Fast algorithms for the continuous wavelet transform

It is shown that filter banks arise naturally when implementing the continuous wavelet transform (CWT). The conditions under which the CWT can be computed exactly using discrete filter banks are determined, and fast CWT algorithms are derived. The complexity of the resulting algorithms increases linearly with the number of octaves. They are easily implemented by repetitive application of identical cells, to which various methods are applied for reducing the number of operations: FFT (fast Fourier transform) algorithms are most efficient for large filter lengths; for small lengths, fast running FIR (finite impulse response) algorithms are preferred