Biomedical signal processing (in four parts). Part 2. The frequency transforms and their inter-relationships

The Role of Surface Electromyography in Data Fusion with Inertial Sensors to Enhance Locomotion Recognition and Prediction

Locomotion recognition and prediction is essential for real-time human–machine interactive control. The integration of electromyography (EMG) with mechanical sensors could improve the performance of locomotion recognition. However, the potential of EMG in motion prediction is rarely discussed. This paper firstly investigated the effect of surface EMG on the prediction of locomotion while integrated with inertial data. We collected EMG signals of lower limb muscle groups and linear acceleration data of lower limb segments from ten healthy participants in seven locomotion activities. Classification models were built based on four machine learning methods—support vector machine (SVM), k-nearest neighbor (KNN), artificial neural network (ANN), and linear discriminant analysis (LDA)—where a major vote strategy and a content constraint rule were utilized for improving the online performance of the classification decision. We compared four classifiers and further investigated the effect of data fusion on the online locomotion classification. The results showed that the SVM model with a sliding window size of 80 ms achieved the best recognition performance. The fusion of EMG signals does not only improve the recognition accuracy of steady-state locomotion activity from 90% (using acceleration data only) to 98% (using data fusion) but also enables the prediction of the next steady locomotion (∼370 ms). The study demonstrates that the employment of EMG in locomotion recognition could enhance online prediction performance.

Towards Prediction of Heart Arrhythmia Onset Using Machine Learning

Current study aims at prediction of the onset of malignant cardiac arrhythmia in patients with Implantable Cardioverter-Defibrillators (ICDs) using Machine Learning algorithms. The input data consisted of 184 signals of RR-intervals from 29 patients with ICD, recorded both during normal heartbeat and arrhythmia. For every signal we generated 47 descriptors with different signal analysis methods. Then, we performed feature selection using several methods and used selected feature for building predictive models with the help of Random Forest algorithm. Entire modelling procedure was performed within 5-fold cross-validation procedure that was repeated 10 times. Results were stable and repeatable. The results obtained (AUC = 0.82, MCC = 0.45) are statistically significant and show that RR intervals carry information about arrhythmia onset. The sample size used in this study was too small to build useful medical predictive models, hence large data sets should be explored to construct models of sufficient quality to be of direct utility in medical practice.

Phenomenology of neurophysiologic changes during surgical treatment of carotid stenosis using signal analysis

Objective

To describe the changes in the shape and topology of the somatosensory evoked potential (SSEP) during carotid endarterectomy, with particular reference to the time of clamping.

Methods

Routine intraoperative monitoring was performed on 30 patients undergoing carotid endarterectomy (15) or undergoing stenting (15) using median nerve SSEPs. Post-operatively the first and second derivatives of the potential were examined. Separate analysis of the SSEP using wavelets was also performed.

Results

In no instances did changes in the SSEP reach clinical significance. The first derivative showed significant changes that were temporally related to the clamp period. After clamping the 'velocity' was higher than baseline. There were changes in the wavelets related to the clamp period with more marked spectral edges at the conclusion of the procedure than baseline. In all instances the patient had a good clinical outcome.

Conclusions

Wavelet and derivative analysis of evoked potentials show changes that are not apparent with measures of amplitude and latency. The clinical relevance of these changes remains uncertain and await larger studies.

Significance

Increased velocity and spectral edges may be markers of increased cerebral blood flow, at least in the setting of pre-existing carotid stenosis.

Design of a novel biomedical signal processing and analysis tool for functional neuroimaging

In this paper, a MATLAB-based graphical user interface (GUI) software tool for general biomedical signal processing and analysis of functional neuroimaging data is introduced. Specifically, electroencephalography (EEG) and electrocardiography (ECG) signals can be processed and analyzed by the developed tool, which incorporates commonly used temporal and frequency analysis methods. In addition to common methods, the tool also provides non-linear chaos analysis with Lyapunov exponents and entropies; multivariate analysis with principal and independent component analyses; and pattern classification with discriminant analysis. This tool can also be utilized for training in biomedical engineering education. This easy-to-use and easy-to-learn, intuitive tool is described in detail in this paper.

The effect of contralateral submaximal contraction on the development of biceps brachii muscle fatigue

OBJECTIVE

The aim of this study was to determine if a submaximal contraction in the contralateral limb affected the fatigability of the dominant limb.

BACKGROUND

Muscle fatigue is a known risk factor for musculoskeletal injury; however, it is unknown whether a submaximal contraction in the nondominant limb, such as for stabilizing a tool or load, affects the rate of development of fatigue, potentially increasing risk of injury. Current ergonomic assessments of injury risk do not involve consideration of submaximal contralateral demands. It was hypothesized that increased neuromuscular drive and active muscle mass during bilateral contractions would increase fatigability.

METHOD

Twelve males isometrically maintained a 30% unilateral contraction and a 30% dominant + 15% nondominant bilateral contraction until failure on two different collection days, separated by 7 days.

RESULTS

No statistically significant differences were found for time to task failure (p = .6204), decrease in maximal force (p = .1698), or alterations in electromyography amplitude (p = .7223) or frequency (p = .3292) between unilateral and bilateral conditions.

CONCLUSION

The hypothesis that the addition of a lesser submaximal isometric contraction would increase fatigability was rejected.

APPLICATION

These findings indicate that in ergonomic settings, muscle fatigability can be estimated by the more demanding task and do not need to be complicated by lesser submaximal contractions in the opposing limb.

A study of leakage rates through mine seals in underground coal mines

The National Institute for Occupational Safety and Health conducted a study on leakage rates through underground coal mine seals. Leakage rates of coal bed gas into active workings have not been well established. New seal construction standards have exacerbated the knowledge gap in our understanding of how well these seals isolate active workings near a seal line. At a western US underground coal mine, we determined seal leakage rates ranged from about 0 to 0.036 m³/s for seven 340 kPa seals. The seal leakage rate varied in essentially a linear manner with variations in head pressure at the mine seals.

A note on the phase locking value and its properties

We investigate the properties of the Phase Locking Value (PLV) and the Phase Lag Index (PLI) as metrics for quantifying interactions in bivariate local field potential (LFP), electroencephalography (EEG) and magnetoencephalography (MEG) data. In particular we describe the relationship between nonparametric estimates of PLV and PLI and the parameters of two distributions that can both be used to model phase interactions. The first of these is the von Mises distribution, for which the sample PLV is a maximum likelihood estimator. The second is the relative phase distribution associated with bivariate circularly symmetric complex Gaussian data. We derive an explicit expression for the PLV for this distribution and show that it is a function of the cross-correlation between the two signals. We compare the bias and variance of the sample PLV and the PLV computed from the cross-correlation. We also show that both the von Mises and Gaussian models are suitable for representing relative phase in application to LFP data from a visually-cued motor study in macaque. We then compare results using the two different PLV estimators and conclude that, for this data, the sample PLV provides equivalent information to the cross-correlation of the two complex time series.

An estimate of fetal autonomic state by time-frequency analysis of fetal heart rate variability

In this study we present a noninvasive method that enables the investigation of the fetal heart rate (FHR) fluctuations. The objective was to design a quantitative measurement to assess the fetal autonomic nervous system and to investigate its development as a function of the gestational age. Our Medical Physics group has developed a complex algorithm for online beat-to-beat detection of the fetal ECG (FECG), extracted from the maternal abdominal ECG signal. We used our previously acquired FECG data, which includes noninvasive recordings of 200 maternal abdominal ECG signals. From these, we chose 35 cases of healthy pregnancies that we divided into three groups according to gestational age: Group 1, 23 +/- 2 wk; Group 2, 32 +/- 1 wk; and Group 3, 39 +/- 1 wk. The FHR variability was analyzed by a time-frequency decomposition based on a continuous wavelet transform. We showed that, independent of the gestational age, most of the FHR power is concentrated in the very-low-frequency range (0.02-0.08 Hz) and in the low-frequency range (0.08-0.2 Hz). In addition, there is power in the high-frequency range that correlates with the frequency range of fetal respiratory motion (0.4-1.7 Hz). In the intermediate-frequency range (0.2-0.4 Hz), the power is significantly smaller. The changes in the average power spectrum in relation to gestation time were carefully and quantitatively examined. The results imply that there is a neural organization during the last trimester of the pregnancy, and the sympathovagal balance is reduced with the gestational age.

Ability of short-time Fourier transform method to detect transient changes in vagal effects on hearts: a pharmacological blocking study

Conventional spectral analyses of heart rate variability (HRV) have been limited to stationary signals and have not allowed the obtainment of information during transient autonomic cardiac responses. In the present study, we evaluated the ability of the short-time Fourier transform (STFT) method to detect transient changes in vagal effects on the heart. We derived high-frequency power (HFP, 0.20-0.40 Hz) as a function of time during active orthostatic task (AOT) from the sitting to standing posture before and after selective vagal (atropine sulfate 0.04 mg/kg) and sympathetic (metoprolol 0.20 mg/kg) blockades. The HFP minimum point during the first 30 s after standing up was calculated and compared with sitting and standing values. Reactivity scores describing the fast and slow HFP responses to AOT were calculated by subtracting the minimum and standing values from the sitting value, respectively. The present results, obtained without controlled respiration, showed that in the drug-free condition, HFP decreased immediately after standing up (P < 0.001) and then gradually increased toward the level characteristic for the standing posture (P < 0.001), remaining lower than in the sitting baseline posture (P < 0.001). The magnitudes of the fast and slow HFP responses to AOT were abolished by the vagal blockade (P < 0.001) and unaffected by the sympathetic blockade. These findings indicate that HFP derived by the STFT method provided a tool for monitoring the magnitude and time course of transient changes in vagal effects on the heart without the need to interfere with normal control by using blocking drugs.

Analysis of rapid heart rate variability in the assessment of anticholinergic drug effects in humans

Anticholinergic agents have widespread therapeutic indications in clinical medicine. In addition, certain other drug groups-such as neuroleptics, antidepressants and antihistamines-possess distinct anticholinergic properties that reduce tolerance and compliance. Especially in patients with heart disease, attention should be paid to cardiac anticholinergic drug effects. The analysis of short-term heart rate variability (HRV) provides a noninvasive tool to estimate vagal cholinergic outflow. In this review article, we present the basic principles of the most relevant techniques to study rapid HRV: the time domain analysis methods RMSSD and pNN50, and the high-frequency (HF) spectral component of HRV. We provide examples of previously reported effects of anticholinergic agents on these measures and also describe how adrenergic drugs may influence them. We have the following recommendations for a clinical pharmacologist investigating anticholinergic agents. (1) If the breathing rate of the study subject can be controlled during the assessment and the electrocardiogram recordings contain good-quality, stationary segments that are at least a few minutes long, then the HF power of HRV should be the method of choice. (2) During uncontrolled conditions, RMSSD should be included in the analyses, because it is less affected by changes in the respiratory pattern and it can be measured from shorter segments of electrocardiogram data. (3) Reduced short-term HRV suggests an anticholinergic, but not necessarily an antimuscarinic drug effect, since the inhibition of cholinergic vagal efferent activity may also originate from central or peripheral adrenergic influences.

Ultrasonic colour flow imaging

Real-time ultrasonic colour flow imaging, which was first demonstrated to be feasible only about a decade ago, has come into widespread clinical use. Ultrasound is scattered by ensembles of red blood cells. The ultrasonic frequency that gives the best signal-to-noise ratio for backscattering from blood depends on the required penetration. The frequency of ultrasound backscattered from flowing blood is shifted by the Doppler effect. The direction of flow can be determined by phase quadrature detection, and range selectivity can be provided by pulse-echo time-delay measurements. The Doppler frequency spectrum can be determined by Fourier analysis. Early two- and three-dimensional flow-imaging systems used slow manual scanning; velocity colour coding was introduced. Real-time colour flow imaging first became feasible when autocorrelation detection was used to extract the Doppler signal. Time-domain processing, which is a broad-band technique, was also soon shown to be practicable, for analysing both radio-frequency pulse-echo wavetrains and two-dimensional image speckle. Frequency- and time-domain processing both require effective cancellation of stationary echoes. The time-domain approach seems to have advantages in relation to both aliasing and the effects of attenuation in overlying tissues. Colour-coding schemes that can be interpreted without the need to refer to keys have been adopted, for both velocity and flow disturbance. Colour coding according to signal power has also been reintroduced. Three-dimensional display has been demonstrated. In interpreting colour flow images, it is important to understand the functions of critical system controls and the origins of artifacts. Various strategies can be adopted to increase the image frame rate. The problems of performance measurement and safety need to be kept under review. There are numerous opportunities for further development of ultrasonic colour flow imaging, including improvements in system design, methods of image display, the use of contrast agents and the solution of previously unexplored clinical problems.

A novel in vivo procedure for volumetric flow measurements

We report on a novel procedure for invasive volumetric blood flow measurements using a commercially available Doppler flow wire system, which could, until now, only measure flow velocity. We here describe a method applicable in vivo to generate both velocity and cross-sectional area information from the same pulsed-wave Doppler signal for volumetric flow assessment. We demonstrate its feasibility and validation in vivo in pig coronary arteries. Our Doppler-derived volumetric flow measurements were compared with the respective transit-time flow and showed an excellent correlation (r = 0.969; p < 0.0001). Agreement between transit-time and Doppler-derived flow measurements could be observed for flow conditions ranging from 30 to 180 mL/min. The mean values for the two methods were 71.4 +/- 43.7 mL/min and 71.3 +/- 42.2 mL/min, respectively. We conclude that this technique might possibly be introduced into future clinical practice as an invasive procedure of choice for the assessment of volumetric blood flow.

[To understand blood pressure and heart rate variability]

OBJECTIVES

To review current data on the heart rate and blood pressure variability.

DATA SOURCES

Search through Medline databases of articles in french or english.

DATA SELECTION

Original articles and case reports were selected according to their quality and main advances. The articles were analysed in order to obtain current data about the methods of study and clinical application of blood pressure and heart rate variability.

DATA SYNTHESIS

Various regulatory systems in the cardiovascular system play crucial roles in controlling and assuring adequate perfusion of the peripheral tissues. Among them the baroreceptor reflex is the most important regulatory mechanism in the short-term control of the heart rate and blood pressure, and operates through the autonomic nervous system. The gain of the cardiac baroreflex further referred to, as baroreflex sensitivity is an interesting way to study this system. Unfortunately, with our current knowledge, it is not possible to predict the instantaneous output of the baroreceptor in response to instantaneous changes in input within a frequency range of physiological importance. The fast Fourier transform can describe variables as the sum of elementary oscillatory components and it has been established as practical clinical methods for detecting abnormalities in cardiovascular control. A time-frequency distribution provides an indication of how the spectral energy distribution varies with time and it is an interesting tool in non-stationary data. One of the major motivations behind spectral analysis is the hope that the combination of time-domain and frequency-domain analyses will provide dynamical informations about the relation between blood pressure and heart rate.

Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence

This paper introduces the use of wavelet analysis to follow the temporal variations in the coupling between oscillatory neural signals. Coherence, based on Fourier analysis, has been commonly used as a first approximation to track such coupling under the assumption that neural signals are stationary. Yet, stationary neural processing may be the exception rather than the rule. In this context, the recent application to physical systems of a wavelet-based coherence, which does not depend on the stationarity of the signals, is highly relevant. This paper fully develops the method of wavelet coherence and its statistical properties so that it can be practically applied to continuous neural signals. In realistic simulations, we show that, in contrast to Fourier coherence, wavelet coherence can detect short, significant episodes of coherence between non-stationary neural signals. This method can be directly applied for an 'online' quantification of the instantaneous coherence between two signals.

In vitro validation of volumetric blood flow measurement using Doppler flow wire

Determination of any volumetric blood flow requires assessment of mean blood flow velocity and vessel cross-sectional area. For evaluation of coronary blood flow and flow reserve, however, assessment of average peak velocity alone is widely used, but changes in velocity profile and vessel area are not taken into account. We studied the feasibility of a new method for calculation of volumetric blood flow by Doppler power using a Doppler flow wire. An in vitro model with serially connected silicone tubes of known lumen diameters (1.5, 2.0, 2.5, 3.0, 3.5 and 4.0 mm) and pulsatile blood flow ranging from 10 to 200 mL/min was used. A Doppler flow wire was connected to a commercially available Doppler system (FloMap(R), Cardiometrics) for online calculation of the zeroth (M(0)) and the first (M(1)) Doppler moment, as well as mean flow velocity (V(m)). Two different groups of sample volumes (at different gate depths) were used: 1. two proximal sample volumes lying completely within the vessel were required to evaluate the effect of scattering and attenuation on Doppler power, and 2. distal sample volumes intersecting completely the vessel lumen to assess the vessel cross-sectional area. Area (using M(0)) and V(m) (using M(1)/M(0)) obtained from the distal gates were corrected for scattering and attenuation by the data obtained from the proximal gates, allowing calculation of absolute volumetric flow. These results were compared to the respective time collected flow. Correlation between time collected and Doppler-derived flow measurements was 0.98 (p < 0.0001), with a regression line close to the line of equality indicating an excellent agreement of the two measurements in each individual tube. The mean paired flow difference between the two techniques was 1.5 +/- 9.0 mL/min (ns). Direct volumetric blood flow measurement from received Doppler power using a Doppler flow wire system is feasible. This technique may potentially be of great clinical value because it allows an accurate assessment of coronary flow and flow reserve with a commercially available flow wire system.

Motor patterns for human gait: backward versus forward locomotion

Seven healthy subjects walked forward (FW) and backward (BW) at different freely chosen speeds, while their motion, ground reaction forces, and electromyographic (EMG) activity from lower limb muscles were recorded. We considered the time course of the elevation angles of the thigh, shank, and foot segments in the sagittal plane, the anatomic angles of the hip, knee, and ankle joints, the vertical and longitudinal ground reaction forces, and the rectified EMGs. The elevation angles were the most reproducible variables across trials in each walking direction. After normalizing the time course of each variable over the gait cycle duration, the waveforms of all elevation angles in BW gait were essentially time reversed relative to the corresponding waveforms in FW gait. Moreover, the changes of the thigh, shank, and foot elevation covaried along a plane during the whole gait cycle in both FW and BW directions. Cross-correlation analysis revealed that the phase coupling among these elevation angles is maintained with a simple reversal of the delay on the reversal of walking direction. The extent of FW-BW correspondence also was good for the hip angle, but it was smaller for the knee and ankle angles and for the ground reaction forces. The EMG patterns were drastically different in the two movement directions as was the organization of the muscular synergies measured by cross-correlation analysis. Moreover, at any given speed, the mean EMG activity over the gait cycle was generally higher in BW than in FW gait, suggesting a greater level of energy expenditure in the former task. We argue that conservation of kinematic templates across gait reversal at the expense of a complete reorganization of muscle synergies does not arise from biomechanical constraints but may reflect a behavioral goal achieved by the central networks involved in the control of locomotion.

Two-dimensional spectral processing of sequential evoked potentials

The processing of sequential evoked potentials (EPs) is investigated using two-dimensional processing techniques. Two-dimensional EP arrays or images are formed by stacking sequential recordings. Processing is accomplished in the frequency domain by 2-D low-pass filtering using Gaussian filters. Auditory brainstem responses (ABRs), which are the early auditory EPs, are used to investigate the effects of the 2-D filtering on real data. Gaussian filtering improves signal-to-noise ratios by reducing high frequency noise effectively in both intra-EP and inter-EP dimensions. Applications to intra-operative monitoring are simulated with real ABR data.

Descriptive multidimensional statistical methods for analysing signals in a multifactorial biomedical database

A methodology is presented to analyse multidimensional signals from several recording periods resulting from an experimental study on human or other living systems. The methodology is divided into two stages: intra-period analysis and inter-period analysis. The purpose of the first stage is to highlight general trends in multidimensional signal changes and the more informative components of the signals. The purpose of the second stage is to assess the influence of environmental or individual difference factors on a given signal component that appears to be discriminant in the first stage. To take into account the multivariable state of the system and the multi-observational aspect, a multidimensional descriptive statistical approach is used. The methods are correspondence analysis and hierarchical clustering. They are illustrated through an occupational medicine application from a study of sedentary posture.

Heart rate variability: technique and investigational applications in cardiovascular medicine

OBJECTIVE

To describe heart rate variability (HRV) analysis, especially time- and frequency-domain analyses, and some of its investigational applications in clinical cardiovascular medicine.

DESIGN

We provide a brief introduction to the magnitude of sudden cardiac death and the factors that influence life-threatening ventricular arrhythmias as a backdrop to the potential importance of the autonomic nervous system and how this system might be assessed by the analysis of HRV.

MATERIAL AND METHODS

We reviewed the literature from 1973 to 1994 that described beat-to-beat changes in heart rate, heart rate signal recording and processing, and investigational applications of HRV analysis to cardiovascular medicine.

RESULTS

Beat-to-beat changes in heart rate are partly influenced by the autonomic nervous system. Briefly, changes in sympathetic input to the sinoatrial node affect low-frequency HRV, whereas changes in parasympathetic input affect high-frequency HRV. Multiple physiologic and nonphysiologic determinants of HRV exist, and therefore analysis of HRV as a direct "window" to autonomic tone is problematic.

CONCLUSION

In selected patient populations, analysis of HRV yields important information about sinoatrial responsiveness to autonomic input and mortality risk stratification. Routine application of HRV analysis to clinical cardiovascular medicine awaits further investigation, however.

Considering imperfections using 3D imaging system in angle obtaining, angle signal distance computing and multivariate distance graphing

Fields such as medicine, biomechanics or ergonomics need to measure the positions and the rotational movements of body segments. The aim of this article is to underscore the problem of imperfection on angle measurement using a three-dimensional television system. First, the error on a single angle value is assessed through the classical Taylor's formula and through a simulating approach. Then the error is considered for an entire signal through either an experimental design or a simulating approach. To take into account such an error when comparing two angle multidimensional signals, a specific coding technique is suggested. Finally, two graphical patterns are proposed to show globally the distance between the signals with regard to the error.

Characterization of pressure changes in the lower urinary tract during coughing with special reference to the demands on the pressure recording equipment

The exact demands on urodynamic equipment for measurement of coughs and cough associated pressure changes in the lower urinary tract have been analyzed from high-speed pressure recordings using a double microtip transducer and a storage oscilloscope. The equipment was tested in vitro by the step-test method. The natural frequency response was 175.6 Hz and the rise-time 2.5 ms, resulting in accurate measurements of frequencies up to about 60 Hz, which is way above the clinically measured frequencies. Four men and 2 women, all of whom were healthy volunteers, were examined in the supine position with an empty bladder. Pressures were measured in the bladder and in the external sphincter zone of the urethra. The spectral power density of the bladder and urethral pressures were calculated by Fourier analysis. The pressure changes in the urethra were in all volunteers equal to or slower than in the bladder. The analysis of the spectral power density showed that 99% of the pressure changes could be recorded with an instrument capable of recording 9 Hz frequencies, i.e., with a sampling rate of 18 Hz or more.

Fluctuations in blood flow to acral skin in humans: connection with heart rate and blood pressure variability

1. Spontaneous fluctuations in blood flow in arteries supplying acral skin were investigated with Doppler ultrasound in human subjects. Finger blood pressure, heart rate (HR) and cardiac output were measured simultaneously and noninvasively. 2. Synchronous fluctuations in flow were found in arteries supplying the hands and feet. The fluctuations were larger and more rapid than the flow variations which have been demonstrated with other methods. The magnitude of the total flow fluctuations in the hands and feet was estimated to be 5-10% of cardiac output in resting subjects. This range of flow fluctuations is made possible by spontaneous opening and closing of skin arteriovenous anastomoses (AVAs). 3. The fluctuations in skin blood flow were accompanied by inverse fluctuations in mean blood pressure (MAP). The power spectra of skin vascular conductance and MAP both contained maximum intensity at low frequencies, below 0.15 Hz, with high coherence. 4. The central circulatory events connected with the skin blood flow fluctuations were calculated from the experimental data with the use of transfer function analysis. There was a rise in HR, cardiac output and MAP starting 1-4 s before a cutaneous vasoconstriction. This indicates that the HR and MAP responses are not only passive effects of changes in peripheral resistance, but are the result of a simultaneous activation of the peripheral vascular and cardiac efferent branches of the autonomic nervous system. The HR and MAP responses are then modified, probably by baroreceptor activation.

Biomedical signal processing (in four parts). Part 3. The power spectrum and coherence function

This is the third in a series of four tutorial papers on biomedical signal processing and concerns the estimation of the power spectrum (PS) and coherence function (CF) od biomedical data. The PS is introduced and its estimation by means of the discrete Fourier transform is considered in terms of the problem of resolution in the frequency domain. The periodogram is introduced and its variance, bias and the effects of windowing and smoothing are considered. The use of the autocovariance function as a stage in power spectral estimation is described and the effects of windows in the autocorrelation domain are compared with the related effects of windows in the original time domain. The concept of coherence is introduced and the many ways in which coherence functions might be estimated are considered.