Presently, there is no generally accepted approach to automated measurement of pulse duration in cardiac cycles. This makes it difficult to compare the results obtained by different cardiograph models. At present, this problem is not very urgent because the duration of cardiopulses is still measured manually from the ECG records with an accuracy of about 10 msec [8, 13]. However, methods of comparison of the results of repeated examinations of the same patient during a significant length of time that are presently being introduced used into medical practice require the accuracy of the measurements to be at least 1 msec. Electrocardiographs providing such accuracy of measurements are available, but differences in algorithms of automated measurement in this case becomes a significant problem.The goal of this work was to consider various algorithms of measurement of duration, or, more precisely, various algorithms of determining the beginning and end of cardiopulses, which allows the duration of the pulse to be easily calculated. Development of such algorithms is one of the tasks of mathematical statistics. A comparative survey of algorithms given below treats this problem from the point of view of electrocardiography. Noise stability and accuracy of determination of the beginning of a pulse are chosen as the criteria for comparison of various algorithms. Specific Physiological Features of the Be~nning of Cardiac Cycle PulsesRecent studies show [20] that the shape of cardiopulses at their beginning is rather complicated and has various phases. Each cardiopulse (especially the P wave) is preceded with a fluctuation process of spontaneous generation of artifacts (background myographic noise). At a certain moment in time, sinoatrial node ceils undergo collective excitation which is transmitted to adjacen t regions of the myocardial auricles. The steepness and shape of the leading edge of the excitation pulse are determined by the rate of excitation transmission and changes in the total volume of depolarized ceils. Initially, the process propagates in three dimensions, so it can be concluded that its rate is proportional to the third power of time. The measured rate is proportional to the third power of time because of the vector selectivity of ECG leads. Taking into account the thickness of myocardial walls (several mm in the region of the auricles), it can be concluded that the first steep phase of the process occurs within 1-4 msec. It is followed by a more flattened phase and the end of the pulse. The shape of P wave at its beginning is determined by the geometry of auricle muscles, anisotropy of excitation transmission rates, and vector selectivity of the lead.The process of appearance of the QRS complex is different from that described above. The QRS complex is preceded by the repolarization process in auricles and signals from the atrioventricular node, which transmit excitation with a delay to the His' bundle. A branched network of the His' bundle conducting paths distributes excitation over the endocardial pap...

Presentation of a biomedical signal (in particular, cardiological signal) in tabulated form in PC memory is the first and often most important stage of its automatic analysis. The simplest form of such presentation is sampiing of a signal at a constant step. There are also more sophisticated methods of sampling. The goal of such sampling is to compress the data so that all important information is retained in a minimum volume of information.Methods of transformation of ECG developed in 1959 independently by Pipberger and Kaseres have received wide acceptance. These methods are based on automatic determination of coordinates of separate ECG waves and measurement of their amplitude and time parameters. This approach, which has now become classical, has gained such wide acceptance because it imitates the methods used by skilled physicians. During the evolution of this approach, the method of transformation of an ECG into a cardiointervalogram was developed. A eardiointervalogram is a time series made up of durations of successive cardiocyctes. Studies of cardiac rhythm later became an independent branch of medical science.The two fundamental approaches on which the first stage of automatic analysis of cardiological information is based were developed and tested for the purpose of ECG processing. This was mainly due to specific properties of ECG signal which make it the most feasible of all physiological signals for automatic analysis. Also, ECG provides very valuable diagnostic information.The goal of this work was to describe an algorithm of partial or complete morphological analysis of car- 27 formation (LST) to be performed. It allows diagnostically valuable elements of cardiosignaI within a narrow frequency band to be selected and noise to be eliminated. The problem of morphological analysis can be reduced to determination of coordinates of local extremums of the transformed curve. The algorithm should determine the coordinates over the entire frequency range.Consider differences of order i of the following type:where {X,} is the series of discrete values of the signal; {Y,} is the series of values of differences of order i; V is the differential operator with a shift back; K, is the shift (decimation) coefficient; i is the order of the difference. Equation (2) is expanded as follows:-i

Automatic algorithms for measurement and decoding of ECG have been developed since the mid 1970's. Now, virtually all manufacturers of electrocardiographs offer such software. Therefore, the problem of compatibility is rather urgent, and a unified approach to assessment of efficiency and measuring accuracy of devices available from different manufacturers is required. This can be implemented using a unified reference (standard) test signal. Presently, the correctness of the results of measurements is evaluated by physician expert. Therefore, all programs and algorithms include a correction mode, which allow the results obtained automatically to be corrected by the physician expert. Initially, this mode was rather convenient, although at the present state of development of measuring systems there is a distinct demand for fully automatic mode of data processing. Indeed, there is no need to correct the results of measurements of an ordinary ruler or other measuring instruments. It should be emphasized that Significant diversity of ECG forms inevitably results in the situations where automatic processing is impossible. However, advanced processing algorithms should distinguish between such situations and simple cases, when physician help is not required. The range of automatic diagnosis should be specified in the documentation.Domestic medical industry produces several models of generators of standard reference ECG signals. GF05 and GF07 generators are available from the Ekran Scientific-Manufacturing Association (Moscow). These devices have been developed just in time to provide metrological support of electrocardiographic equipment up to the early 1990's. However, new models of electrocardiographic equipment are based on stochastic methods of determination of the R--R interval, which require more sophisticated test signals. In addition, a two-channel signal should be synthesized to test these devices.An ECG monitor should simultaneously measure a large number of parameters and decode the ECG waves. Therefore, the reference signal for testing measuring algorithms should have rather an elaborate shape. It should simulate an ECG signal with sufficiently high accuracy. However, the reference signal for testing measuring algorithms should meed additional requirements. The ECG measuring algorithms should be sufficiently insensitive to power line noise and noise artifacts. Therefore, the ECG measuring algorithms should be supplemented by a reference power line noise signal and a reference signal of noise artifacts. The decision making procedure should also be unified. This includes evaluation of systematic errors, mean square value of random error, efficiency of contour analysis (recognition of the cardiac cycle components), and threshold values of minimum signal resolution. For example, either the amplitude of the P-wave or its double-humped character could be poorly resolved. Either the Q-wave or its beginning could be resolved insufficiently against the background of well-resolved R-wave. The problem of identification ...

Progressively increasing use of digital devices produces a significant increase in the accuracy of detection and processing of biophysical signals. Such increase in the measuring accuracy gives rise to the development of new instrumental methods of medical examination. Therefore, the requirements for the analysis of possible sources of errors has become more stringent and methods of their elimination more urgent. The goal of this work was to apply KoteInikov's transformation theorem to analysis of signal conversion from analog to digital form.Analog-to-digital converters (ADC) are used in most modem diagnostic devices. Signal conversion is based on the fundamental Kotelnikov transformation theorem [3, 8, 9].The structure of an analog-to-digital conversion is illustrated in Fig. 1. The converter consists of an input Falter, which limits the frequency band of the signal; a multiplier of the signal by a sequence of f-pulses with repetition frequency Fq (ADC, in the case considered in this work); and a output interpolation filter designed to restore the analog signal. Kotelnikov's transformation of ideal signals is noiseless. However, this is not true in actual electronic devices, ha this work we consider the errors inherent in actual characteristics of input and interpolation filters.In terms of frequency conversion, Kotelnikov's transformation can be represented by a heterodyne frequency shift provided that sampling (e.g., analog-to-digital conversion) is implemented by a mixer or a multiplier. The spectrum of the heterodyne sequence &pulses is discrete with the repetition frequency equal to the sampling frequency. Multiplication of functions in temporal space is equivalent to their convolution in spectral space. Therefore, the spectrum of the output signal has wings about each line of a discrete spectrum of &pulses. If the spectrum of the input signal is restricted to Fq/2, heterodyne transformation does not cause spectral superposition, and the resulting spectrum can be restored without garbling (Fig. 2). Instrumental implementation of the Kotelnikov's transformation requires an input Falter to limit the input frequency band and to match it to the ADC frequency range, sampling frequency Fq, and the frequency range of the output interpolation filter. The frequency characteristics of the ideal Kotelnikov's filter are rectangular, and they cannot be achieved in practice. Below we consider the deviations of actual spectral characteristics of Kotelnikov's filters from ideal.1. Requirements for the input filter. If the spectrum of the input biological signal is limited, the input filter is not required. However, actual useful signal is accompanied by external artifacts and noise, as well as internal noise of the amplification tract, which usually have a very wide spectrum. Therefore, the input filter is required to avoid noise interference with the heterodyne effect of spectral mixing described above. The input filter should meet rather stringent requirements, provided that the noise dispersion does not exceed an allow...