Recursive filtering

Abstract

Digital filters are applied to seismic data to eliminate noise and enhance signal. Various techniques are described for the implementation of recursive filters which are inherently more efficient as compared to direct convolution. The computation of recursive time- and frequency- responses lead to low-pass filter algorithms for direct, cascade, parallel and lattice structures described as the ratio of two polynomials of the z-transform variable. Low-pass designs are then extended to yield high-pass, band-pass and band-stop filters with linear phase responses. Four main types of filters are considered: Butterworth, Chebyshev, Bessel and Windowing functions. The first three use analog conversion to convert desirable analog filter equations into their digital equivalents, while the latter uses predefined window functions. Finally, execution time is further improved using ILP (Instruction Level Parallelism) software optimization and parallelization techniques. In addition, these recursive designs provide a platform on which more sophisticated methods such as multidimensional, velocity, deconvolution, zero-phase and minimum-phase filtering are described.