Discrete wavelet transform
Given a scaling function ?0, mother wavelet ?0, and maximum scale level J, DWT is a mapping from x(t) to the approximation coefficients ax and detail coefficients dx:
x(t) ?{ax(J, k), dx(j, k), j ? [1, J], k ? Z}
ax(j, k) = ?x, ?j, k ?, dx(j, k) = ?x, ?j, k ?
?j, k = 2-j/2 ?0 (2-jt - k), ?j, k = 2-j/2 ?0 (2-jt - k), k ? Z
Wavelet decomposition is: