Hybrid optical implementation of discrete wavelet transforms : a tutorial

Abstract Recently, there has been a great deal of interest in the use of wavelets to supplement or replace traditional Fourier transform signal processing. Because wavelet operations can be expressed as either a convolution/correlation operation or ā linear filter bank, they are well suited to optical implementations. This paper provides a tutorial on wavelets and the hybrid optical implementation of discrete wavelet transforms. Various approaches for implementing the wavelet transform are reviewed, including traditional Vander Lugt correlators, different types of spatial light modulators, joint time-frequency representations, holographic and interferometric implementations, and acousto-optic correlators. Finally, the concept for a new architecture is proposed using acousto-optic finite impulse response (FIR) filters to implement wavelets with perfect reconstruction properties.