Time reversed filtering in real-time

Abstract

A technique is developed for indirectly realizing true time-reversed convolution for continuous inputs of infinite duration. This real-time technique is based on a novel extension of sectioned convolution methods using an infinite impulse response (IIR) filter and local time reversal using last-in, first-out (LIFO) memory stacks. This new architecture is shown to be free from zero input limit cycle and overflow oscillations even if the IIR filter on which it is based exhibits both. No constraints are placed on the magnitude or phase response characteristics of the IIR subfilter used in the time-reversed convolution scheme which permits the use of standard magnitude-only IIR filter design programs. Computer simulations are used to verify the expected magnitude and phase response. The conditions required for system time invariance are investigated both analytically and through computer simulations. The relationship between the number of samples per convolution section and the total harmonic distortion of the system is established through simulation. It is demonstrated that if the number of samples per section is greater than the number of samples required for the impulse response of the subfilter H(z) to decay below a threshold value, a stable, linear, time-invariant system results with noncausal transfer function H(z/sup -1/). >