| 1/f-spectral trend | Trend in which the power of the spectrum is inversely proportional to the frequency f according to a 1/f A power law |
| Acrophase | see Cosinor Analysis |
| Akaike information criterion | Method for the order selection of autoregressive models |
| Aliasing | Error occurring when the sampling frequency of analog-to-digital conversion is lower than twice the highest frequency contained in the signal (Nyquist frequency) |
| Anacrotic pulse | A small slow-rising pulse with a notch on the ascending limb |
| Analytic signal | Signal with Fourier transform equal to 0 for frequencies lower than 0 |
| Alpha index | Estimate of the sensitivity of the baroreceptor-heart rate reflex based on frequency-domain analysis of spontaneous variability of systolic blood pressure and R-R interval. |
| Approximate entropy | Measure of the regularity or predictability of time series |
| Attractor | Object to which the time series in a phase space is attracted to |
| Autocorrelation function | Measure of the dependence of time series values at one time on the values at another time |
| Autoregressive modeling | Time-series modeling based on the assumption that each value of the series depends on a weighted sum of the previous values of the same series plus “noise” |
| Autoregressive moving
average modeling |
Time-series modeling based on the assumption that each value of the series depends on a weighted sum of previous values and of the present and previous values of a different time series with the addition of "noise" |
| Barahona-Poon test | Test suitable to detect nonlinear dynamics in short, noisy time series |
| Baroreflex Effectiveness Index | Ratio between the number of systolic blood pressure ramps followed by the respective reflex pulse interval ramps and the total number of systolic blood pressure ramps observed in a given time window |
| Bartlett | Type of data window |
| Bisferiens pulse | A pulse with two peaks during systole |
| Bivariate autoregressive modeling | Modeling of two time-series based on the assumption that each value of the two series depends on a weighted sum of the previous values of the same series plus a second weighted sum of the present and previous values of the other series plus “noise” |
| Bispectrum | See higher-order spectra |
| Blackmann-Tukey method | Estimate of power spectral density of a time series based on the evaluation of the autocorrelation function and on the computation of its Fourier transform |
| Broadband spectrum | Spectrum providing spectral estimates over a frequency region wider (sometimes much wider) that the region usually explored by the standard spectral procedures employed in a given field |
| Broadband smoothing | Smoothing technique for power spectra in which the resulting frequency resolution and estimation variance are not constant over the frequency axis, as in conventional spectra |
| Cardiac events series | HRV signal derived from the ECG by considering the occurrence of each R-wave an event, and by expressing the events by infinitesimal pulses or delta-functions |
| Chaos | Aperiodic behaviour of a given variable of a bounded deterministic system which may appear as random behaviour |
| Choi-Williams distribution | Time-frequency distribution derived from the Wigner-Ville distribution |
| Coarse graining
spectral analysis |
Technique useful to separate random fractal components from a time series in the frequency domain |
| Coefficient of variation | measure of relative dispersion defined by: CV=100x(standard deviation/mean), used in those conditions where mean and standard deviation tend to change together |
| Coherence function | Degree of linear correlation between two signals as a function of the frequency |
| Complex demodulation | Procedure which allows to describe particular frequency components of a time series as a function of time |
| Cosinor analysis | Least square approximation of time series using a cosine function of known period |
| Correlation dimension | A measure of the fractal dimension of the time series. |
| Cross-correlation function | Estimates the linear correlation coefficient between two signals as a function of a time lag between the two. |
| Cross Mutual Information Function | see Mutual Information |
| Cross-terms | Oscillatory positive and negative peaks, affecting some time-frequency distributions, due to interferences between spectral components |
| Cubic splines | See Spline Funtion |
| Cumulants | Extension of the concept of autocorrelation for multiple lags, used to define higher-order spectra |
| Data window | A function of time that is multiplied by a data segment. It is mainly used before computing the FFT spectrum of the data segment, and its purpose is to smooth or otherwise shape the resulting spectrum |
| Determinism | Rule allowing to determine the evolution of a system or a variable when the causes are known. Similar causes induce similar effects. |
| Detrended fluctuation analysis | Method for quantifying the correlation property in nonstationary time series based on the computation of a scaling exponent d by means of a modified root mean square analysis of a random walk. |
| Diastogram | Time series derived from consecutive diastolic blood pressure values |
| Dicrotic wave | A pulse appearing in the blood pressure wave during the diastolic phase |
| Discrete time Fourier transform | See Fourier Transform |
| ECG-Derived Respiration | Respiratory signal derived from the ECG by assessing the fluctuations in the cardiac electric axis due to respiration. |
| Embedding dimension | Number of axis of a return map sufficient to describe the properties of the corresponding phase space |
| Energy | See Power |
| Entropy | Measure of uncertainty in a sequence of symbols |
| Ergodic process | Random process in which every time series produced is the same in statistical properties |
| European Data Format | Standard format for exchange and storage of multisignal biological time series |
| Fast Fourier transform | Family of computationally efficient algorithms for the calculation of the discrete-time Fourier transform |
| Filter (analog) | Device that stops specific components of a signal before A/D conversion, generally used to avoid aliasing or to arrest interferences and noises (e.g., conducted interference or muscle activity in the ECG) |
| Filter (digital) | System that separates specific components of a time series |
| Final prediction error | Method for the order selection of autoregressive models (see Akaike Information Criterion) |
| Fourier Series | Decomposition of a periodic signal into a series of sine and cosine waves |
| Fourier transform | Frequency-domain representation of a signal as a complex-valued function, characterized by a modulus function and a phase function |
| Fractal | Object with self-similar structure across scales, so that resembling structures appear as one zoomes in and out |
| Fractal dimension | Definition of the geometric dimension of an object which includes fractal objects. |
| Frequency resolution | Minimum difference in frequency between two sinusoids which still allows to resolve two distinct peaks in the spectrum |
| Hann | Type of data window |
| Hamming | Type of data window |
| Heart rate | Reciprocal of the R-R interval, expressed in beats per minute |
| Heart rate turbulence | The physiological response of the sinus node to premature ventricular contractions characterized by a short acceleration followed by a deceleration of the heart rate. |
| Heart timing signal | HRV signal used to estimate the spectrum of the modulating input m(t) when the IPFM model is assumed |
| High-Pass | Type of digital filter |
| Hausdorff dimension | see Fractal Dimension |
| Hurst exponent | Measure of the smoothness of fractal time series based on the asymptotic behaviour of the rescaled range of the process |
| Higher order spectra | Spectra obtained from the Fourier transform of cumulants |
| Impulse response | Response of a system when its input is an infinitly short impulse with finite energy. The behaviour of linear systems to any input can be predicted by the convolution between the input signal and the impulse response |
| Interpolation | Mathematical procedure used to estimate an intermediate value between samples of a time series |
| Instantaneous heart rate | HRV signal defined as the series of the reciprocal RR-interval durations as a function of time |
| Integral pulse frequency
modulation model |
System which transforms a continuous input signal into an event series |
| Interval function | HRV signal defined as the series of RR-interval durations as a function of time |
| Interval tachogram | HRV signal defined as the series of RR-interval durations as a function of the interval number |
| Iso-spectral surrogate data | Artificial time series derived from the original time series which has the same linear characteristics (same variance, same spectrum, same mean) as the original time series, but is otherwise random |
| Leakage | Loss of power from a frequency band to several adjacent spectral lines due to the finite data set over which the periodogram is estimated: leakage may be controlled by applying a data window before the spectrum computation |
| Levinson-Durbin algorithm | Efficient computational procedure to solve the Yule-Walker equations |
| Linear system | System which fulfills the principle of linear superimposition: a linear combination of the inputs will produce the same linear combination of the outputs. |
| Lomb periodogram | Method of spectral analysis for unevenly sampled series, such as the beat-to-beat series of cardiovascular signals |
| Low-pass | Type of digital filter |
| Low-pass filtered event series | HRV signal obtained by filtering the R-wave event series by a low-pass filter |
| Lyapunov exponents | Average exponential rates of divergence of initially close orbits in the phase space |
| Marginal conditions | Conditions, satisfied by certain time-frequency distributions, on the integrals over frequency and over time |
| Multivariate parametric models | See autoregressive moving average modeling and bivariate autoregressive modeling |
| Mutual Information | Measure of the statistical dependency between two random variables based on Shannon's entropy |
| Noise | Random signal with specific spectral and energy properties |
| Nonlinear system | a system whose time-evolution equations are non linear (i.e., the variables describing the dynamical properties of the system, such as velocity, accelaration etc. appear in equations in a nonlinear form); this implies that a linear combination of the inputs does not produce the same linear combination of the outputs (see also linear system). |
| Normalized Entropy | Entropy of a time-series divided by a measure of the time-series energy. |
| Nyquist frequency | see Aliasing |
| Nyquist-Shannon theorem | see Sampling theorem |
| P wave | First deflection of the electrocardiogram corresponding to atrial depolarization |
| Passband | Type of digital filter |
| Periodogram | Estimate of power spectral density on the basis of modulus squared Fourier transform |
| Phase resetting | Change in phase induced by an external stimulus |
| Phase space | Space in which each point describes the state of a dynamical system as a function of the non-constant parameters of the system |
| Poincaré section | Intersection between a plane and trajectories in a phase space |
| Polyspectra | Synonym of higher-order spectra |
| Power | Time average of time-series energy |
| Power leakage | see Leakage |
| Power spectral density | Amount of power per unit (density) of frequency (spectral) as a function of the frequency |
| Pulse interval | Time duration between two consecutive systolic blood pressure peaks (see also Systogram) |
| Q wave | First downward deflection of the electrocardiogram following the P-wave, arising from ventricular activation |
| R wave | First upward deflection of the electrocardiogram following the Q-wave, arising from ventricular activation |
| Recurrence plot | Graphic representation of the data used to reveal nonstationarities or periodicity in the phase-space orbits. |
| Rescaled range | Measure characterising the divergence of time series defined as the range of the sum of the deviations of data from the mean divided by the sample standard deviation |
| Return map | Plot of a time series as a function of the current and of the previous values. |
| Resampling | Procedure which derives an evenly-sampled series from a time series sampled on a beat-by-beat basis |
| Reverse arrangement test | Test on the stationarity of a time series |
| RR interval | Time duration between two consecutive R waves of the ECG |
| Run test | Test on the stationarity of a time series |
| S wave | First downward deflection of the electrocardiogram following the R-wave, arising from ventricular activation |
| Sampling frequency | Rate of extraction of discrete numeric data from an analog continuous signal |
| Sampling theorem | The sampling frequency must be higher than twice the highest frequency contained in the signal to allow the original signal to be reconstructed as accurately as desired from the sequence of samples |
| Sequence technique | Method for estimating the sensitivity of the baroreceptor-heart rate reflex by time-domain analysis of spontaneous variability of systolic blood pressure and pulse interval |
| Set point | Specific value of a controlled variable (eg, arterial blood pressure) that should be mantained by a given control mechanism (eg, the arterial baroreflex). |
| Shannon theorem | The sampling frequency of a signal must be higher than twice the highest frequency contained in th signal to allow a reconstruction of the signal without aliasing error. |
| Short-time Fourier transform | Method for Fourier analysis of nonstationary signals, based on a joint time-frequency signal representation |
| Sign Analysis | Analysis of the properties of the increments (signs) of a beat-by-beat time series |
| Smoothness index | Index of the homogeneity of the blood pressure reduction induced by antihypertensive treatment over the 24 hours |
| Spectral technique | Method for estimating the sensitivity of the baroreceptor-heart rate reflex based on the computation of the Alpha Index |
| Spectrogram | Method for the study of nonstationary signals based on splitting the signal in short-time sliding windows and on getting the Fourier spectrum in each window, in order to obtain a time-varying spectral description. |
| Spectrum | Description of a quantity as any function of frequency. See also Power Spectral Density |
| Spectrum of counts | Power spectrum of the cardiac event series |
| Spline function | Interpolating function which guarantees global smoothness up to some order derivative (e.g., cubic splines produce an interpolated function continuous up to the 2nd derivative) |
| Stationarity | Property of a time series in which probability distributions involving values of the time series are independent of time translations |
| Step response | Response of a system when its input is a step function |
| Surrogate data | see iso-spectral surrogate data |
| Symbolic dynamics | Coarse graining the data by transforming the time-series in a sequence of symbols. |
| Systogram | Time series derived from consecutive systolic blood pressure values |
| T wave | Upward deflection of the electrocardiogram following the S wave, due to ventricular repolarization |
| Tachogram | Time series derived from the occurrence time of the R-wave. See also cardiac events series, interval tachogram, interval function, instantaneous heart rate , heart timing signal and low-pass filtered event series |
| Time-Frequency Distribution | Description of energy or power of a signal as a two-dimensional funtion of both time and frequency |
| Toeplitz matrix | a matrix composed by elements which are constant along the diagonals |
| Turbulence | see Hear Rate Turbulence |
| Transfer function | Complex-valued function of the frequency expressing the relationship between output and input of a system |
| Transfer function technique | Method for estimating the sensitivity of the baroreceptor-heart rate reflex by assessing the transfer function between systolic blood pressure and R-R interval |
| Trigonometric
regressive
spectral analysis |
Decomposition of beat-by-beat time series (RR intervals, peripheral blood pressure) into a small number of periodic oscillations and a non-rhythmic residual variance on the base of trigonometric regressive functions |
| Trough-to-peak ratio | Index of the distribution of the blood pressure reduction induced by treatment throughout the dosing interval |
| U wave | Small upward deflection of the electrocardiogram of uncertain origin sometimes seen following the T wave |
| Variance | For time-series, it is the time average of the square of deviations from the mean value (see also Power) |
| Warner model | Set of equations describing the heart-rate responses to the frequencies of stimulation of vagus and sympathetic efferent nerves |
| Wavelets analysis | Analysis which expands the signal in terms of “small waves”, or wavelets: this is done analogeous to Fourier transform where the signal is expanded in sinusoids |
| Welch method | Periodogram estimate based on the splitting of the time series in overlapped segments multiplied by data windows, and on the ensemble average of periodograms computed in each data window |
| Window | see Data Window |
| Windowed Fourier transform | Synonym of short-time Fourier transform |
| Wigner-Ville distribution | Time-frequency distribution of a signal with very high time and frequency resolution |
| Yule-Walker equations | Set of linear equations relating the parameters of an AR model with the autocorrelation sequence |
| Z analysis | Statistical evaluation of the relationship between systolic blood pressure and heart rate based on the calculation of the Z coefficient |
| Zero-padding | Method used to artificially increase the length of a time series by adding zero-value samples before computing the Fast Fourier Transform |
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