Filtering of kinematic signals using the Hodrick-Prescott filter

The use of the Hodrick-Prescott (HP) filter is presented as an alternative to the traditional digital filtering and spline smoothing methods currently used in biomechanics. In econometrics, HP filtering is a standard tool used to decompose a macroeconomic time series into a nonstationary trend component and a stationary residual component. The use of the HP filter in the present work is based on reasonable assumptions about the jerk and noise components of the raw displacement signal. Its applicability was tested on 4 kinematic signals with different characteristics. Two are well known signals taken from the literature on biomechanical signal filtering, and the other two were acquired with our own motion capture system. The criterion for the selection of cutoff frequency was based on the power spectral density of the raw displacement signals. The results showed the technique to be well suited to filtering biomechanical displacement signals in order to obtain accurate higher derivatives in a simple and systematic way. Namely, the HP filter and the generalized cross-validated quintic spline (GCVSPL) produce similar RMS errors on the first (0.1063 vs. 0.1024 m/s2) and second (23.76 vs. 23.24 rad/s2) signals. The HP filter performs slightly better than GCVSPL on the third (0.209 vs. 0.236 m/s2) and fourth (1.596 vs. 2.315 m/s2) signals.     

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.     

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.     

Effects of low-pass filter combinations on lower extremity joint moments in distance running

Inverse dynamics is a standard tool in biomechanics, which requires low-pass filtering of external force and kinematic signals. Unmatched filtering procedures are reported to affect joint moment amplitudes in high impact movements, like landing or cutting, but are also common in the analysis of distance running. We analyzed the effects of cut-off frequencies in 94 rearfoot runners at a speed of 3.5 m/s. Additionally, we investigated whether the evaluation of footwear interventions is affected by the choice of cut-off frequencies. We performed 3D inverse dynamics for the hip, knee and ankle joints using different low-pass filter cut-off frequency combinations for a recursive fourth-order Butterworth filter. We observed fluctuations of joint moment curves in the first half of stance, which were most pronounced for the most unmatched cut-off frequency combination (kinematics: 10 Hz; ground reaction forces (GRFs): 100 Hz) and for more proximal joints. Peak sagittal plane hip joint moments were altered by 94% on average. We observed a change in the ranking of subjects based on joint moment amplitude. We found significant (p < 0.001) footwear by cut-off frequency combination interaction effects for most peak joint moments. These findings highlight the importance of cut-off frequency choice in the analysis of joint moments and the assessment of footwear interventions in distance running. Based on our results, we propose to use matched cut-off frequencies around 20 Hz in order to avoid large artificial fluctuations in joint moment curves while at the same time avoiding a severe removal of physiological high-frequency signal content from the GRF signals.     

A general solution for the time delay introduced by a low-pass Butterworth digital filter: An application to musculoskeletal modeling

Low-pass Butterworth digital filters are commonly used in biomechanics-related research. In general, the input signal is filtered in the forward and reverse directions so that a temporal shift in the output signal does not occur. There are times, however, when introducing a specific time delay is an important consideration when modeling a physiological event. Filtering the data in the forward direction only can be used as an efficient method to account for a specific time delay. Specific delays are possible by carefully selecting the filter order and cut-off frequency. The purpose of this paper is to present the analytical formulation of a general solution for the time delay introduced by a low-pass Butterworth digital filter.     

The prediction of EEG signals using a feedback-structured adaptive rational function filter

 In this article, we present a feedback-structured adaptive rational function filter based on a recursive modified Gram-Schmidt algorithm and apply it to the prediction of an EEG signal that has nonlinear and nonstationary characteristics. For the evaluation of the prediction performance, the proposed filter is compared with other methods, where a single-step prediction and a multi-step prediction are considered for a short-term prediction, and the prediction performance is assessed in normalized mean square error. The experimental results show that the proposed filter shows better performance than other methods considered for the short-term prediction of EEG signals. Received: 22 September 1998 / Accepted in revised form: 29 February 2000     

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.     

Spectral analysis of photoplethysmographic signals: The importance of preprocessing

Heart rate variability (HRV) is an important and useful index to assess the responses of the autonomic nervous system (ANS). HRV analysis is performed using electrocardiography (ECG) or photoplethysmography (PPG) signals which are typically subject to noise and trends. Therefore, the elimination of these undesired conditions is very important to achieve reliable ANS activation results. The purpose of this study was to analyze and compare the effects of preprocessing on the spectral analysis of HRV signals obtained from PPG waveform. Preprocessing consists of two stages: filtering and detrending. The performance of linear Butterworth filter is compared with nonlinear weighted Myriad filter. After filtering, two different approaches, one based on least squares fitting and another on smoothness priors, were used to remove trends from the HRV signal. The results of two filtering and detrending methods were compared for spectral analysis accomplished using periodogram, Welch's periodogram and Burg's method. The performance of these methods is presented graphically and the importance of preprocessing clarified by comparing the results. Although both filters have almost the same performance in the results, the smoothness prior detrending approach was found more successful in removing trends that usually appear in the low frequency bands of PPG signals. In conclusion, the results showed that trends in PPG signals are altered during spectral analysis and must be removed prior to HRV analysis.     

空间频率通道中噪声对体视匹配的影响

本工作希望了解噪声在各空间频率通道中对体视的影响.产生从5%至35%每隔5%的七个等级的随机点噪声图象,参照Wilson四通道模型的频率分别用两种不同滤波器对随机点立体图对(RDS)及噪声图象进行滤波,然后在各通道图对中加入不同通道噪声进行匹配观察.得到:1.高频通道的体视抗干扰能力高于低频通道.2.Gabor函数滤波后图对的体视抗干扰能力高于Butterworth滤波器滤波后的,但均低于未滤波的.3.当噪声大于15%时,低频噪声对低频图对及高频噪声对高、低频图对的体视匹配有抑制作用,而低频噪声对高频图对则影响很小.4.未滤波及各通道图对的最大噪声容限均不超过25%.     

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.     

Optimal noise filtering in the chemotactic response of Escherichia coli

Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.     

Separation of time and frequency

In the analysis of time-varying signals various functions of time and frequency are used in order to describe the signal as a composition of several frequency bands with varying contributions to the intensity of the signal. For some of them, e.g. the spectrogram, a trade-off has to be made between spectral and temporal resolution. For others, e.g. the complex energy-density function, the interpretation is complicated and confusing. Another function of time and frequency, the Wigner distribution of the analytic signal, lacks both these undesirable properties. The lucid and transparent way in which this real function displays the temporal as well as the spectral characteristics of a real signal, make it a powerful tool in the analysis of time-varying physiological signals.     

肌肉动态收缩期间表面肌电信号的时频分析

介绍了用于肌肉动态收缩期间非平稳表面肌电信号的时频分析方法。用短时傅里叶变换、Wigner-Ville分布及Choi-Williams分布计算了表面肌电信号的时频分布,用于信号频率内容随时间演化的可视化观察。通过计算瞬时频谱参数,对肌肉疲劳的电表现进行量化描述。分析了反复性的膝关节弯曲和伸展运动期间从股外侧肌所记录的表面肌电信号。发现和在静态收缩过程中观察到的平均频率线性下降不同,在动态收缩期间瞬时平均频率的变化过程是非线性的并且更为复杂,且与运动的生物力学条件有关。研究表明将时频分析技术应用于动态收缩期间的表面肌电信号可以增加用传统的频谱分析技术不能得到的信息。     

Characterisation of vortex shedding in vascular anastomosis models using pulsed Doppler ultrasound.

Vortex shedding at vascular anastomoses were investigated in vitro using a 20 MHz pulsed-wave Doppler velocimeter. Centreline velocity measurements were made at various axial distances in simplified polyurethane models of proximal and distal end-to-side anastomoses of angles 15, 30, 45, 60 and 80 degrees using pulsatile flow waveforms similar to those in femoropopliteal bypass grafts. The in-phase and quadrature Doppler signals were recorded and the maximum frequency waveform, averaged over 64 cycles, was obtained using short-time Fourier transform. A fourth-order Butterworth low-pass filter was employed to separate the vortex velocity signal from the convective velocity. The vortex signal envelope was calculated using a Hilbert transform method and the vortex amplitude was taken as the maximum of this envelope. The results show that higher vortex amplitude were found in the proximal anastomoses and under resting flow conditions. Although the vortex amplitudes generally increased with angles of anastomosis, they were found to be higher in the 60 degrees than in the 80 degrees proximal anastomosis. The vortex structures were investigated using spectrograms and these show prominent features at 40-50 Hz indicative of the short-duration oscillatory signals during the decelerative phase of systole expected from the passage of vortices. The study indicates that flow disturbances due to vortex shedding may be a common feature in femoropopliteal bypass grafts.     

Nonstationary Heart Rate Variability in Respiratory Tests

A new method was proposed for processing a nonstationary heart rate by using frequency-modulated signals rather than amplitude-modulated signals equally spaced over several points of time as in the conventional method. A frequency-modulated signal is a set of identical Gaussian peaks that coincide with the true time points of heart beats. A continuous wavelet transform was used to quantitatively describe the heart rhythm signal. A test with controlled breathing was performed as an example and included three consecutive stages: rest, rhythmic breathing at a specified frequency, and exhalation. Tachograms recorded during the breath test was found to be a nonstationary signal with the alternation of peaks of different spectral ranges. A system of quantitative parameters was developed to describe the dynamics of changes in the spectral properties of the tachogram in transitional areas. A static clustering by the effect of the respiratory test and a dynamic clustering in order to identify the time points when the autonomic nervous system is stressed were performed for all subjects. The article discusses the prospects of using the method as a means to analyze the transient effects in various functional tests and as biofeedback that would help to change the heart rhythm.     

心电图信号放大和记录中50Hz干扰滤波的新技术——符合滤波

介绍一种用硬、软件系统实现的滤波器,它能实时滤除ECG信号中50Hz及其高次谐波的干扰,该技术称为符合滤波。在信号处理过程中,当干扰发生变化时滤波器能跟踪这种变化,保持滤波器性能不变。     

A new method for evaluation of cavitation near mechanical heart valves

Evaluation of cavitation in vivo is often based on recordings of high-pass filtered random high-frequency pressure fluctuations. We hypothesized that cavitation signal components are more appropriately assessed by a new method for extraction of random signal components of the pressure signals. We investigated three different valve types and found a high correlation between the two methods (r2: 0.8806-0.9887). The new method showed that the cavitation signal could be extracted without a priori knowledge needed for setting the high-pass filter cut off frequency, nor did it introduce bandwidth limitation of the cavitation signal.