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Subsections

6.20.3 Member functions

6.20.3.1 abs

Syntax:

Take absolut value of all data values of signal s. If sample values are complex, abs(s) returns the complex modulus (magnitude) of each sample.


6.20.3.2 acf

Syntax:

Input arguments:

Autocorrelation function for real scalar signals, using fft (of length len). If len is ommited a default value is calculated. The maximum of the calculated length is 128.

6.20.3.3 acp

Syntax:

Input arguments:

Auto crossprediction function for real scalar signals for increasing dimension. The default value for maxdelay is 25% of the input signal's length. The default for maxdim is 8 and for nref it is 10% of the input signal's length.

6.20.3.4 amutual

Syntax:

Input arguments: Auto mutual information function for real scalar signals, can be used to determine a proper delay time for time-delay reconstruction. The default value for maxtau is 25% of the input signal's length. The default number of bins is 128.

$\displaystyle I=\sum P(A,B)\log_2\frac{P(A,B)}{P(A)P(B)}
$

6.20.3.5 amutual2

Syntax:

Input arguments:

Auto mutual information (average) function for real scalar signals using 128 equidistant partitions.

6.20.3.6 analyze

Syntax:

Input arguments:

Try to do a automatic analysis procedure of a time series. The time series is embedded using the first zero of the auto mutual information function for the delay time.

6.20.3.7 arch

Syntax:

Input arguments:

Archetypal analysis of column orientated data set: Default value for mode is 'normalized'.

6.20.3.8 boxdim

Syntax:

Input arguments:

Compute the boxcounting (capacity) dimension of a time-delay reconstructed timeseries s for dimensions from 1 to D, where D is the dimension of the input vectors using boxcounting approach. The default number of bins is 100.


6.20.3.9 cao

Syntax: Input arguments:

Estimate minimum embedding dimension using Cao's method.

The second output argument, E2, can be used to distinguish between deterministic and random data.

6.20.3.10 center

Syntax:

Center signal by removing it's mean.


6.20.3.11 corrdim

Syntax: Input arguments:

Compute the correlation dimension of a time-delay reconstructed timeseries s for dimensions from 1 to D, where D is the dimension of the input vectors using boxcounting approach. The default number of bins is 100.


6.20.3.12 corrsum

Syntax: Input arguments: Compute scaling of correlation sum for time-delay reconstructed timeseries s (Grassberger-Proccacia Algorithm), using fast nearest neighbor search. Default number of bins is 20.


6.20.3.13 corrsum2

Syntax: Input arguments: Compute scaling of correlation sum for time-delay reconstructed timeseries s (Grassberger-Proccacia Algorithm), using fast nearest neighbor search.


6.20.3.14 crosscorrdim

Syntax: Input arguments: Compute scaling of cross-correlation sum for time-delay reconstructed timeseries s against signal s2 (with same dimension as s), using fast nearest neighbor search. Reference points are taken out of signal s, while neigbors are searched in s2. The default number of bins is 32.


6.20.3.15 cut

Syntax: Input arguments: Cut a part of the signal. If stop is ommited only the data at start is cutted.


6.20.3.16 db

Syntax: Compute decibel values of signal relative to a reference value that is determined by the signal's yunit values below dbmin are set to dbmin. If dbmin is ommited it is set to -120.


6.20.3.17 delaytime

Syntax: Input arguments: Compute optimal delaytime for a scalar timeseries with method of Parlitz and Wichard.


6.20.3.18 diff

Syntax: Compute the nth numerical derivative along dimension 1. s has be to sampled equidistantly.


6.20.3.19 dimensions

Syntax: Input arguments: Output arguments: Compute boxcounting, information and correlation dimension of a time-delay reconstructed timeseries s for dimensions from 1 to D, where D is the dimension of the input vectors using boxcounting approach.

Scale data to be within 0 and 1. Give a sortiment of (integer) partitionsizes with almost exponential behaviour.


6.20.3.20 display


6.20.3.21 embed

Syntax: Input arguments: Output arguments: Embeds signal s with embedding dimension dim and delay delay (in samples). s must be a scalar time series. The default values for dim and delay are equal to one. The default value for windowtype is 'Rect', which is currently the only possible value.


6.20.3.22 fft

Syntax: Output arguments: Fourier transform of scalar signal s.


6.20.3.23 filterbank

Syntax: Filter scalar signal s into $ 2^{\text{\tt depth}}$ bands of equal bandwith, using maximally flat filters.


6.20.3.24 firstmax

Syntax: Give information about first local maximum of scalar signal s.


6.20.3.25 firstmin

Syntax: Give information about first local minimum of scalar signal s.


6.20.3.26 firstzero

Syntax: Give information about first zero of scalar signal s, using linear interpolation.


6.20.3.27 fracdims

Syntax: Input arguments: Compute fractal dimension spectrum D(q) using moments of neighbor distances for time-delay reconstructed timeseries s.

Do the main job - computing nearest neighbors for reference points.


6.20.3.28 getaxis

Syntax: Get one of the currend xaxes.


6.20.3.29 gmi

Syntax: Input arguments: Generalized mutual information function for a scalar time series


6.20.3.30 histo

Syntax: Histogram function using equidistantly spaced partitions.


6.20.3.31 infodim

Syntax: Input arguments: Compute the information dimension of a time-delay reconstructed timeseries s for dimensions from 1 to D, where D is the dimension of the input vectors. Using boxcounting approach. Scale data to be within 0 and 1. Give a sortiment of (integer) partitionsizes with almost exponential behaviour.


6.20.3.32 infodim2

Syntax: Input arguments: Compute scaling of moments of the nearest neighbor distances for time-delay reconstructed timeseries s. This can be used to calculate information dimension D1.

Numerically compute first derivative of $ \log\gamma(k)$ after $ k$ .


6.20.3.33 int

Syntax: Numerical integration along dimension 1 signal s has to be sampled equidistantly.


6.20.3.34 intspikeint

Syntax: Compute the interspike intervalls for a spiked scalar timeseries, using transformation on ranked values.


6.20.3.35 intspikint

Syntax: Compute the interspike intervalls for a spiked scalar timeseries, using transformation on ranked values.


6.20.3.36 largelyap

Syntax: Input arguments: Output arguments: Compute the largest lyapunov exponent of a time-delay reconstructed timeseries s, using formula (1.5. of Nonlinear Time-Series Analysis, Ulrich Parlitz 1998 [146]).


6.20.3.37 level_adaption

Syntax: Each channel of signal s is independently divided by a scaling factor that adapts to the current level of the samples in this channel. The adaption process is simulated using a cascade of feedback loops (Püschel 1998) which consists of low pass filters with time constants given as second argument to this function. The number of time constants given determines the number of feedback loops that are used.

Higher values for time constants will result in slower adaption speed. Short time changes in the signal will be transmitted almost linearily. In each feedback loop, a nonlinear compressing characteristic (see Stefan Münkner 1993) limits the signal values to be within [-dynamic_limit dynamic_limit]. A low value for dynamic_limit will introduce nonlinear distortions to the signal.

To prevent the feedback loops from adapting to a zero level (in case all input values are zero), a tiny threshold is given as 4th argument. The scaling factors will not shrink below this threshold.


6.20.3.38 localdensity

Syntax: Input arguments: Uses accelerated searching, distances are calculated with euclidian norm.


6.20.3.39 max

Syntax: Give information about maximum of scalar signal s.

Example:

disp('maximum of signal : ')
disp(['y = ' num2str(m) ' ' label(yunit(s))]);
disp(['x = ' num2str(xpos) ' ' label(a)]);


6.20.3.40 medianfilt

Syntax: Moving median filter of width len samples for a scalar time series (len should be odd).


6.20.3.41 merge

Syntax: Input arguments: Merges signal s1 and s2 into a new signal with energy ration dB (in decibel) a positive value of dB increases the amount of signal1 in the resulting signal.


6.20.3.42 min

Syntax: Give information about minimum of scalar signal s.

Example:

disp('minimum of signal : ')
disp(['y = ' num2str(m) ' ' label(yunit(s))]);
disp(['x = ' num2str(xpos) ' ' label(a)]);


6.20.3.43 minus

Syntax: Input arguments: Calculate difference of signals s1 and s2 or substract a scalar value from s.


6.20.3.44 movav

Syntax: Moving average of width len (samples) along first dimension.


6.20.3.45 multires

Syntax: Multires perform multiresolution analysis. Y = MULTIRES (X,H,RH,G,RG,SC) obtains the SC successive details and the low frequency approximation of signal in X from a multiresolution scheme. The analysis lowpass filter H, synthesis lowpass filter RH, analysis highpass filter G and synthesis highpass filter RG are used to implement the scheme.

Results are given in a scale+1 channels. The first scale channels are the details corresponding to the scales $ 2^1$ to $ 2^{\text{\tt scale}}$ the last row contains the approximation at scale $ 2^{\text{\tt SC}}$ . The original signal can be restored by summing all the channels of the resulting signal.


6.20.3.46 nearneigh

Syntax: Input arguments: n nearest neighbour algorithm. Find n nearest neighbours (in order of increasing distances) to each point in signal s uses accelerated searching, distances are calculated with euclidian norm.


6.20.3.47 norm1

Syntax: Scale and move signal values to be within [low,upp].


6.20.3.48 norm2

Syntax: Normalize signal by removing it's mean and dividing by the standard deviation.


6.20.3.49 pca

Syntax: Input arguments: Principal component analysis of column orientated data set.


6.20.3.50 plosivity

Syntax: Compute plosivity of a spectrogram. See also: window for list of possible window types.


6.20.3.51 plus

Syntax: Add two signals s1 and s2 or add a scalar value offset to s.


6.20.3.52 poincare

Syntax: Compute Poincare-section of an embedded time series the result is a set of vector points with dimension DIM-1, when the input data set of vectors had dimension DIM. The projection is done orthogonal to the tangential vector at the vector with index.


6.20.3.53 power

Syntax: Calculate squared magnitude of each sample.


6.20.3.54 predict

Syntax: Input arguments: Local constant iterative prediction for scalar data, using fast nearest neighbor search. Four methods of computing the prediction output are possible.


6.20.3.55 predict2

Syntax: Input arguments: Local constant iterative prediction for phase space data (e.g. data stemming from a time delay reconstruction of a scalar time series), using fast nearest neighbor search. Four methods of computing the prediction output are possible.


6.20.3.56 rang

Syntax: Transform scalar time series to rang values.


6.20.3.57 removeaxis

Syntax: Remove axis one of the current xaxes. No bound checking for dim.


6.20.3.58 return_time

Syntax: Input arguments: Compute histogram of return times.


6.20.3.59 reverse

Syntax: Reverse signal along dimension 1.


6.20.3.60 rms

Syntax: Calculate root mean square value for signal along dimension 1.


6.20.3.61 scale

Syntax: Scale signal by factor f.


6.20.3.62 scalogram

Syntax: Scalogram of signal s using morlet wavelet. See also: spec2.


6.20.3.63 setaxis

Syntax: Change one of the current xaxes.


6.20.3.64 setunit

Syntax: Change unit of one of the current xaxes.


6.20.3.65 shift

Syntax: shift signal on axis No. dim by distance (measured in the unit of the axis) to the right


6.20.3.66 signal

Syntax:

A signal object contains signal data, that is a collection of real or complex valued samples. A signal can be one or multi-dimensional. The number of dimensions is the number of axes that are needed to describe the the data.

An example for an one-dimensional signal is a one-channel measurement (timeseries), or the power spectrum of a one-channel measurement. An example for a two-dimensional signal is a twelve-channel measurement, with one time axis and a 'channel' axis. Another example for a two-dimensional signal is a short time spectrogramm of a time series, where we have a time axis and a frequency axis.

Each axis can have a physical unit(e.g. 's' or 'Hz'), a starting point and a step value. E.g. if a time-series is sampled with 1000 Hz, beginning at 1 min 12 sec, the unit is 's', the starting point is 72 and the step value (delta) is 0.001.

But not only the axes have physical units, also the sample value themselve can have a unit, maybe 'V' or 'Pa', depending on what the sampled data represent (=> yunit)

All units are stored as objects of class 'unit', all axes are stored as objects of class 'achse' (this somewhat peculiar name was chosen because of conflicts with reserved matlab keywords 'axis' and 'axes', which otherwise would have been the first choice).

Example for creating a 2-dimensional signal with y-unit set to 'Volt', the first dimension's unit is 'second' (time), the second dimension's unit is 'n' (Channels).

Examples:


6.20.3.67 spacing

return spacing values for xaxis nr. dim


6.20.3.68 spec

Syntax: compute power spectrum for real valued scalar signals. Multivariate signals are accepted but may produce unwanted results as only the spectrum of the first column is returned.


6.20.3.69 spec2

Syntax: Input Arguments: spectrogramm of signal s using short time fft

Examples:

view(spec2(sine(10000, 1000, 8000), 512, 'Hanning'))


6.20.3.70 stts

Syntax: Input Arguments: Spatiotemporal prediction conforming to U. Parlitz, NONLINEAR TIME-SERIES ANALYSIS Chapter 1.10.2.1.


6.20.3.71 sttserror

Syntax: Input Arguments: compute error function for prediction of spatial-temporal systems
see U. Parlitz "Nonlinear Time Series Analysis", Section 1.10.2.2 Eq. 1.10


6.20.3.72 surrogate1

Syntax: create surrogate data for a scalar time series by randomizing phases of fourier spectrum
see : James Theiler et al.'Using Surrogate Data to Detect Nonlinearity in Time Series', APPENDIX : ALGORITHM I


6.20.3.73 surrogate2

Syntax: create surrogate data for a scalar time series
see : James Theiler et al.'Using Surrogate Data to Detect Nonlinearity in Time Series', APPENDIX : ALGORITHM II


6.20.3.74 surrogate3

Syntax: create surrogate data for a scalar time series by permuting samples randomly


6.20.3.75 surrogate_test

Syntax: Input Arguments: Output Arguments: surrogate_test runs an automatic surrogate data test task. It generates ntests surrogate data sets an performs the func function to each set. func is a string with matlab-code who returns a signal s with a scalar time series.

Example:

st = surrogate_test(s, 10, 1, 1, 'largelyap(embed(s,3,1,1), 128,20,10);');


6.20.3.76 swap

Syntax: Exchange signal's dimensions (and axes)


6.20.3.77 takens_estimator

Syntax: Input Arguments: Takens estimator for correlation dimension


6.20.3.78 tc3

Syntax: Input Arguments: Output Arguments:

This function calculates a special value for the original data set and the n generated surrogate data sets. The $ T_{C3}$ value is defined as followed:

$\displaystyle T_{C3}(\{x_n\},\tau)=\frac{\langle
x_nx_{n-\tau}x_{n-2\tau}\rangle}{\vert\langle x_nx_{n-\tau}\rangle\vert^{\frac
3 2}}
$

In terms of surrogate data test this is a test statistics for higher order moments. The original tc3 function is located under utils/tc3.m and use simple matlab vectors.


6.20.3.79 trend

Syntax: trend correction
calculate moving average of width len (samples) for a scalar time series (len should be odd) and remove the result from the input signal


6.20.3.80 trev

Syntax: Input Arguments: Output Arguments:

This function calculates a special value for the original data set and the n generated surrogate data sets. The $ T_{REV}$ value is defined as followed:

$\displaystyle T_{REV}(\{x_n\},\tau)=\frac{\langle
(x_n-x_{n-\tau})^3\rangle}{\langle(x_n-x_{n-\tau})^2\rangle^{\frac 3
2}}
$

In terms of surrogate data test this is a test statistics for time reversibility. The original trev function is located under utils/trev.m and use simple matlab vectors.


6.20.3.81 upsample

Syntax: Input Arguments: Change sample rate of signal s by one-dimensional interpolation


6.20.3.82 view

Syntax: Signal viewer that decides from the signal's attributes which kind of plot to produce, using the signal's plothint entry to get a hint which kind of plot to produce
Possible plothints are:


6.20.3.83 write

Syntax: writes a signal object to file filename (uses matlab's file format)
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