Design and responses of Butterworth and critically damped digital filters

For many years the Butterworth lowpass filter has been used to smooth many kinds of biomechanical data, despite the fact that it is underdamped and therefore overshoots and/or undershoots data during rapid transitions. A comparison of the conventional Butterworth filter with a critically damped filter shows that the critically damped filter not only removes the undershooting and overshooting, but has a superior rise time during rapid transitions. While analog filters always create phase distortion, both the critically damped and Butterworth filters can be modified to become zero-lag filters when the data are processed in both the forward and reverse directions. In such cases little improvement is realized by applying multiple passes. The Butterworth filter has superior ‘roll-off’ (attenuation of noise above the cutoff frequency) than the critically damped filter, but by increasing the number of passes of the critically damped filter the same ‘roll-off’ can be achieved. In summary, the critically damped filter was shown to have superior performance in the time domain than the Butterworth filter, but for data that need to be double differentiated (e.g. displacement data) the Butterworth filter may still be the better choice.     

Adaptive usage of the Butterworth digital filter

The Butterworth lowpass filter is a conventional tool that has been commonly used in gait analysis applications. Its operation mainly depends on the selection of the cut-off frequency, which must be done based on the condition of the raw signal assuming that it is stationary. This tool is unable to deal with nonstationary signals especially if impact is involved. In this paper, a modified version of the Butterworth filter that can handle nonstationary signals is presented. The new filter has a variable cut-off frequency distribution defined for each data point, which is determined by local signal characteristics. Because of its adaptive nature, it is possible for the filter to accommodate changes in the frequency content of the signal.     

The influence of digital filter type,amplitude normalisation method,and co-contraction algorithm on clinically relevant surface electromyography data during clinical movement assessments

There is a large and growing body of surface electromyography (sEMG) research using laboratory-specific signal processing procedures (i.e., digital filter type and amplitude normalisation protocols) and data analyses methods (i.e., co-contraction algorithms) to acquire practically meaningful information from these data. As a result, the ability to compare sEMG results between studies is, and continues to be challenging. The aim of this study was to determine if digital filter type, amplitude normalisation method, and co-contraction algorithm could influence the practical or clinical interpretation of processed sEMG data. Sixteen elite female athletes were recruited. During data collection, sEMG data was recorded from nine lower limb muscles while completing a series of calibration and clinical movement assessment trials (running and sidestepping). Three analyses were conducted: (1) signal processing with two different digital filter types (Butterworth or critically damped), (2) three amplitude normalisation methods, and (3) three co-contraction ratio algorithms. Results showed the choice of digital filter did not influence the clinical interpretation of sEMG; however, choice of amplitude normalisation method and co-contraction algorithm did influence the clinical interpretation of the running and sidestepping task. Care is recommended when choosing amplitude normalisation method and co-contraction algorithms if researchers/clinicians are interested in comparing sEMG data between studies.     

Filtering the surface EMG signal: Movement artifact and baseline noise contamination

The surface electromyographic (sEMG) signal that originates in the muscle is inevitably contaminated by various noise signals or artifacts that originate at the skin-electrode interface, in the electronics that amplifies the signals, and in external sources. Modern technology is substantially immune to some of these noises, but not to the baseline noise and the movement artifact noise. These noise sources have frequency spectra that contaminate the low-frequency part of the sEMG frequency spectrum. There are many factors which must be taken into consideration when determining the appropriate filter specifications to remove these artifacts; they include the muscle tested and type of contraction, the sensor configuration, and specific noise source. The band-pass determination is always a compromise between (a) reducing noise and artifact contamination, and (b) preserving the desired information from the sEMG signal. This study was designed to investigate the effects of mechanical perturbations and noise that are typically encountered during sEMG recordings in clinical and related applications. The analysis established the relationship between the attenuation rates of the movement artifact and the sEMG signal as a function of the filter band pass. When this relationship is combined with other considerations related to the informational content of the signal, the signal distortion of filters, and the kinds of artifacts evaluated in this study, a Butterworth filter with a corner frequency of 20 Hz and a slope of 12 dB/oct is recommended for general use. The results of this study are relevant to biomechanical and clinical applications where the measurements of body dynamics and kinematics may include artifact sources.     

Elimination of electrocardiogram contamination from electromyogram signals: An evaluation of currently used removal techniques.

Trunk electromyographic signals (EMG) are often contaminated with heart muscle electrical activity (ECG) due to the proximity of the collection sites to the heart and the volume conduction characteristics of the ECG through the torso. Few studies have quantified ECG removal techniques relative to an uncontaminated EMG signal (gold standard or criterion measure), or made direct comparisons between different methods for a given set of data. Understanding the impacts of both untreated contaminated EMG and ECG elimination techniques on the amplitude and frequency parameters is vital given the widespread use of EMG. The purpose of this study was to evaluate four groups of current and commonly used techniques for the removal of ECG contamination from EMG signals. ECG recordings at two intensity levels (rest and 50% maximum predicted heart rate) were superimposed on 11 uncontaminated biceps brachii EMG signals (rest, 7 isometric and 3 isoinertial levels). The 23 removal methods used were high pass digital filtering (finite impulse response (FIR) using a Hamming window, and fourth-order Butterworth (BW) filter) at five cutoff frequencies (20, 30, 40, 50, and 60 Hz), template techniques (template subtraction and an amplitude gating template), combinations of the subtraction template and high pass digital filtering, and a frequency subtraction/signal reconstruction method. For muscle activation levels between 10% and 25% of maximum voluntary contraction, the template subtraction and BW filter with a 30 Hz cutoff were the two best methods for maximal ECG removal with minimal EMG distortion. The BW filter with a 30 Hz cutoff provided the optimal balance between ease of implementation, time investment, and performance across all contractions and heart rate levels for the EMG levels evaluated in this study.     

Discrete wavelet transform: a tool in smoothing kinematic data

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.     

便携式心电监护中实时信号处理方法研究

针对心电信号处理过程中的心电信号数字滤波、心电波形的动态显示、心电数据存储等问题,阐述了3个可用于心电信号实时处理的方法：一是运用滤波器频谱的周期性减少了滤波器系数个数,提高了运算速度,并根据卷积公式特点实现了数字滤波的实时性;二是运用基于内存虚拟屏幕技术实现心电波形动态显示,解决了屏幕闪烁和绘图不连续问题;三是采用嵌入式数据库SQLITE实现了心电数据存储。所有方法均考虑实时性要求,并已成功用于课题组开发的便携式心电监护仪,效果较为理想,具有很强的实用价值。     

Electromechanical delay in the vastus lateralis muscle during dynamic isometric contractions

Electromechanical delay (EMD) values were obtained using a cross-correlation technique for a series of 14 repetitive submaximal dynamic isometric contractions of the vastus lateralis performed by five subjects. To avoid a phase lag, which is introduced with one-way filtering, the EMG was processed with a bi-directional application of a second-order Butterworth filter. A mean EMD value of 86 ms (SD = 5.1 ms) was found. Moreover, contraction and relaxation delays were computed and compared. There was a significant difference between the contraction and relaxation delays (P less than 0.005). The mean contraction delay was 81.9 ms and the mean relaxation delay was 88.8 ms. Despite this significant difference, the computed contraction and relaxation delay values lie in the same range as the total phase lag, calculated with the cross-correlation technique. The magnitude of EMD values found supports the need to account for this delay when interpreting temporal aspects of patterns of intermuscular coordination.     

Determining the optimal system-specific cut-off frequencies for filtering in-vitro upper extremity impact force and acceleration data by residual analysis

The fundamental nature of impact testing requires a cautious approach to signal processing, to minimize noise while preserving important signal information. However, few recommendations exist regarding the most suitable filter frequency cut-offs to achieve these goals. Therefore, the purpose of this investigation is twofold: to illustrate how residual analysis can be utilized to quantify optimal system-specific filter cut-off frequencies for force, moment, and acceleration data resulting from in-vitro upper extremity impacts, and to show how optimal cut-off frequencies can vary based on impact condition intensity. Eight human cadaver radii specimens were impacted with a pneumatic impact testing device at impact energies that increased from 20J, in 10J increments, until fracture occurred. The optimal filter cut-off frequency for pre-fracture and fracture trials was determined with a residual analysis performed on all force and acceleration waveforms. Force and acceleration data were filtered with a dual pass, 4th order Butterworth filter at each of 14 different cut-off values ranging from 60Hz to 1500Hz. Mean (SD) pre-fracture and fracture optimal cut-off frequencies for the force variables were 605.8 (82.7)Hz and 513.9 (79.5)Hz, respectively. Differences in the optimal cut-off frequency were also found between signals (e.g. Fx (medial-lateral), Fy (superior-inferior), Fz (anterior-posterior)) within the same test. These optimal cut-off frequencies do not universally agree with the recommendations of filtering all upper extremity impact data using a cut-off frequency of 600Hz. This highlights the importance of quantifying the filter frequency cut-offs specific to the instrumentation and experimental set-up. Improper digital filtering may lead to erroneous results and a lack of standardized approaches makes it difficult to compare findings of in-vitro dynamic testing between laboratories.     

Design principles of biochemical oscillators

Cellular rhythms are generated by complex interactions among genes, proteins and metabolites. They are used to control every aspect of cell physiology, from signalling, motility and development to growth, division and death. We consider specific examples of oscillatory processes and discuss four general requirements for biochemical oscillations: negative feedback, time delay, sufficient 'nonlinearity' of the reaction kinetics and proper balancing of the timescales of opposing chemical reactions. Positive feedback is one mechanism to delay the negative-feedback signal. Biological oscillators can be classified according to the topology of the positive- and negative-feedback loops in the underlying regulatory mechanism.     

The effect of different high-pass filter settings on peak latencies in the event-related potentials of schizophrenics,patients with Parkinson's disease and controls

Eighteen schizophrenic patients, 16 patients with idiopathic Parkinson's disease, and the same numbers of age, sex and education matched controls were examined with oddball experiments for the generation of P3. Individual averages were high-pass filtered at different cut-off frequencies with single-pole digital filters with equivalent analogue Butterworth filter profiles. The purpose of this procedure was to simulate analogue high-pass filters used in clinical studies from different centres and to examine their potential effect on group differences. Increasing high-pass filters resulted in a phase lead for all peaks examined (N1, P2, N2, P3). The only group differences were found for P3, which showed a greater phase lead in controls than in the patient groups, usually resulting in a more pronounced group difference. Similar wave forms and filter properties could be modelled by synthetic wave forms consisting of sine waves of different frequencies.     

Endpoint error in smoothing and differentiating raw kinematic data: An evaluation of four popular methods

‘Endpoint error’ describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's (1982, J. Biomechanics 15, 99–105) modification of the Pezzack et al. (1977, J. Biomechanics, 10, 377–382) raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack et al. (1977) data set. In fact, the quintic spline performed best with non-padded data (cumulative error=48.0 rad s⁻²). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error=226.6 rad s⁻²). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error=68.8 rad s⁻²) than when applied to analogous subsets padded by reflection (average cumulative error=86.1 rad s⁻²).     

A rapid algorithm for processing digital physiologic signals: Application to skeletal muscle contractions

Quantifying mechanical output is fundamental to understanding metabolism that fuels muscle contraction and more recent attempts to understand signal transduction and gene regulation. The latter requires long-term application of exercise protocols that result in large amounts of data on muscle performance. The purpose of this study was to develop software for automated quantification of skeletal muscle contractions. An in situ mouse sciatic nerve stimulation model was used to produce contractions over a broad range of frequencies and recorded as both digital and analog signals using a PC analog to digital converter board and chart recorder, respectively. Spectral analysis of the noise components formed the basis for designing a smoothing Chebyshev filter. Algorithms implemented in custom software identified twitches and estimated baseline levels from the smoothed signal. The time to peak force, peak force, tension-time integral, and half-relaxation time were determined for each twitch after baseline correction. The automated results were compared to those obtained from manual measurements of the analog signal. Bland–Altman analysis of the parameters computed from digital signals compared with the corresponding measurements by manual planometry demonstrates the agreement of the digital processing algorithm with planometry over a wide range of twitch characteristics. This program may also be used to study the mechanics of other preparations from isolated muscles, human proximal limb performance, and other digital physiologic signals. Adaptation of the filter function is required to apply the analysis to another experimental apparatus with differing noise characteristics. A full version of the program and instructions for its use are available for download at www.rad.msu.edu.     

Extraction of the EPP Component from the Surface EMG

A surface electromyogram (EMG), especially when recorded near the neuromuscular junction, is expected to contain the endplate potential (EPP) component which can be extracted with an appropriate signal filter. Two factors are important: the EMG must be recorded in monopolar fashion, and the recording must be done so the low frequency signal corresponding the EPP is not eliminated. This report explains how to extract the EPP component from the EMG of the masseter muscle in a human subject. The surface EMG is recorded from eight sites using traditional disc electrodes aligned along over the muscle, with equal inter-electrode distance from the zygomatic arch to the angle of mandible in response to quick gum clenching. A reference electrode is placed on the tip of the nose. The EPP component is extracted from the raw EMGs by applying a high-cut digital filter (2nd dimension Butterworth filter) with a range of 10-35 Hz. When the filter is set to 10 Hz, the extracted EPP wave deflects either negative or positive depending on the recording site. The difference in the polarity reflects the sink-source relation of the end plate current, with the site showing the most negative deflection corresponding to the neuromuscular junction. In the case of the masseter muscle, the neuromuscular junction is estimated to be located in the inferior portion close to the angle of mandible. The EPP component exhibits an interesting oscillation when the cut-off frequency of the high-cut digital filter is set to 30 Hz. The EPP oscillation indicates that muscle contraction is adjusted in an intermittent manner. Abnormal tremors accompanying various sorts of diseases may be substantially due to this EPP oscillation, which becomes slower and is difficult to cease.Download video file.^{(79M, mp4)}     

An internal model architecture for novelty detection: implications for cerebellar and collicular roles in sensory processing

The cerebellum is thought to implement internal models for sensory prediction, but details of the underlying circuitry are currently obscure. We therefore investigated a specific example of internal-model based sensory prediction, namely detection of whisker contacts during whisking. Inputs from the vibrissae in rats can be affected by signals generated by whisker movement, a phenomenon also observable in whisking robots. Robot novelty-detection can be improved by adaptive noise-cancellation, in which an adaptive filter learns a forward model of the whisker plant that allows the sensory effects of whisking to be predicted and thus subtracted from the noisy sensory input. However, the forward model only uses information from an efference copy of the whisking commands. Here we show that the addition of sensory information from the whiskers allows the adaptive filter to learn a more complex internal model that performs more robustly than the forward model, particularly when the whisking-induced interference has a periodic structure. We then propose a neural equivalent of the circuitry required for adaptive novelty-detection in the robot, in which the role of the adaptive filter is carried out by the cerebellum, with the comparison of its output (an estimate of the self-induced interference) and the original vibrissal signal occurring in the superior colliculus, a structure noted for its central role in novelty detection. This proposal makes a specific prediction concerning the whisker-related functions of a region in cerebellar cortical zone A(2) that in rats receives climbing fibre input from the superior colliculus (via the inferior olive). This region has not been observed in non-whisking animals such as cats and primates, and its functional role in vibrissal processing has hitherto remained mysterious. Further investigation of this system may throw light on how cerebellar-based internal models could be used in broader sensory, motor and cognitive contexts.     

Empirical mode decomposition based filtering techniques for power line interference reduction in electrocardiogram using various adaptive structures and subtraction methods

Electrocardiogram (ECG) is a vital sign monitoring measurement of the cardiac activity. One of the main problems in biomedical signals like electrocardiogram is the separation of the desired signal from noises caused by power line interference, muscle artifacts, baseline wandering and electrode artifacts. Different types of digital filters are used to separate signal components from unwanted frequency ranges. Adaptive filter is one of the primary methods to filter, because it does not need the signal statistic characteristics. In contrast with Fourier analysis and wavelet methods, a new technique called EMD, a fully data-driven technique is used. It is an adaptive method well suited to analyze biomedical signals. This paper foregrounds an empirical mode decomposition based two-weight adaptive filter structure to eliminate the power line interference in ECG signals. This paper proposes four possible methods and each have less computational complexity compared to other methods. These methods of filtering are fully a signal-dependent approach with adaptive nature, and hence it is best suited for denoising applications. Compared to other proposed methods, EMD based direct subtraction method gives better SNR irrespective of the level of noises.     

Abundance estimation of rocky shore invertebrates at small spatial scale by high-resolution digital photography and digital image analysis

We have tested both the usefulness of high-resolution digital photography for data acquisition and digital image analysis, by non-supervised classification and high pass filter, for recognition and abundance estimation of benthic intertidal organisms. These digital tools were compared with visual scan and photo quadrat conventional methods. The comparison was done using 40 quadrats (10×5 cm) randomly selected along a 5-m transect on the rocky shore of the Pemaquid Point, Maine, USA. ANOVA for repeated measures was used to test differences among methods. Monte Carlo simulation analysis was used to explore differences among methods over a large set of data (n=100, 500, 1000 quadrats). Differences among methods were observed when 40 quadrats were used. Tukey multiple comparison test showed that abundance estimation from visual scan, photo quadrat and digital image analysis by high pass filter do not differ significantly among them but differ from non-supervised classification results. Due to its accurate estimation, high pass filter (Prewitt) method was chosen as the most reliable digital method to estimate species abundance. Monte Carlo simulation of visual scan, photo quadrat and high pass filter results showed significant differences when the number of quadrats was larger. These results showed that the combined use of digital photography and digital image analysis techniques for the acquisition and analysis of recorded data is a powerful method for the study of intertidal benthic organisms. Results produced using these techniques were similar than those produced by conventional methods but were obtained in a much-reduced time.     

Estimating joint kinematics from skin motion observation: modelling and validation

Modelling of soft tissue motion is required in many areas, such as computer animation, surgical simulation, 3D motion analysis and gait analysis. In this paper, we will focus on the use of modelling of skin deformation during 3D motion analysis. The most frequently used method in 3D human motion analysis involves placing markers on the skin of the analysed segment which is composed of the rigid bone and the surrounding soft tissues. Skin and soft tissue deformations introduce a significant artefact which strongly influences the resulting bone position, orientation and joint kinematics. For this study, we used a statistical solid dynamics approach which is a combination of several previously reported tools: the point cluster technique (PCT) and a Kalman filter which was added to the PCT. The methods were tested and evaluated on controlled human-arm motions, using an optical motion capture system (Vicon^TM).

The addition of a Kalman filter to the PCT for rigid body motion estimation results in a smoother signal that better represents the joint motion. Calculations indicate less signal distortion than when using a digital low-pass filter. Furthermore, adding a Kalman filter to the PCT substantially reduces the dispersion of the maximal and minimal instantaneous frequencies. For controlled human movements, the result indicated that adding a Kalman filter to the PCT produced a more accurate signal. However, it could not be concluded that the proposed Kalman filter is better than a low-pass filter for estimation of the motion. We suggest that implementation of a Kalman filter with a better biomechanical motion model will be more likely to improve the results.     

基于DSP与FPAA的电化学信号滤波器

目的：研究对自主研发的DNA电化学分析仪所采集电化学信号的噪声的滤除方法。方法：根据电化学噪声信号的特征及其频率分布范围,采用由现场可编程模拟阵列（FPAA）实现的有高阶低通滤波器和基于DSP实现的FIR数字滤波器相结合的方式,对混合在电化学信号中的高频噪声信号进行滤除。结果：对滤波结果进行分析,频率在100HZ以上的噪声信号基本滤除。结论：FPAA与DSP芯片的结合构成了一个稳定性高,线性相位特性好,实时性强的高效滤波器。