
Local Polynomial Phase Modeling and Estimation ◾ 217
e coecient estimate
is now given as
α=
∏τ
=
−
ˆ
!
1
1
M
iM
iM
k
M
k
(6.66)
Henceforth, we use only the modied forms of HIM and HAF for analysis
because they provide more reliable estimates for the coecients.
We can now summarize how the HAF technique works:
1. Assume a variable r and initialize it as r = M, that is, the highest
order or degree. We haveΓ=Γ()
r
for r = M.
2. Compute the HIM
−
[(); ]
Py
r
using Equation (6.64).
3. Compute the HAF Γωτ
−
[();
Py
r
using Equation (6.65) and deter-
mine the frequency
corresponding to the spectral peak.
4. Estimate the coecient α
ir
us ...