OPWAVELET Wavelet operator.
opWavelet(P,Q,FAMILY) creates a Wavelet operator of given FAMILY for
signals of size P-by-1. The wavelet transformation is computed using
the Rice Wavelet Toolbox. The values supported for FAMILY are
'Daubechies' and 'Haar'.
opWavelet(P,Q,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 and Q do not need to be divisible by 2^LEVELS.
However, if LEVELS is bigger than LOG2(MIN(P,Q)), then LEVELS is
adjusted to be equal to FLOOR(LOG2(MIN(P,Q))).
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