LiftingWaveletTransform i think but that does not support MeyerWavelet.
With DiscreteWaveletTransform only the HaarWavelet gives the 2^r dimensions.
In[280]:= test = RandomReal[{0, -10}, 128];
dwd = DiscreteWaveletTransform[test, #[],
4] & /@ {BattleLemarieWavelet, BiorthogonalSplineWavelet,
CoifletWavelet, DaubechiesWavelet, HaarWavelet, MeyerWavelet,
ReverseBiorthogonalSplineWavelet, ShannonWavelet, SymletWavelet};
#["Wavelet"] -> #["Dimensions"] & /@ dwd
Out[282]= {BattleLemarieWavelet[3,
10] -> {{0} -> {74}, {1} -> {74}, {0, 0} -> {47}, {0,
1} -> {47}, {0, 0, 0} -> {33}, {0, 0, 1} -> {33}, {0, 0, 0,
0} -> {26}, {0, 0, 0, 1} -> {26}},
BiorthogonalSplineWavelet[4,
2] -> {{0} -> {67}, {1} -> {67}, {0, 0} -> {37}, {0,
1} -> {37}, {0, 0, 0} -> {22}, {0, 0, 1} -> {22}, {0, 0, 0,
0} -> {14}, {0, 0, 0, 1} -> {14}},
CoifletWavelet[
2] -> {{0} -> {69}, {1} -> {69}, {0, 0} -> {40}, {0,
1} -> {40}, {0, 0, 0} -> {25}, {0, 0, 1} -> {25}, {0, 0, 0,
0} -> {18}, {0, 0, 0, 1} -> {18}},
DaubechiesWavelet[
2] -> {{0} -> {65}, {1} -> {65}, {0, 0} -> {34}, {0,
1} -> {34}, {0, 0, 0} -> {18}, {0, 0, 1} -> {18}, {0, 0, 0,
0} -> {10}, {0, 0, 0, 1} -> {10}},
HaarWavelet[] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}},
MeyerWavelet[3,
10] -> {{0} -> {74}, {1} -> {74}, {0, 0} -> {47}, {0,
1} -> {47}, {0, 0, 0} -> {33}, {0, 0, 1} -> {33}, {0, 0, 0,
0} -> {26}, {0, 0, 0, 1} -> {26}},
ReverseBiorthogonalSplineWavelet[4,
2] -> {{0} -> {67}, {1} -> {67}, {0, 0} -> {37}, {0,
1} -> {37}, {0, 0, 0} -> {22}, {0, 0, 1} -> {22}, {0, 0, 0,
0} -> {14}, {0, 0, 0, 1} -> {14}},
ShannonWavelet[
10] -> {{0} -> {74}, {1} -> {74}, {0, 0} -> {47}, {0,
1} -> {47}, {0, 0, 0} -> {33}, {0, 0, 1} -> {33}, {0, 0, 0,
0} -> {26}, {0, 0, 0, 1} -> {26}},
SymletWavelet[
4] -> {{0} -> {67}, {1} -> {67}, {0, 0} -> {37}, {0,
1} -> {37}, {0, 0, 0} -> {22}, {0, 0, 1} -> {22}, {0, 0, 0,
0} -> {14}, {0, 0, 0, 1} -> {14}}}
In[278]:=
dwd = LiftingWaveletTransform[test, #[],
4] & /@ {BiorthogonalSplineWavelet, CDFWavelet, CoifletWavelet,
DaubechiesWavelet, HaarWavelet, ReverseBiorthogonalSplineWavelet,
SymletWavelet};
#["Wavelet"] -> #["Dimensions"] & /@ dwd
Out[279]= {BiorthogonalSplineWavelet[4,
2] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}},
CDFWavelet[
"9/7"] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}},
CoifletWavelet[
2] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}},
DaubechiesWavelet[
2] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}},
HaarWavelet[] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}},
ReverseBiorthogonalSplineWavelet[4,
2] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}},
SymletWavelet[
4] -> {{0} -> {64}, {1} -> {64}, {0, 0} -> {32}, {0,
1} -> {32}, {0, 0, 0} -> {16}, {0, 0, 1} -> {16}, {0, 0, 0,
0} -> {8}, {0, 0, 0, 1} -> {8}}}