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prony matlab toolbox

PTbox can preprocess the original data range or specific data range signal. Several data preprocessing options are available:


Remove Mean:

It subtracts the signal sample mean from each sample. It also changes the time range of signals. The time range of negative values is discarded and positive values are picked up during the Remove Mean operation. It scales the PCR signals; amplitude of all other signal is unchanged. The pulsed voltage signals and the pulsed current signals are scaled by a factor of 242000 and 710 respectively.

Detrend:

It removes the linear trend from the signal. It computes the least-squares fit of a straight line (or composite line for piecewise linear trends) to the data and subtracts the resulting function from the data (MATLAB Help 2002).

No change:

It results in no preprocessing of the signal.

By pressing the Go push button, the selected data preprocessing is implemented. After data preprocessing is performed, the data is ready to send to the Perform PA GUI. This is done by pressing the Perform Prony Analysis push button.

Perform PA GUI
The main features of this GUI are as follows:

Model Order:

The user has to specify a model order in the editable text box. The GUI uses the user-specified value to perform the PA. 

Graphic Mode:

This refers to the graphic display of the PA fit in time or frequency domain. The frequency domain description of the Prony fit is obtained by computing the Fast Fourier Transform (FFT) of the Prony estimated signal in the sample or time domain.

Number of Residues:

The number of residues to be retained for the results display must be specified by the user in an editable box. This number is used to choose only specific residues according to the selection criteria. The total number of residues specified cannot exceed the model order previously given. If it exceeds, then a dialog box appears and prompts the user to specify a number of residues less than or equal to the model order. For a specific number of residues, the GUI also checks that the conjugate of the last residue is always included in the PA if it indeed exists. The GUI has been programmed such that it automatically increments the number of residues by one and picks up the conjugate mode, if the user missed selecting it.

Mode Sorting Criteria:

The GUI sorts the Prony residues according to two criteria:

Amplitude:

Sorts the Prony residues according to their amplitude.

Energy:

Sorts the Prony residues according to their energy level.

Mode Selection Options:

This feature provides the flexibility of choosing the residues according to the following options:

All Modes:

All the PA result modes are considered.

Selected Modes Only: 

In this option, only the user selected modes are considered. The user can select multiple modes by pressing CTRL+ left mouse button. 

All But Selected Modes: 

This is a complement option to the Selected modes only option. In this case, all the modes are considered except the selected modes.

Results:

The GUI shows the PA results in a list box. It displays amplitude, frequency, damping coefficient and energy of the modes according to the mode sorting criteria and mode selection options.

Plots:

This feature provides the following types of plots to assist the user in validating the Prony fit:

Squared Error: 

In this option, the square of the error between the original signal and Prony fit is plotted with respect to time.This plot is a quick indication of the performance of the Prony fit. A large squared error is an indication of incorrect model order or number of residues or missing signal modes during the mode selection process.

Poles:

This shows the poles of the Prony model.

Residues:

This shows the selected as well as all residues. This plot helps the user to estimate the correct model order.

Energy:

This shows the energy of the Prony modes.

Mean squared error (MSE):

MSE is the mean of the squared error over the sample data length. MSE is an important statistic that provides information about the performance of the Prony fit. The main advantage of MSE over the squared error is that it is a single number.

Save PA session:

The current PA session can be saved by selecting Save from the Session menu. The GUI saves the sessions in the MATLAB workspace, and an unlimited number of sessions can be saved. The Session menu also has an option of saving the current session as a file. It saves the session as a CMP-file, which can be opened in the Compare PA Sessions GUI. When the user saves a PA session, the Compare Sessions push button is enabled.

Compare PA Sessions GUI
This GUI compares several PA sessions simultaneously. Its features include the following:

Compare Set Menu:

To compare sessions, first the user has to specify the data to be compared by either loading the data from the workspace or importing the data from a CMP-file. This menu has options to load the data from the workspace or open the CMP- file.

Sessions List: 

The GUI displays all the specified saved sessions in a list box. For each session it displays the data file name, data set, data preprocessing option, decimation option, decimation factor, data range option, model order, number of modes, mode sorting criteria and mode selection option.

Plots: 

The GUI plots the poles, squared error, energy and residues for the selected PA sessions.

Export Data GUI
PTbox provides the flexibility of saving, analyzing and plotting the PA results according to the user needs, by exporting the results associated with the Prepare Prony Data GUI, Perform PA GUI and Compare PA Sessions GUI. Figure 4.9.1 shows the Export Data GUI. The GUI consists of several check boxes and edit boxes. Each check box refers to particular axis data from the other GUIs. The edit box provides the flexibility for the user to specify the data structure name. The data can be exported to the MATLAB workspace as well as to a file. When the user saves the data in a file, PTbox stores the data in a single structure named Exported_Data in the user specified file name. The data structure can be expanded in the workspace using the following MATLAB commands:

load filename;

%Loads the data in the base workspace of MATLAB.

mmv2struct(Exported_Data);

%Unpacks the Exported_Data Structure.

Context Menu:
A context menu is designed for each axis in PTbox. The context menu provides the ability to draw the axis plot in a new figure. It is activated by right-clicking the mouse on the axis. It provides the flexibility to edit the axis properties and customize it according to the user抯 requirements.

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Prony Toolbox Help: Prony Analysis 
Prony analysis has been shown to be a viable technique to model a linear sum of complex exponentials to signals that are uniformly sampled. The Prony method was developed by Gaspard Riche, Baron de Prony in 1795 in order to explain the expansion of various gases (Marple 1987). In his original paper, Prony proposed fitting a sum of exponentials to equally spaced data points and extended the model to interpolate at intermediate points. The Prony method is not only a signal analysis technique but also a system identification method, which is widely used in the areas of power system electromechanical oscillation, biomedical monitoring, radioactive decay, radar, sonar, geophysical sensing and speech processing.

As compared to other oscillatory signal analysis techniques such as those of Fourier, Prony analysis has the advantage of estimating damping coefficients apart from frequency, phase and amplitude. In addition, it best fits a reduced-order model to a high-order system both in time and frequency domains (Marple 1987). 

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