Frequency synthesis of digital filters based on repeatedly applied unweighed moving average operations.

Simple formulae are presented for designing filters based on repeatedly applied moving average operations with unit coefficients. Design formulae are derived to synthesise the filter in a way that satisfies specified passband and stopband specifications. These filters are attractive because of the reasonable frequency characteristics, the computational efficiency of the design and filter algorithms, and the uncomplicated implementation in software.

Spectra of data sampled at frequency-modulated rates in application to cardiovascular signals: Part 1. Analytical derivation of the spectra.

Beat-to-beat cardiovascular signals, e.g. a series of systolic pressure values, can be considered as time series which are pulse amplitude modulated (PAM) and pulse frequency modulated (PFM). The latter process, due to variations in heart rate, causes the series to become non-uniformly spaced in time. If PAM is to be quantified by spectral analysis, the influence of PFM must be known. An analytical expression is therefore derived for the spectrum of sinusoids which are sampled according to the output event series of a linear integral pulse frequency modulator (IPFM). We conclude that two spectral components arise at the difference and sum of the PFM and PAM frequencies, fp +/- fx, with amplitudes proportional to the PFM modulation depth. These components appear as a DC component and as a first harmonic if both modulating frequencies are equal. In addition, a cluster of spectral components appears around the mean pulse frequency fo (i.e. mean heart rate), at frequencies fo-nfp +/- fx, which may leak into the signal band. From these theoretical considerations, we conclude that the amplitude spectrum of a sinusoidally varying systolic blood pressure series can contain up to 20-30% spurious components, owing to the heart rate modulation process.

Spectra of data sampled at frequency-modulated rates in application to cardiovascular signals: Part 2. Evaluation of Fourier transform algorithms.

For three direct Fourier transform algorithms we quantified the influence of pulse frequency modulation (PFM) on the spectral estimation of pulse amplitude modulation (PAM). The simulation study is based on sinusoid functions sampled according to a pulse sequence which is the output of an integral pulse frequency modulator (IPFM). One algorithm exactly reproduces the theoretical spectrum derived in Part 1. The other two, including the classical FFT, scale all PFM-induced components in a different way, and in addition, generate higher modulating frequency harmonics. For a PFM depth below 30%, the sum of spurious PFM components is almost linearly dependent on this modulation depth, for all three algorithms. Dividing the effect of PFM in a 'harmonic' and 'aliasing' distortion, we found that the FFT has a relatively high harmonic distortion, compared to an algorithm that takes into account the non-uniform character of the data. In the cardiovascular (worst) case of 30% modulation in heart rate (PFM) at a frequency of 0.1 Hz, the FFT spectrum of beat-to-beat systolic blood pressure variations contains approximately 20% of spurious components caused solely by the modulation in time occurrences of the blood pressure samples. The 'non-uniform' algorithm performs twice as well in this case.

Methods in heart rate variability analysis: which tachogram should we choose?

We investigated the practical impact of the representation of the cardiac rhythm--the cardiotachogram--on two elementary spectral indexes in heart rate variability analysis: the low-frequency (0.07-0.14 Hz) and high-frequency (0.14-0.40 Hz) powers. Five commonly used tachograms (inter-beat interval function/series, counts, instantaneous heart rate function/series) were compared. Measurements were done on seven volunteers in the supine and standing positions. Ratios, and their deviations from 100%, of alternative power values were calculated. Mean low-frequency and high-frequency ratio deviations ranged from 0 to 5% and from 6 to 37%. The spectrum of counts yielded on average more (15-37%) high-frequency power. Spectra were incomparable without normalization of the tachogram with respect to heart rate. In conclusion, (i) the choice of a particular spectrum may lead to differing conclusions on the vagal contribution to heart rate variability and (ii) inconclusive results from studies using different tachogram variants can partly be due to the omission of normalization.

Recording and processing of fetal movements and sounds obtained with the Inpho inductive transducer.

A recently developed transducer based on an inductive principle allows recording of fetal displacement signals on the maternal abdominal wall. The transducer is a relatively passive device, in contrast to commonly applied ultrasound transducers. This permits long-term observation of fetal movements and sounds. The bandwidth of the system is DC-200 Hz (+/- 3 dB), and signal-to-noise ratios of more than 96 dB have been measured in a laboratory setup, whereas in the practical situation a signal-to-noise ratio of 78 dB has been established. The transducer has been applied to study fetal respiratory sinus arrhythmia, which means that fetal breathing movements have to be extracted from the transducer's output. This proved possible by digital filtering of the displacement signal as detected by the transducer. The transducer has also been applied in a study where the signal-to-noise ratio of fetal heart sounds as a function of location of the fetus and position of the transducer on the maternal abdominal wall has been studied. It proved possible to adequately record fetal heart sounds for measurement of fetal heart rate. Also uterine activity could be recorded using the sensor's DC output.

Coherent average technique--a tutorial review.

This paper highlights the effects of digitization in relation to the effective numberical range over which the signal to be averaged has to be resolved. The effect of quantization noise on the number of averaging cycles is assessed and it is shown that for averaging weak signals such as the HIS bundle electrogram, high resolution analogue-to-digital (A/D) conversion is required so as to prevent a substantial increase in the number of averaging cycles. Also the requirement for adequate low-pass filtering is discussed and relationships between the numerical range of the A/D conversion process, the order of the low-pass filter, its cut-off frequency and sampling frequency are formulated.

Recording fetal breathing movements with a passive transducer based on an inductive principle.

A new transducer has been developed, based on an inductive principle, for recording fetal movements and sounds. The compliance of this transducer, the INductive PHOno-sensor (INPHO), can be matched to that of the maternal abdomen to provide an optimal transfer of displacement between maternal abdomen and transducer. In this manner, it is possible to detect fetal breathing movements by digital filtering of the INPHO signal in a frequency band between 0.5 and 2.0 Hz. Singular breathing movements can be detected and this was verified by real time ultrasound imaging. The INPHO transducer shows a flat (+/- 1.5 dB) frequency response between 0.2 and 200 Hz. The signal-to-noise ratio of the transducer system is better than 95 dB, and enables very weak movements and sounds to be detected. Spectral analysis of the processed signal shows that modulation of fetal breathing by maternal breathing takes place. The measuring setup allows for the quantitative assessment of fetal respiratory sinus arrhythmia.

A comparative experimental study of fetal phono- and movement-sensors from Amsterdam, Cambridge and Edinburgh.

This paper describes the experimental studies and results of a collaborative investigation between three European institutes: Amsterdam, Cambridge and Edinburgh. The object of this investigation and the collaborative exchanges was to evaluate and compare different sensors for recording fetal sounds and movements from each centre. This would be carried out in a series of experimental and clinical tests involving researchers from each of the European institutes, and using three sensors: one from each centre. Experimental measurements have been performed regarding the conversion gain, frequency response, equivalent input noise and dynamic range of the transducers. The measurements were carried out using a vibration-free table testing rig to evaluate these characteristics of each of the sensors. The equivalent input noise ranged from 50 nm to 1600 nm for the transducers studied.

Spectral analysis of spontaneous heart rate variation in diabetic patients.

In 28 diabetic patients and 62 control subjects spectral analysis of spontaneous beat-to-beat RR interval variations was performed. The spectral analysis focused on the dominant frequency of the mid-frequency band (0.04-0.12 Hz) or baro-oscillatory phenomenon (BOP). Compared with control subjects the dominant frequency of the BOP (BOP frequency) in the diabetic patients was lower (p less than 0.001), and the difference increased with age. The shift of the BOP frequency was positively correlated with the reduced variation in heart rate during deep breathing (r = 0.80, p less than 0.001) in the diabetic patients. These findings indicate that determination of the BOP frequency is a useful method for assessing cardiovascular autonomic function, supplementary to the known cardiovascular reflex tests. Measurement of the BOP frequency has the advantage that no active patient co-operation is required.

A transducer for detection of fetal breathing movements.

The paper describes a new transducer for detection of fetal movements and sounds from the maternal abdominal wall. This transducer is based on an inductive principle. The compliance of the transducer should match the compliance of the maternal abdominal wall in order to detect the very weak acoustic signal caused by individual fetal breathing movements. The contact area of the transducer is supported on a membrane, the tension of which can be adjusted so as to match the compliances of tissue and transducer. The goal of this paper is to investigate detection of fetal movements in order to monitor fetal condition and motility. The more specialized field of investigating fetal heart rate variability by studying the relationship between fetal breathing movements and fetal heart rate may become of more interest in the future. The inductive phonometer (INPHO) shows a flat (+/- 1.5 dB) frequency response between 0.2 and 200 Hz which is not affected by the compliance adjustment. Some in vivo measurements have been performed. The transducer signal is stored on a 20MB hard disk of an Olivetti M24 Personal Computer (PC) simultaneously with a control signal indicating the presence of breathing movements. Ultrasound imaging is exclusively used for verification of breathing movements. The images are stored on videotape simultaneously with control signals from the PC for synchronization of data and image. Substantial digital filtering is necessary to discriminate between actual breathing movements and other fetal activities. It is shown that optimal adjustment of the transducer's compliance to that of the maternal abdominal wall is possible and that individual breathing movements can indeed be measured.

A transducer for recording fetal movements and sounds based on an inductive principle.

Recording fetal breathing movements requires a transducer with a large dynamic range. The compliance of the transducer should be matched to the compliance of the maternal abdominal wall in order to pass the very weak acoustic signal caused by heart sounds and fetal breathing movements on to the transducer. The output signal is stored on the hard disc of a personal computer (PC) simultaneously with a control signal indicating the presence of breathing movements. Ultrasound imaging is exclusively used for verification of breathing movements. The images are stored on videotape simultaneously with control signals from the PC for synchronisation of data and image. Substantial digital filtering is necessary to discriminate between actual breathing movements and other fetal activities. It is shown that by optimal adjustment of the transducer's compliance to that of the maternal abdominal wall individual breathing movements can indeed be measured.

Coherent averaging technique: a tutorial review. Part 1: Noise reduction and the equivalent filter.

Coherent averaging is used to recover the response to repetitively applied stimuli when that response is embedded in random noise, and when the signal/noise ratio is fractional. In this paper the improvement in s/n ratio due to averaging is calculated; it is also shown that averaging acts as a filter which attenuates periodic interference when it is not time-locked to the stimulus; the characteristics of this filter are derived.

Coherent averaging technique: a tutorial review. Part 2: Trigger jitter, overlapping responses and non-periodic stimulation.

In Part 1 the principles of coherent averaging were discussed. In Part 2 expressions are developed for the effect on the average of fluctuations in the stimulus-response time. Overlapping responses may cause errors in the averaged response: these errors are analysed. It is shown that the application of non-periodic stimuli may improve the results for both periodic interference and overlapping responses.

A special-purpose computer for on-line statistical analysis of the heart rate.

At present electronic instruments, in particular measuring devices, are widely used in hospitals. However, the usage of information processing systems is mainly limited to academic hospitals because of the costs, the need of skilled staff, etc. In this paper a relatively simple special purpose computer is described for the on-line generation of the tachogram, histogram, and joint interval distribution of a continuously updated series of RR intervals. Moreover mean value and variance of this series are calculated. This instrument has been in clinical use in a nonacademic hospital for one year and has proven to be a useful aid in patient monitoring. Some suggestions for improvement are discussed.