Essentials of Geophysical Data Processing

A filter may be a physical system or computational algorithm with an input and output. If the filter is linear, then the relationship between input and output is the same regardless of the amplitude of the input. Throughout this chapter and the entire book we consider only time-invariant linear filters, that is, linear filters whose properties do not change with time. As a consequence, linear systems and filters obey a superposition principle, so that when two inputs are added together the output is the sum of the separate outputs that would result from separate inputs. Another consequence is that a single-frequency sinusoidal input produces a sinusoidal output at exactly the same frequency and no other. As a result, linear systems and filters are preferred models for physical processes and for data processing because they allow analysis and implementation in both the frequency and time domains. The DFT presented in theis the main tool for frequency domain analysis and implementation. This chapter develops important elements used in time domain implementation: digital filter equations and discrete convolution; the transfer function; and the impulse response. These concepts are extended to the properties of a cascade of linear filters (the successive application of several different filters to a time series) and are used to define the concept of an inverse filter. Example applications of linear filters in data processing, as models of physical processes, and in methods for finding practical inverse filters appear inand .