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Doube-click `kSpectra', and the Start-up window will appear:
By using the toolbar you can access the following functions of the toolkit:
Data needs to be in the form of ASCII columns. The 'Data I/O' functions from the Tools are used to import data. However, if a multi-column file (matrix ) is read using 'Vector' in ASCII, only the second column is read into a vector, while the first column, assumed to be time values, is ignored.
Values in the time series must be equally spaced in time. The sampling interval is assumed to be unity (1) by default. If it is not unity, each tool needs to be told individually what the sampling interval is using the "Sampling" box. The resulting spectra are then plotted accordingly. If, for example, the input data are sampled every 2 months, the Nyquist interval on the frequency axis will be labeled from 0 to 0.25 cycles/month. File data with NaN values (case insensitive) are treated as missing. To analyze such data Univariate Gap-Filling and Multivariate Gap-filling methods are provided.
There are three options for spectrum normalization throughout the Toolkit that can be selected in Preferences panel in kSpectra menu. The default option is for the power spectrum to be normalized by the length of the time series - (InputUnit)2. Next is power spectral density (PSD) which is the power spectrum divided by the frequency range - (InputUnit)2/Hz, and finally the square-root of PSD.
User can choose EPS or PDF file format for saving plots, and the default font for labels and legends. If "Update plot continously" is checked, any change in Graph Controls settings is applied immediately to the ActivePlot (see below). If it is unchecked, user can adjust several settings and then apply all the changes to ActivePlot at once with Apply button.
Also, number of cross-validation tests for gap-filling can be set here (see MSSA and SSA gap-filling sections), as well as option to connect points (linear interpolation) through gaps for datasets with missing data, when plotting. Restore option return defaults values.
We will work through examples using each tool on a univariate time series of monthly values of the Southern Oscillation Index (SOI), a climatic index that characterizes El Niño (Bjerknes, 1969), see Climate example in the distribution.
The 690 month series was obtained from monthly mean sea-level pressures at Tahiti and Darwin, Australia, by removing their seasonal cycles, dividing the resulting anomalies by the corresponding standard deviations, and then taking the Tahiti-minus-Darwin difference. The SOI series considered here is for the time interval from January 1942 through June 1999, during which no observations are missing. The complete project of analyzing SOI time series can be found in Examples/Climate folder of kSpectra distribution. Next figure shows the 'Data I/O' panel for data in soi.tkt after double-clicking on it in a Finder:
This panel allows to import data from file and store in a named vector or matrix. kSpectra Toolkit allows you to handle many time series at once; these might typically be a raw input time series and a filtered series derived using the Toolkit. These time series and results of the computation are stored internally as vectors or matrices, each of which are named dataobjects. The Matrices and Vector tables provide information about dimensions, i.e. the number of elements in a vector (length) and number of rows and columns for a matrix (rows and cols). For Matrices it is possible to setup a 2-D grid for by factoring number of columns (cols) and set col1 and col2 values as col=col1*col2. The total size of the dataobject in kB as listed, as well as its type.
`Diff' buttom in Vectors (Matrices) tables computes difference between two selected data objects and stores the result in a new data object. In addition rms (root-mean-squared) of the result is calculated; for vectors it is a number, and for matrices it is a newly created 1*cols matrix with results of calculation.
The vector (matrix) time series can be imported for analysis using the `Load' button in Vectors (Matrices) table view, or just simply by using Drag-and-Drop of the file to the relevant table view. The vector (matrix) time series can be also saved using the `Save' button (available only in a licensed copy of kSpectra Toolkit). For `Load' option the panel will open, where file with the input time series can be selected:
For files in ASCII format, both Load and Drag-and-Drop options will import and export data with a name of the file.
The Utilities tab provides usefull features for comparison two vectors (Compare Vectors), and two spectral etsimates (Compare Spectra), side by side on a single plot.
Manage Data utility allows to copy specified Column(s) or Row(s) of Matrices or Vector, from a source data object selected in Data, to a new target data object set in To. If Columns or Rows field is left empty, then by default all will be copied. The type of a target object, Vector or Matrix, is selected in As. The Start and End sliders control the range of copied data from the source.
In addition, optional operations can be performed on the target. If it is Matrix, these options will act on its columns. Center and Normalize will remove the mean from, and normalize by std. deviation, respectively. De-cycle removes harmonic cycle, i.e. setting there 12 and checking the box will remove an annual cycle from a monthly time series. Pad will increase length of the target up to the closest power of 2, and fill extra entries with zeros.
Single projects files containing all data and plots, can be opened and saved with Open, Open Recent, Save and Save As menu features (saving is available only in a licensed copy of kSpectra Toolkit). By default the project file is given the .tkt extension. Clear All option removes all the data from the application's memory and closes all the windows with plots. Close option closes all the plots.
At the bottom of the main window there is a Task Manager. When the computation has been started with any of the tools, an entry appears in the Task Manager with a progress bar. The user can stop any task by checking a Cancel flag next to a progress bar:
When there are no active computation tasks running, the Task Manager becomes invisible.
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