Answer: Is symmlet 8 (S8) considered a 'Daubechies' wavelet?

[Viara Van Raad (v.van-raad@unsw.edu.au)]

Reply to WD 11.5 Topic 5140

Well, the Symlets and the Daubechies are different wavelets!

See for Symlets:
Symlets Wavelets

General characteristics: Compactly supported wavelets with
least assymetry and highest number of vanishing moments
for a given support width.
Associated scaling filters are near linear-phase filters.

Family Symlets
Short name sym
Order N N = 2, 3, ...
Examples sym2, sym8

Orthogonal yes
Biorthogonal yes
Compact support yes
DWT possible
CWT possible

Support width 2N-1
Filters length 2N
Regularity
Symmetry near from
Number of vanishing
moments for psi N

Reference: I. Daubechies,
Ten lectures on wavelets,
CBMS, SIAM, 61, 1994, 194-202.
For Daubechies:

Daubechies Wavelets

General characteristics: Compactly supported
wavelets with extremal phase and highest
number of vanishing moments for a given
support width. Associated scaling filters are
minimum-phase filters.

Family Daubechies
Short name db
Order N N strictly positive integer
Examples db1 or haar, db4, db15

Orthogonal yes
Biorthogonal yes
Compact support yes
DWT possible
CWT possible

Support width 2N-1
Filters length 2N
Regularity about 0.2 N for large N
Symmetry far from
Number of vanishing
moments for psi N

Reference: I. Daubechies,
Ten lectures on wavelets,
CBMS, SIAM, 61, 1994, 194-202.
therefore, symlets are with least assymetry, daubechies -- no symmetry
The scaling filters of DB are minimum phase filters- e.g. all of the zeros are within the unit circle.