Implementation of Dyadic Correlation

Correlation techniques provide a powerful means of extracting signals from noise and analyzing the spectrum of complex signals. The dyadic correlation function defined in Walsh-Fourier analysis is analogous to the usual correlation function in Fourier analysis. Circuits can be derived that produce this correlation function. The basic correlator circuit described here uses a dyadic shift register, which shifts a signal f(t) by modulo 2 addition into f(t ¿ ¿), several multipliers and one integrator. A switching matrix composed of only singlepole single-throw switches is used to compute the desired dyadic translations of the input signal within the dyadic shift register. Furthermore, by partitioning the input signal into any desired number of binary partitions the principle of operation of a dyadic correlator can be economically implemented in digital technology using the properties of dyadic invariant systems. A binary timing circuit consisting of a cascaded array of flip-flops produces trigger pulses for the switching matrix to sequentially produce each dyadic translation. Hence, correlation based on Walsh-Fourier analysis can be implemented economically by digital circuits for signals that are partitioned into as many binary intervals as desired.