Continuously time‐variable recursive digital band‐pass filters for seismic signal processing

Abstract

A design technique is described for continuously time‐variable recursive digital band‐pass filters for seismic signal processing. Two types of band‐pass filters are considered: a cascade of a low‐pass and a high‐pass filter, and a direct band‐pass filter, with all filters being derived from a continuous unit‐bandwidth Butterworth low‐pass prototype. Linear interpolation of the filter coefficients between points at which they are known exactly is used to reduce the computational overhead. Data are given for determining the length of the interpolation interval to meet prescribed worst case magnitude and frequency error criteria. A zero‐phase response is achieved by filtering in the forward time direction followed by filtering in the reverse time direction. An example is included.

Time-varying filtering in switching systems

“…< a for Q <w (12) The general filtering requirements given by (12) enable the synthesis of constant component filters. Of course, using relation (12) one can not explicitly determine the filter structure and its parameters.…”

“…The mentioned quality coefficient does not take into account the altering parameters of the spectral characteristic. Using the formula (1) which determines the power spectral density of the filter output signal, the new, spectral "measure" of the quality for constant component filters fulfilling relation (12) has been proposed in the form of the following coefficient: 9r ,J IK(jr) 2dT, Vn::::: (8) where K(jr1) is the filter transfer function for t -> oc, and Iq = ' is the normalized frequency.…”

“…The idea of the choice of the quality coefficient in the form (17) can be supported by the following reasoning: the first factor, i.e. the operation time, expresses the duration of the transient state under spectral assumptions (12), the second one determines additional damping of the harmonic components of the signal (comparing to the damping resulting from assumptions (12)). It can be easily perceived that minimizing the coefficient k one improves the quality of the filter [14].…”

“…Very good results were achieved e.g. in seismic data processing [11], [12] and medical measurements [13].…”

A novel concept of phase-compensated continuous-time filters

“…Very good results were achieved in seismic data processing [13], medical measurements [14], navigation systems [15], speech analysis [16], and digital signal processing [17,18].…”