Continuous wavelet coefficient object with octave/voice access
ContinuousWaveletData[{{oct1, voc1} -> coef1, …}, wave]
InverseContinuousWaveletTransform[ContinuousWaveletData[{{2, 1} -> {1, 0, 3, 3, 0, 2}, {3, 2} -> {-2, 2.5, 1, 1, 0, 0}}, PaulWavelet[]]]
→ {2.6904946380512436, -5.868849798715048, 7.855517159794535, -2.7082764629436356, 0.471980022032464, 1.3134493970173104}