The Scaling Equation 2.6 2002/01/31 2004/08/04 13:01:38.088 GMT-5 Phil Schniter schniter@ee.eng.ohio-state.edu Charlet Reedstrom charlet@rice.edu Phil Schniter schniter@ee.eng.ohio-state.edu Scaling equation wavelet scaling equation wavelet coefficients mother wavelet Haar wavelet DWT Perfect Reconstruction Filterbanks Power symmetry This module covers scaling equations and coefficients for the discrete wavelet transform. Consider the level-1 subspace and its orthonormal basis: V 1 span φ 1 , n t n φ 1 , n t 1 2 φ 1 2 t n Since V1 V0 (i.e., V 0 is more detailed than V 1 ) and since φ 1 , 0 t V 0 , there must exist coefficients h n n such that φ 1 , 0 t n h n φ 0 , n t ⇔ 1 2 φ 1 2 t n h n φ t n Scaling Equation φ t 2 n h n φ 2 t n To be a valid scaling function, φ t must obey the scaling equation for some coefficient set h n .