
Continuous Wavelet Transforms ◾ 89
fringe frequency or the phase, respectively. e instantaneous frequency
is obtained from values of a(b) on the ridge while the phase is returned,
modulo 2π, from
φ=
ℜ
tan
{(
}
Wab
f
f
(3.31)
where
and
denote the real and imaginary parts of the CWT, respec-
tively, and are evaluated on the ridge. e exact form of the expression for
ϕ′(b) depends on the normalization adopted, that is, whether the wavelets
are scaled by1/ a or by 1/a. Li et al. [4] provided expressions for both cases,
in addition to useful formulae for determining the minimum and maxi-
mum values of the scaling parameter a to use in the ...