and subsume two other
families of wavelets: the Morse or Paul wavelets for γ = 1 and the DoG
wavelets for γ = 2 [25]. Examples of GMWs for a range of values of ( ...