Cursor Sigma Readouts

Macro: CursMode=Sigma

• Introduction
• Waveform Display Mode
• Spectrum Display Mode

Introduction:

Cicking on the Delta button will convert the readout to Sigma mode. (The Sigma symbol looks somewhat like an bent 'E'.)

Sigma is a summation mode, but it behaves differently depending on whether you are viewing a waveform or a spectrum. In all cases, however, it considers all points between and including the cursors. The solid cursor channel is always assumed. Even if the dotted cursor is set to another channel, its position still sets the solid cursor Sigma limit. The sigma symbol is shown in the color of the solid cursor as a reminder.

Waveform Display Mode:

In waveform mode, Sigma computes the true Root Mean Square (RMS) by summing the squares of the points, dividing by the number of points to get the mean, and then taking the square root.

However, when Sigma is used with the Histogram of a waveform it is a simple summation of the contents of the histogram "bins". This gives you the percent of samples whose amplitudes fall between the cursors.

For a Post-Stimulus Time Histogram (PSTH) the same simple summation is used. The PSTH shows the percent of frames that had events above the PSTH threshold at each time point. For example, if the threshold is set to zero and the signal is a pure sine wave, we expect to see PSTH spikes of 100% at each positive-going zero crossing.

However, in real-world cases this is rarely seen. Even if the response signal is nominally a "pure" sine wave, there may be noise or jitter that causes the threshold to be reached a little earlier or later on successive cycles. Instead of a 100% spike for each zero-crossing, there would be a distribution of spikes that together should total 100%. The Sigma readout allows you to see that total. If you are doing a jitter analysis, you can adjust the cursors to measure the total percent at various distances from the mean.

But use Sigma with caution on PSTHs. If the signal has more than one threshold event per frame (as in the sine wave example), then setting the cursors too far apart may encompass more than one event region. Sigma dutifully reports the total percent, which may be well over 100. Sometimes this may be just what you want to know, but use it with discretion.

Spectrum Display Mode:

In linear (non-Y-log) Spectrum mode, Sigma computes the square root of the sum of squares of the magnitudes at each spectral line. (There is no "Mean" as in waveform RMS.) The result is the "effective" amplitude of a sine wave that has the same energy as the components between the cursors. For example, if there are two components, each with an amplitude of 0.500 volt, then Sigma is 0.707. That's the amplitude (zero to peak) of a single sine that has the same heating ability, which is equivalent to an energy measurement.

However, the above assumes that all the energy of the two components is between the cursors. That would typically require creating the signals with the Generator using the Step Lines frequency entry mode to insure that each component falls exactly on a spectral line without using a Window function. In the more usual situation, each component will appear to have a lower spectral peak, with "skirts" draped over many lines due to spectral leakage; to get an accurate Sigma reading you would need to insure that the cursors included as much of these skirts as possible.

But precisely because of those draped spectral skirts, many users will chose to use a Window function to reduce them and improve peak amplitude measurements when the frequencies don't fall exactly on a spectral line. Essentially, the windowing operation squeezes the broad drooping skirts into a much narrower and taller band about each true peak frequency. By default, the new bands are scaled to show the true peak amplitudes. That's fine for peak measurements, but such scaling causes the total energy in the band to be too large.

So, if you are going to be using Sigma with spectral windows, you should also apply BW Correction. That changes the scaling to preserve the correct total energy, at the sacrifice of not showing the correct peak values.

Note that the Spectrum Cursor Peak option has no effect on the Sigma readout. It enhances the resolution of peaks under each cursor by interpolating from adjacent spectral lines. The energy from those lines may thus cause a peak to be boosted, but the total energy remains unchanged. (The Peak option only increases the displayed amplitude of the peak, it does not correspondingly reduce the displayed amplitudes of the adjacent lines.)

If Spectrum RMS is toggled on, with or without Windowing and/or BW Correction, it simply applies a factor of 0.707 to all values; the preceding 0.500 volt components would show as 0.353 VRMS each (0.707 * 0.500) in Step Lines mode without windowing, and Sigma would read 0.500 VRMS. (Note that 'RMS' appears over the Y axis, but is not shown after the readout labels.)

The preceding Spectrum Sigma discussion assumed that Y-log was toggled off. With it on, the two 0.500 volt components would each show as -6.02 dB, relative to the default 1.000 volt full-scale range for 0 dB. Sigma would show the root sum of these as -3.01 dB.

Macro Notes:

CursMode=Sigma sets the Sigma cursor readout mode, CursMode=Delta sets Delta mode, and CursMode=x toggles between them.

DeltX and DeltY are internal read-only variables that hold the current Delta X and Y values, respectively, in the same units that are shown on-screen. If Sigma mode is active, DeltY actually returns the Sigma value.

See also Cursors and Readouts, Cursor Delta Readouts, Spectrum Cursor Peak, Spectrum Cursor Track, Spectrum Cursor Ratio