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Spectrum Averager Theory
To see this, set up the experiment suggested to demonstrate Synchronous Waveform Averaging and then enter Spectrum display mode. Invoke the Spectrum Averager dialog (CTRL+A or the thin bar under the Averager toggle button at the upper left of the screen). Make sure that Linear is set, frames is 32, and Artifact limits are set for +/-100%... these are the defaults.
Before starting the average, the trace will show a line at the frequency and approximate Level you set for the Sine. There will also be a broad "floor" due to the noise, at a lower amplitude. It will be very busy. Hit the Averager button (or ALT+A) and you will see the noise floor resolve to a smoother line at the average value of all the original bouncy values. With many frames averaged, this line will tend to become perfectly flat.
Since the spectrum shows magnitudes, the average value is not zero. This makes sense, since if we imagine the FFT response at any given frequency to be due to an equivalent input sine wave at that frequency, then even if the next frame contained that exact sine wave but with opposite polarity, it would still have the same frequency and magnitude... whereas for synchronous waveform averaging the two waveforms would cancel.
More relevant to real applications, try toggling Trigger off. If you toggle back to the waveform display, the trace will show an unsynchronized, "rolling" free-run noisy sine wave, and waveform averaging will bring this to a very low value... just as it would for any unsynchronized noise. But spectral averaging shows hardly any difference whether Trigger is active or not.
Think of the FFT spectrum as similar to what your ear does when listening to a tone: You detect the loudness of the tone and its pitch, but not (usually) its polarity. A guitar string sounds pretty much the same whether plucked on an upstroke or downstroke, and rapidly plucking up and down certainly doesn't sound softer than plucking only down or only up.
The White noise generator puts out equal energy at all frequencies, when averaged over enough frames. But this average level is much lower than the Level value shown in the control dialog for that stream. Why is this? There are two reasons: First of all, the Level setting is a misleading value for these purposes. It reflects the peak waveform values that you actually see on the waveform trace, just like the Sine stream Level shows the peak values of the sine wave. But whereas a sine wave hits its peak values each cycle, the same is not true for the noise. It hits its peaks only rarely, so the equivalent energy is not the same.
The second reason the noise level seems low is that the energy is evenly distributed across all frequencies, not concentrated into one frequency like the sine wave. So of course any one of those noise frequencies will not have the same level as the single sine frequency.
Although spectral averaging doesn't actually reduce the average noise level, it makes the spectrum display look less noisy by reducing the trace-to-trace variablity. This can actually help detect a signal in a noisy background, if the trace-to-trace noise peaks are taller than the signal peak, yet the signal peak happens to be larger than the averaged noise floor. This ability may be important in cases where you can't synchronize to the signal in order to use the true noise reduction afforded by synchronous waveform averaging.
See also Averager.
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