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Waveform Amplitude Histogram

Controls: Wave Avg Dialog >> Histogram
Macro: WavgMode=Hist

This is not really an "average" in the conventional sense, but rather a statistical record of the individual values in a signal. The X axis shows all the possible values, similar to the Y axis in a conventional waveform display. The histogram Y axis shows the percent of input samples that had each corresponding value. Histograms behave like Linear averages in that they accumulate a discrete number of frames as set by the Frames Request.

You can think of the histogram operation as a row of bins that incoming samples are sorted into, according to value. Each bin holds only the count of samples that go into it, not the values themselves. If one sample value appears more often than others, its bin will end up with more counts.

For example, suppose the input signal is a square wave with Level set to 30%, such that all samples are either +30% amplitude or -30%. The histogram will show this as two vertical lines, at -30 and +30. Since half of the samples go into the -30 bin and half into the +30 bin, we expect each line to have a height of 50%.

If you try this experiment for yourself, you may find that the two peak heights differ, even though their total always equals 100%. This can happen since the wave may not include an integer number of whole cycles in each frame. If each frame is in sync with the start of a cycle, there may be a remainder that is less than a full cycle. Toggling Trigger off reduces this effect since the fractional cycle may then appear anywhere. Alternatively, you may want to try setting the Tone Frequency to get an exact integer number of cycles. (Hint: The Step Lines frequency entry mode may be useful here.)

Now consider a ramp or triangle; each value in its amplitude range appears an equal number of times, so the histogram is a rectangular plateau... but at a much lower level, because the values are spread over more amplitude bins. This is called a "uniform" distribution of values, for obvious reasons.

Just as for the square wave, you may not get a flat plateau if Trigger is active.

But how high is this uniform plateau? The X axis of the display is 512 bins wide, so each bin is 1/512 of the full-scale range. If the ramp signal range exactly equals the full-scale range, we'd expect one sample in each bin, so that the plateau would extend the entire width of the trace at just under 0.2%. If the ramp covers only half the range, there would be a central plateau that was only half the width of the trace, but it would be twice as tall as before, nearly 0.4%.

With an amplitude histogram, the sum of all the bins will always equal 100%. That's because every sample of the output will always be counted in one or another of the bins.

You can use the Sigma option of the cursor readouts to find the sum of the bins between cursors.

Histograms are generally most useful with random signals. The histogram of a White wave is uniform, while that of a Gaussian is the traditional bell-shaped curve. Pink and Band-limited noise also show bell-shaped histograms, though the Pink source has a lot of low-frequency energy present that causes the histogram to wobble while it is accumulating. You can create a triangular distribution by adding two different White streams with Levels at 50%.

Due to the fact that most distributions of interest are fairly broad, they will have rather low percentage values. Just magnify the trace using the Up arrow button at the top of the Y axis, or the PgUp key. The histogram magnification setting is maintained separately from that for the ordinary waveform display; hitting unPause afterward will return to the waveform display with its original magnification.

You can use the Screen Zero control to magnify about some vertical position other than zero. Just enter the Y-axis percent value directly.

Macro Notes:

WavgMode=Hist or WavgMode=2 sets Histogram mode. See Macro Notes under Waveform Averager Mode for the complete list of mode numbers and names.

See also Averager, Waveform Averager Mode, and Waveform Averager Controls.


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