The QtiPlot Handbook
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# The Analysis Menu

The commands available in this menu change depending upon whether a table or a plot is selected.

## Commands for the analysis of data in tables

Statistics on Columns

  Creates a new table providing basic statistical information about the selected columns in the active table: average, variance, standard deviation, max value, etc...

  If you select several columns in one table, one line of statistical information will be created for each selected column. However, you can not select columns from different tables and obtain one single table of statistics.

Statistics on Rows

  Creates a new table providing basic statistical information about the selected rows in the active table: average, variance, standard deviation, max value, etc.

  See the Statistics on Columns command command for more details.

Sort Column

  Sorts the selected columns. If more than one column is selected, you have the option to sort them:

  - separately: each column will be sorted independently in ascending or descending order

  - together: the column selected as the leading column will be sorted into ascending or descending order. The other selected columns will be sorted so as to keep the rows unchanged.

Sort Table

  This command functions in the the same manner as the Sort Column command, except that it operates on all columns of the active table.

Normalize

  These commands are used to normalize data in tables. In this case, normalization is the process of dividing each entry in the column by the column's maximum positive value, making the maximum range value equal to 1. Data is not re-centered so negative values will remain negative and the minimum value may be less than -1. Columns are normalized separately. The command does not create new columns for the normalized data but replaces the values in the selected columns with their normalized values. There are 2 variants of this command:

  Normalize -> Columns

    Normalizes only the selected column or columns. If you want the normalized data in a new column, use the Add Column command to create a new column, fill it using a "copy/paste" sequence and then normalize the new column.

  Normalize -> Table

    Normalizes all the columns of the table. It is not a global normalization of all values of the table: each column is normalized separately.

FFT...

  Computes a direct or inverse Fast Fourier Transform. The parameters used can be set with the FFT dialog. See the fft section of the Analysis chapter for more details.

Correlate

  Does a cross-correlation of the two columns which are selected. See the correlate section of the Analysis chapter for more details.

Autocorrelate

  Does a cross-correlation of the selected column with itself (auto-correlation). See the correlate section of the Analysis chapter for more details.

Convolute

  Does a convolution of two selected columns. The first one being the response and the second the signal. See the convolution section of the Analysis chapter for more details.

Deconvolute

  Does a deconvolution of two selected columns. The first one being the response and the second the signal. See the deconvolution section of the Analysis chapter for more details.

Fit Wizard... (Ctrl-Y)

  Opens the Non-linear Fit dialog, allowing you to choose the curve to fit, the algorithm and tolerance to use, and the number of iterations to be performed. You also enter the analytical function, the names of the fitting parameters and their initial (guessed) values. See the Non Linear Curve Fit section of the Analysis chapter for more details.

## Commands for the analysis of curves in plots

The following items are enabled only if the active window is a 2D Multilayer Plot Window. If the active plot layer contains more than one curve, and the Data Range Selectors are not enabled, a dialog window will pop-out allowing you to select the curve you want to analyze.

In most of the cases (except for integration), a new red curve is added to the active plot layer and a a new table containing the data used to plot this curve is added to the workspace. Useful information about the operation performed will be showed in the Results Log display.

The commands FFT... and Fit Wizard... are presented in the Table Analysis Menu.

Analysis -> Differentiate

  Creates a new plot displaying the resulting curve of the numerical differentiation. The computation of the derivative is done by centered finite differences.

  This command creates a new table which contains one column for X-values and one column for derivatives of Y-values. It also creates a new plot of the derivative.

Analysis -> Integrate...

  Opens the Integration dialog, allowing to choose the curve to integrate and the integration method.

  This command can't be used to obtain a cumulative curve from a selected curve, it can only compute the integral of the data between two limits. The result is given in the Log Panel.

Analysis -> Smooth

  .

  Savitski-Golay

    This command performs a smoothing of the selected curve with the Savitzky-Golay method. The formula used to smooth the curve defined by the points yi=f(xi) is:

    The fi values are computed by fitting the data points to a polynomial. They depend on the number of points used for the smoothing of the curve and the order of the polynomial. Compared to the moving window average method, the advantage of this smoothing method is that the values of extrema are not truncated. The dialog allows specification of the curve which will be smoothed, the order of the polynomial, the number of data points used for the polynomial fit before and after each point, and the color used to draw the smoothed curved. A new table will be created to store the data points xi, zi.

    Figure 3-1. The Smooth -> Savitsky-Golay... dialog.

  Moving Window Average...

    This command performs a smoothing of the selected curve with the moving window average method. The formula used to smooth the curve defined by the points yi=f(xi) is:

    The greater the number of points, n, the smoother the resulting curve zi=f(xi) will be. The dialog allows specification of the curve which will be smoothed, the value of n and the color used to draw the smoothed curve. A new table will be created to store the data points xi, zi.

    Figure 3-2. The Smooth -> Moving Window Average... dialog.

  Lowess...

    This command performs a smoothing of the selected curve using the Lowess (aka Loess) algorithm. It provides a robust locally weighted regression and is well suited to smooth data for which no formal model exists.

    The parameter f is the fraction of points which define the local neighborhood. A value of 0.2 uses 20% of the curve total points as neighbors for each data point (+/- 10%). Values of f closer to 1 yield smoother curves. The iterations parameter specifies the number of times to run the algorithm runs over the entire data set, each time refining the local weights. In most cases, two iterations will be sufficient.

    Figure 3-3. The Smooth -> Lowess... dialog.

Analysis -> FFT Filter

  Low Pass...

    This command uses an FFT based digital filter to attenuate the high frequencies present in an input signal. See the filtering section for more details. A dialog box will be opened in which you can select the curve (input signal) to filter and the cut-off frequency of the filter.

    Figure 3-4. The FFT Filter -> Low Pass... dialog.

    This command creates a new table containing the filtered data, and adds a new curve to the current layer. The curve is a plot of the filtered data.

  High Pass...

    This command uses an FFT based digital filter to attenuate the low frequencies present in an input signal. See the filtering section for more details. A dialog box will be opened in which you can select the curve to filter and the cut-off frequency of the filter.

    Figure 3-5. The FFT Filter -> High Pass... dialog.

    >This command creates a new table containing the filtered data, and adds a new curve to the current layer. The curve is a plot of the filtered data.

  Band Pass...

    This command uses an FFT based digital filter to attenuate both high and low frequencies present in an input signal. See the filtering section for more details. A dialog box will be opened in which you can select the curve to filter and both the low and high cutoff frequencies of the filter.

    Figure 3-6. The FFT Filter -> Band Pass... dialog.

    >This command creates a new table containing the filtered data, and adds a new curve to the current layer. The curve is a plot of the filtered data.

  Band Block...

    This command uses an FFT based digital filter to remove a band of frequencies from a signal while leaving those frequencies above and below the stop band. See the filtering section for more details. A dialog box will be opened in which you can select the curve to filter and both the lower and upper stop-band frequencies of the filter.

    Figure 3-7. The FFT Filter -> Band Block... dialog.

    This command creates a new table containing the filtered data, and adds a new curve to the current layer. The curve is a plot of the filtered data.

Analysis -> Interpolate...

  Performs an interpolation. The curve must have enough data points to compute interpolated points, if not a warning message will be popped up.

  The available interpolation methods are Linear (the curve must contain at least 3 points), Cubic Spline (the curve you analyze must contain at least 4 points), Non-rounded Akime spline (the curve you analyze must contain at least 5 points). See the Analysis chapter for a comparison of the different methods.

  Figure 3-8. The Interpolate... dialog.

  This command creates a new curve on the current layer, and a new table.

Analysis -> FFT...

  Performs a forward or inverse FFT of the selected curve. The parameters used can be set with the FFT dialog.

  The inverse FFT transform of a forward transform will result in a data set identical to that used for the forward transform.

Analysis -> Fit Linear

  Performs a linear fit of the selected curve. The results will be given in the Log panel

Analysis -> Fit Polynomial...

  Opens the Polynomial Fit dialog, allowing you to choose the curve to fit, the order of the polynomial function to use, the number of points of the resulting curve and the abscissa limits for the fit.

Analysis -> Fit Exponential Decay

  There are 3 forms of exponential decay available:

  First Order...

    Opens the Exponential Fit dialog, allowing you to choose the curve to fit and the initial guesses for the fit parameters.

  Second Order...

    Opens a dialog, allowing you to choose the curve to fit and the initial guesses for the fit parameters.

  Third Order...

    Opens a dialog, allowing you to choose the curve to fit and the initial guesses for the fit parameters.

Analysis -> Fit Exponential Growth...

  Performs an exponential growth fit to the selected curve.

Analysis -> Fit Lorentzian

  Performs a Lorentzian fit to the selected curve. It can be used to obtain the correlation equation of a bell shaped data set.

Analysis -> Fit Gaussian

  Performs a Gaussian fit to the selected curve. It can be used to obtain the correlation equation of a bell shaped data set.

Analysis -> Fit Bolzmann (sigmoidal)

  Performs a fit to a Boltzmann function on the selected curve. It can be used to obtain the correlation equation of an S shaped data set.

Analysis -> Fit Multi-peak ->Gaussian...

  Performs a fit to a sum of N Gaussian functions on the selected curve.

Analysis -> Fit Multi-peak -> Lorentzian...

  Performs a fit to a sum of N Lorentzian functions on the selected curve.

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