New Features of the v1.100 Prolate1 Software


The above image (click for full-size JPEG) shows a test EEG dataset generated by a sine function sweeping across the surface of the prolate spheroid. The display shows an interpolation of the spectrum magnitude and spectrum phase at the principle frequency of this data, along with magnitude and phase cascade plots for one sensor of this data.


New features of the v1.100 Prolate1 software consist of the following:

  1. New document format.
  2. 1d time-series traces.
  3. Trace settings.
  4. Trace tool.
  5. FFT spectra.
  6. Spectral settings.
  7. Spectrum magnitude.
  8. Spectrum phase.
  9. Creating separate time-series plot windows.
  10. Plot window settings.
  11. Spectral plot windows.
  12. Polar plot windows.
  13. Cascade plot windows.


1. New document format.

There is a new document file format for v1.100. You can still open v1.000 documents, but they will be converted to the new format, and you will be prompted to resave them. A suffix of .new will automatically be added to the file name during the prompt.



2. 1d time-series traces.

There are four new buttons at the lower left corner of the main display which are concerned with the creation and display of embedded 1d traces in the 3d display. These button are:

The trace display will show the same data as the 3d display, but for each individual sensor. The 3d display is interpolated from the individual sensor datasets. The traces are linked to the 3d display, and will show time-series data (etc...) if that menu item is selected. Scrolling the 3d display through the frame data will also scroll the traces. The number of each sensor is displayed in the trace.

You can select a trace with the mouse to bring its display to the front of the stack. The trace will then be outlined in green. You can delete a single trace by selecting it and pressing the delete key.



3. Trace settings.

Choose "Trace Settings..." from the Edit menu to display the trace settings dialog. You can set the following parameters:



4. Trace tool.

Click the "Tr Tool" (trace tool) button to activate the trace cursor. This will also display the sensor locations on the spheroid. You may need to click "Clr Trs" (clear traces) first to delete any traces you have already created. Click the trace cursor near any sensor location to create a trace for that sensor. This will also select the newly created trace, so you can delete it immediately (if necessary) by pressing the delete key.



5. FFT spectra.

This version of the Prolate1 software can peform spectral analysis of data using multi-record windowed Fast Fourier Transforms. This term means the following:

Here is a schematic of the process of performing the FFT transforms:

Note that the shifts performed between each FFT can either be overlapping or non-overlapping. Each FFT produces one "record" of the entire transform for a single sensor. The time-series data is not zero-padded at the beginning and ending records, so that each FFT record must overlap an entire window of data.

Thanks to John Green (green_jt@vsdec.npt.nuwc.navy.mil) for providing a public domain library containing the basic FFT function used in this program.



6. Spectral settings.

Choose "Spectrum Settings..." from the Edit menu to show the spectrum dialog. You can set the following parameters:

Changing any of these parameters and clicking OK will cause a new spectrum analysis to be performed.



7. Spectrum magnitude.

To show the magnitude of the spectrum of the data, choose the "Spectrum-Magnitude" item of the Plot menu.

If an FFT analysis has not yet been performed, it will be performed now. Note that performing an FFT analysis takes a lot of memory. If enough memory is not available, you will see an alert telling you that the FFT cannot be performed. In this case you must either (1) increase the memory partition of the program and relaunch, (2) decrease the window width of the FFT, or (3) increase the record offset of the FFT.

Whenever an FFT analysis is performed, the resulting complex coefficients (real and imaginary components) are converted into complex magnitudes and phases. You may display either the magnitude or the phase of the result. Since the time-series data is all real, only the resulting positive frequencies are retained (since the negative frequency values are just the complex conjugate of the positive values). Only frequencies up to the Nyquist limit (1/2 of the sampling rate) are retained by the FFT.

Saving a document after an FFT analysis has been performed will significantly increase the size of the file (e.g. from 1.6 Mb to 13.6 Mb). You may delete all FFT data from the document by choosing "Clear Spectrum Data..." from the Edit menu. You can perform another FFT analysis, or clear the FFT data, at any time.

When you are showing a spectrum result, the horizontal slider will scroll through the FFT records. After an FFT analysis is performed, the frame step size is set to the FFT record offset, so that one record is scrolled with each step of the slider. The frame and time indicators will show the position of the center of the FFT record. The 3d display will show an interpolation of the FFT result (magnitude or phase) from each of the sensors, analagous to the time-series interpolation which is shown when "Time-Series" is selected from the Plot menu. Note that since the first and last records extend to the beginning and end of the dataset, respectively, and because data is not zero-padded, these records correspond to more frames of displayed data than other, interior, records.

If you are showing 1d traces, each trace will show the corresponding spectrum record for each sensor. As the horizontal slider is scrolled, each trace display will be updated with the animation to show a new spectrum record.

A vertical slider will also be displayed in spectrum mode. This slider controls the frequency at which the interpolated 3d display is created. Frequencies between 0 Hz and the Nyquist limit (1/2 the sampling rate) may be displayed. On the 1d traces, a green line will show the currently displayed 3d frequency. You can also set the currently displayed 3d frequency from the frequency dialog, by choosing "Frequency Settings..." from the Edit menu. Note that not all intermediate frequencies may be available for display, depending on the FFT window width and resulting spectrum resolution.



8. Spectrum phase.

To show the phase of the spectrum of the data, choose the "Spectrum-Phase" item of the Plot menu.

If an FFT analysis has not yet been performed, it will be performed now. Note that performing an FFT analysis takes a lot of memory. If enough memory is not available, you will see an alert telling you that the FFT cannot be performed. In this case you must either (1) increase the memory partition of the program and relaunch, (2) decrease the window width of the FFT, or (3) increase the record offset of the FFT.

Whenever an FFT analysis is performed, the resulting complex coefficients (real and imaginary components) are converted into complex magnitudes and phases. You may display either the magnitude or the phase of the result. Since the time-series data is all real, only the resulting positive frequencies are retained (since the negative frequency values are just the complex conjugate of the positive values). Only frequencies up to the Nyquist limit (1/2 of the sampling rate) are retained by the FFT.

Saving a document after an FFT analysis has been performed will significantly increase the size of the file (e.g. from 1.6 Mb to 13.6 Mb). You may delete all FFT data from the document by choosing "Clear Spectrum Data..." from the Edit menu. You can perform another FFT analysis, or clear the FFT data, at any time.

When you are showing a spectrum result, the horizontal slider will scroll through the FFT records. After an FFT analysis is performed, the frame step size is set to the FFT record offset, so that one record is scrolled with each step of the slider. The frame and time indicators will show the position of the center of the FFT record. The 3d display will show an interpolation of the FFT result (magnitude or phase) from each of the sensors, analagous to the time-series interpolation which is shown when "Time-Series" is selected from the Plot menu. Note that since the first and last records extend to the beginning and end of the dataset, respectively, and because data is not zero-padded, these records correspond to more frames of displayed data than other, interior, records.

If you are showing 1d traces, each trace will show the corresponding spectrum record for each sensor. As the horizontal slider is scrolled, each trace display will be updated with the animation to show a new spectrum record.

A vertical slider will also be displayed in spectrum mode. This slider controls the frequency at which the interpolated 3d display is created. Frequencies between 0 Hz and the Nyquist limit (1/2 the sampling rate) may be displayed. On the 1d traces, a green line will show the currently displayed 3d frequency. You can also set the currently displayed 3d frequency from the frequency dialog, by choosing "Frequency Settings..." from the Edit menu. Note that not all intermediate frequencies may be available for display, depending on the FFT window width and resulting spectrum resolution.



9. Creating separate time-series plot windows.

To create a separate window showing the contents of a sensor trace, simply select and double-click on the trace in the 3d display. This will create a new plot window which will initially show the same data as the trace display. Each new plot window will be entered into the Windows menu, under a sub-menu for the current document. You can create any number of plot windows for a particular sensor. The data in the plot window will initially be autoscaled to fit the window.



10. Plot window settings.

To show the settings dialog for a particular plot window, double-click in that window. You can set the following parameters of a plot:



11. Spectral plot windows.

To create a separate window showing the contents of a sensor trace, simply select and double-click on the trace in the 3d display. This will create a new plot window which will initially show the same data as the trace display. Note that to display a spectrum plot, you must already have performed an FFT analysis as described above. You can also change a plot window to display a spectrum by selecting the appropriate button in the plot settings dialog.

Each new plot window will be entered into the Windows menu, under a sub-menu for the current document. You can create any number of plot windows for a particular sensor. The data in the plot window will initially be autoscaled to fit the window. You can display either the magnitude or the phase of the spectrum for a particular record of the transform. Records can be translated to frames or elapsed time by looking at the main display. Also note that to set the minimum and maximum frequency settings to something other than those set for traces in the main display, you must first uncheck the "Link to main display" item in the plot's settings dialog.



12. Polar plot windows.

To create a polar plot of a spectrum record, first create a plot of the magnitude or phase of the spectrum as described above. Then, select the "Spectrum Polar" button in the plot's settings dialog. The magnitude and phase of the spectrum will then be converted to real and imaginary components, and the spectrum displayed in 2d. Also note that to set the minimum and maximum frequency settings to something other than those set for traces in the main display, you must first uncheck the "Link to main display" item in the plot's settings dialog.



13. Cascade plot windows.

To create a cascade magnitude or phase plot of a spectrum, first create a single-record plot of the magnitude or phase of the spectrum as described above. Then, select the "Magnitude cascade" or "Phase cascade" button in the plot's settings dialog. All FFT records for that sensor will then be displayed in 3d as a "cascade" or "waterfall" plot.

You may want to set the decimation of the cascade plot to a value between 2-10 (e.g.) so that not every record of the spectrum is drawn. This may make the plot much more readable. You may also wish to set the plot background to some color other than white, from the Color menu. Also note that to set the minimum and maximum frequency settings to something other than those set for traces in the main display, you must first uncheck the "Link to main display" item in the plot's settings dialog.

The record and frequency currently shown in the main 3d display will be highlighted in green in the cascade plot.



©Copyright Sky Coyote and Dr. Thomas L. Ferrell, 1998-2002.