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Daqarta for DOS Data AcQuisition And Real-Time Analysis Shareware for Legacy Systems

From the Daqarta for DOS Help system:

Virtual Source Control Menu:

BITS:

Adjusts the bits of resolution produced by the Virtual Source, from 16 down to 1. This allows you to see just how much benefit you might gain or lose by going for a board with more or less resolution. In particular, you should explore this in conjunction with Noise and averaging, since you may find that there is no benefit whatsoever to going to a board with more resolution than the noise level present in your signal.

WAVE:

Selects SINE, RAMP, SQUARE or TRIangle waveform generation by the Virtual Source.

FREQ:

Adjusts the frequency of the Wave from 0 to 65535 Hz in 1 Hz steps, either via direct entry or cursor fine adjust.

LEVEL:

Adjusts the level of the Wave from 0 to full scale in 17 power-of-2 steps. Full scale is determined by the range currently active on the data acquisition Board. If no Board is present, full scale defaults to 1.0 Volt and the level setting defaults to 50% or 500 mV. You can't set Level to full scale if AM is active... it will be limited to half of full scale to allow up to 100% Amplitude Modulation.

NOISE:

Adjusts the level of a separate noise source that is added to the overall Virtual Source "signal" after all modulations (AM and FM) are applied, if any. Noise settings cover the same range as the Level of the wave itself. The presence of noise not only makes the Virtual Source look more like real- world data, but it also allows easy simulations of situations to allow you to evaluate the benefits of averaging versus bits of resolution, etc.

The noise source is a very simple and computationally efficient one, which produces random levels that are evenly distributed over the entire full-scale range (before scaling to get the desired Noise level). This is known as a UNIFORM distribution of values. In the real world, however, most noise sources are the resultant sum of numerous random processes, so they have value distributions that are more GAUSSIAN. A conceptually simple way to make a Gaussian distribution is to add the outputs of several independent uniform noise sources.

UNIFORM vs GAUSSIAN SOURCES:

Imagine that you add two uniform noise sources together. Lets's say that each produces values from -50 to +50 with equal ("uniform") probability. On the average, we expect to see +50 values in about 1 out of every 101 samples (since 0 is a possibility), and -50 values just as often. Since each source is independent of the other, the odds of both of them happening to produce +50 values for the same sample is pretty small, so we don't expect to see too many +100 values in the sum... about 1 out of every 10201 samples (101 × 101). The same is true of -100 values. But since for every positive sample from one source, there is about a 50% chance that the other will be negative, we expect a lot more values around 0.

Now imagine that we add up 16 of these uniform sources. We will almost never see all 16 producing +50 values at the same time, but we will see a lot of values within shouting distance of 0. The distribution of values is bell-shaped, or Gaussian.

But what about the frequencies present in the noise? Since frequencies don't add and subtract like amplitudes, it turns out that we have the same frequencies in the sum as we have in the individual parts. Consider that one source is like a composition of random notes played on a piano, which has a fixed range of notes. Adding 15 more identical pianos can't produce any higher or lower notes, even if they are playing different compositions... but it would be a LOT noisier!

So we wouldn't see any difference in the shape of the spectra between a uniform source and a Gaussian sum of uniform sources, though of course there would be a level difference. But the waveform displays would look quite different. Try setting the Virtual Source wave Level to 0 and bring up the Noise level to some moderate setting. You will notice that although the trace is very random, all the values stay within certain limits... namely, the limits indicated by the Noise setting. There is a fairly discrete band of brightness through the middle region of the trace.

If this was a Gaussian source, however, we would not see such definite limits: The average brightness would be greater in the center of the trace and fade off more gradually toward the top and bottom. Most importantly, some of the instantaneous values would go off the screen, though not very often. But therein lies the rub: What would we do about those values? They could not be handled within the 16-bit range of normal signals. If we reduced the average value of the noise low enough so that we never got any out-of-range values, it would be only 1/16 as great (assuming we had added 16 uniform sources).

A true Gaussian noise source is available in the STIM3A Advanced Stimulus Signal Generator. You can use this with the DEMO driver instead of the Virtual Source to further investigate the properties of this type of noise.

You can visualize the actual amplitude distribution of any signal, including those from the Virtual Source, by using the Histogram option.

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