The autocorrelation plugin calculates correlation values between a series (vector) and a lagged version of itself, using lag values from floor(-(N-1)/2) to floor((N-1)/2), where N is the number of points in the data set. The time vector is not an input as it is assumed that the data is sampled at equal time intervals. The correlation value r at lag k is:

The bin plugin bins elements of a single data vector into bins of a specified size. The value of each bin is the mean of the elements belonging to the bin. For example, if the bin size is 3, and the input vector is [9,2,7,3,4,74,5,322,444,2,1], then the outputted bins would be [6,27,257]. Note that any elements remaining at the end of the input vector that do not form a complete bin (in this case, elements 2 and 1), are simply discarded.

The Butterworth band-pass plugin filters a set of data by calculating the Fourier transform of the data and recalculating the the frequency responses using the following formula

where f is the frequency, fc is the low frequency cutoff, b is the bandwidth of the band to pass, and n is the order of the Butterworth filter. The inverse Fourier transform is then calculated using the new filtered frequency responses.

The Butterworth band-stop plugin filters a set of data by calculating the Fourier transform of the data and recalculating the the frequency responses using the following formula

where f is the frequency, fc is the low frequency cutoff, b is the bandwidth of the band to stop, and n is the order of the Butterworth filter. The inverse Fourier transform is then calculated using the new filtered frequency responses.

The Butterworth high-pass plugin filters a set of data by calculating the Fourier transform of the data and recalculating the the frequency responses using the following formula

where f is the frequency, fc is the high frequency cutoff, and n is the order of the Butterworth filter. The inverse Fourier transform is then calculated using the new filtered frequency responses.

The Butterworth low-pass plugin filters a set of data by calculating the Fourier transform of the data and recalculating the the frequency responses using the following formula

where f is the frequency, fc is the low frequency cutoff, and n is the order of the Butterworth filter. The inverse Fourier transform is then calculated using the new filtered frequency responses.

The chop plugin takes an input vector and divides it into two vectors. Every second element in the input vector is placed in one output vector, while all other elements from the input vector are placed in another output vector.

The convolution plugin generates the convolution of one vector with another. The convolution of two functions f and g is given by:

The order of the vectors does not matter, since f*g=g*f. In addition, the vectors do not need to be of the same size, as the plugin will automatically extrapolate the smaller vector.

The crosscorrelation plugin calculates correlation values between two series (vectors) x and y, using lag values from floor(-(N-1)/2) to floor((N-1)/2), where N is the number of elements in the longer vector. The shorter vector is padded to the length of the longer vector using 0s. The time vector is not an input as it is assumed that the data is sampled at equal time intervals. The correlation value r at lag k is:

The deconvolution plugin generates the deconvolution of one vector with another. Deconvolution is the inverse of convolution. Given the convolved vector h and another vector g, the deconvolution f is given by:

The vectors do not need to be of the same size, as the plugin will automatically extrapolate the shorter vector. The shorter vector is assumed to be the response function g.

The Fit exponential weighted plugin performs a weighted non-linear least-squares fit to an exponential model:

An initial estimate of a=1.0, =0, and b=0 is used. The plugin subsequently iterates to the solution until a precision of 1.0e-4 is reached or 500 iterations have been performed.

The Fit exponential plugin is identical in function to the Fit exponential weighted plugin with the exception that the weight value wi is equal to 1 for all index values i. As a result, the Weights (vector) input does not exist.

The Fit gaussian weighted plugin performs a weighted non-linear least-squares fit to a Gaussian model:

An initial estimate of a=(maximum of the y values), =(mean of the x values), and =(the midpoint of the x values) is used. The plugin subsequently iterates to the solution until a precision of 1.0e-4 is reached or 500 iterations have been performed.

The Fit gaussian plugin is identical in function to the Fit gaussian weighted plugin with the exception that the weight value wi is equal to 1 for all index values i. As a result, the Weights (vector) input does not exist.

The gradient weighted plugin performs a weighted least-squares fit to a straight line model without a constant term:

The best-fit is found by minimizing the weighted sum of squared residuals:

for b, where wi is the weight at index i.

The Fit linear plugin is identical in function to the Fit gradient weighted plugin with the exception that the weight value wi is equal to 1 for all index values i. As a result, the Weights (vector) input does not exist.

The Fit linear weighted plugin performs a weighted least-squares fit to a straight line model:

The best-fit is found by minimizing the weighted sum of squared residuals:

for a and b, where wi is the weight at index i.

The Fit linear plugin is identical in function to the Fit linear weighted plugin with the exception that the weight value wi is equal to 1 for all index values i. As a result, the Weights (vector) input does not exist.

The Fit lorentzian weighted plugin performs a weighted non-linear least-squares fit to a Lorentzian model:

An initial estimate of a=(maximum of the y values), x0=(mean of the x values), and =(the midpoint of the x values) is used. The plugin subsequently iterates to the solution until a precision of 1.0e-4 is reached or 500 iterations have been performed.

The Fit lorentzian plugin is identical in function to the Fit lorentzian weighted plugin with the exception that the weight value wi is equal to 1 for all index values i. As a result, the Weights (vector) input does not exist.

The Fit polynomial weighted plugin performs a weighted least-squares fit to a polynomial model:

where n is the degree of the polynomial model.

The Fit polynomial plugin is identical in function to the Fit polynomial weighted plugin with the exception that the weight value wi is equal to 1 for all index values i. As a result, the Weights (vector) input does not exist.

The Fit sinusoid weighted plugin performs a least-squares fit to a sinusoid model:

where T is the specified period, and n=2+2H, where H is the specified number of harmonics.

The Fit sinusoid plugin is identical in function to the Fit sinusoid weighted plugin with the exception that the weight value wi is equal to 1 for all index values i. As a result, the Weights (vector) input does not exist.

The Interpolation Akima spline plugin generates a non-rounded Akima spline interpolation for the supplied data set, using natural boundary conditions.

The kstinterp akima periodic plugin generates a non-rounded Akima spline interpolation for the supplied data set, using periodic boundary conditions.

The Interpolation cubic spline plugin generates a cubic spline interpolation for the supplied data set, using natural boundary conditions.

The Interpolation cubic spline periodic plugin generates a cubic spline interpolation for the supplied data set, using periodic boundary conditions.

The Interpolation linear plugin generates a linear interpolation for the supplied data set.

The Interpolation polynomial plugin generates a polynomial interpolation for the supplied data set. The number of terms in the polynomial used is equal to the number of points in the supplied data set.

The Noise addition plugin adds a Gaussian random variable to each element of the input vector. The Gaussian distribution used has a mean of 0 and the specified standard deviation. The probability density function of a Gaussian random variable is:

The periodogram plugin produces the periodogram of a given data set. One of two algorithms is used depending on the size of the data set—a fast algorithm is used if there are greater than 100 data points, while a slower algorithm is used if there are less than or equal to 100 data points.

The statistics plugin calculates statistics for a given data set. Most of the output scalars are named such that the values they represent should be apparent. Standard formulas are used to calculate the statistical values.