opWavelet Wavelet operator.
opWavelet(N) creates a Wavelet transform for 1-dimensional signals
of size N. The wavelet transformation is computed using the Rice
Wavelet Toolbox.
opWavelet(N,FAMILY) additionally specifies the FAMILY for the
wavelet. Supported values for FAMILY are 'Daubechies' and 'Haar'.
opWavelet(N,FAMILY,FILTER,LEVELS,REDUNDANT,TYPE) allows for four
additional parameters: FILTER (default 8) specifies the filter
length, which must be even. LEVELS (default 5) gives the number of
levels in the transformation. P does not need to be divisible by
2^LEVELS. However, if LEVELS is bigger than LOG2(P), then LEVELS is
adjusted to be equal to FLOOR(LOG2(P)). The Boolean field REDUNDANT
(default false) indicates whether the wavelet is redundant. TYPE
(default 'min') indictates what type of solution is desired; 'min'
for minimum phase, 'max' for maximum phase, and 'mid' for mid-phase
solutions.
The opWavelet operator is linear but not orthogonal. Therefore, the
transpose of the operator is not the inverse operator. However, the
inverse of the operator can be obtained through a left-inverse
operation. For example:
W = opWavelet(...)
y = W*x
if z = W'*y, then z ~= x
but, u = W\y, then u = x