Med,& Biol. Eng. & Comput., 1977, 15, 534-540
Online digital filters for biological signals: some fast
designs for a small computer
P. A. Lynn
Department of Electrical & Electronic Engineering, University
of Bristol,
Bristol 8, England
Abstract--After reviewing the design of a class of Iowpass recursive digital filters having integer
multiplier and linear phase characteristics, the possibilities for extending the class to include high
pass, bandpass, and bandstop ('notch') filters are described. Experience with a PDP 11 com-
puter has shown that these filters may be programmed simply using machine code, and that
online operation at sampling rates up to about 8 kHz is possible. The practical application of
such filters is illustrated by using a notch design to remove mains-frequency interference
from an e.c.g, waveform
Keywords--Digital filters, On-line computing, Signal processing, Notch filter
1 Introduction
ThE INCREASINO use of digital computers in bio-
medical research has been accompanied by a growing
awareness of the advantages of digital filters over
their more conventional analogue counterparts for a
variety of signal processing applications. These
advantages include freedom from drift in filter
performance due to ageing or temperature change,
and the ease with which filter characteristics may be
modified by adjusting a set of programmed numerical
coefficients. In an early report on an important
biomedical application, WEAVER et al. (1968)
described a suite of computer programs for filter-
ing e.c.g, data on an IBM 7090 computer. More
recently, TAYLOR and MACFARLANE (1974) have
investigated some of the practical problems of
programming digital filters on a small computer
such as the PDP8, and have discussed the relative
speed of operation of a variety of lowpass filters
applied, once again, to the processing of e.c.g.
waveforms.
The speed of operation of a particular digital filter
is likely to be a decisive factor when online working
is required, and many otherwise attractive designs
prove too slow for applications such as the real-time
processing of e.c.g, or e.m.g, signals. The user of a
small digital computer--even if it has high-level
language facilities such as Basic or Fortran--will
often find it necessary to return to machine-code
programming to get a digital filter operating at any-
thing like its maximum speed. Once in machine
code, he will probably be armed with little more
than the basic manipulations of binary arithmetic.
At first sight, therefore, the possibilities for online
First received 28th October and in finn/form 19th November 1976
filtering of biological signals on a small computer
look distinctly limited.
However, there is one class of recursive digital
filters which uses only small integer multipliers, and
which is therefore both simple to program and
fast in execution (LYNN, 1975). The processing of
biological signals with lowpass filters of this type has
been discussed both by LYNN (1971) and TAYLOR
and MACrARLANE (1974), although without specific
reference to online operation. The aim of this paper
is to review the basis of design of such filters, to
extend the class to include highpass, bandpass and
bandstop characteristics, and finally to report some
practical results obtained with an online PDPI1
computer.
2 Class of lowpass recursive digital filters
The basis of design of the class of filters covered
by this paper may be introduced by considering
the filter recurrence formula
fin = Xn--Xn-m
where y. represents the current (filtered) output
sample value from the filter, xn represents the
current (raw-data) input sample, and x,_m repre-
sents the input sample delivered to the filter m
sampling periods previously. This time-domain
description of the filter may be converted into a
transfer function using z-transform notation (JURY,
1964: BO~NER and CONSTA~TINIDES, 1975). Thus
Y(z) = 1.X(z)-z-".X(z),
from which the transfer function G(z) is derived as
Y(z)
G(z)--- - (1--z -m)
X(z)
534 Medical & Biological Engineering & Computing September 1977