Let N represent the Number of averages when exponential averaging is selected. The value of a sample in a
newly averaged frame is calculated as follows:
The value of a sample in a new frame is added to N-1 multiplied by the value of the equivalent sample in the
last ‘averaged’ frame and the total is divided N.
V
newcalc
= (V
new
+ (N-1)V
previouscalc
)/N
Where V
newcalc,
V
new,
V
previouscalc,
all represent samples which are in equivalent positions in a frame with respect to
time and:
V
newcalc
is the newly calculated average for a sample.
V
new
is the most recently measured and transferred value for the equivalent sample.
V
previouscalc
is the previously calculated average for the equivalent sample.
This form of averaging is called exponential averaging because the weighting given to each frame of samples, as
you go back in time, represents an exponentially decaying curve. If N is 4 the weighting given to the samples in
each frame going from the most recent frame backwards is represented by the following series:
V
1
1/4, V
2
3/16, V
3
9/64, V
4
27/256, V
5
81/1024 …
Where V
1
is the amplitude of a sample in the most recent frame and V
5
is the amplitude of the equivalent
sample in the 5
th
most recent frame.
Averaging in the Scope Display
If you wish to do time averaging, you must have a periodic waveform whose phase variation is relatively stable
so you achieve a stable trigger.
Use equal averaging when all frames are equally important (a periodic waveform with noise, for example). Use
exponential averaging when you wish to get the best estimate of the current value of a varying signal (for
example a pulse train with jitter).
Averaging in the Spectrum Display
If you wish to do frequency domain averaging then you should be aware of the difference that Triggered and
Auto frame capture has on averaging. If Triggered has been selected, Cleverscope assumes you have a periodic
waveform and a good trigger, and averaging will be performed in the time domain, before transforming the
resulting average to the frequency domain. If Auto is selected, the signal data is transformed and the averaging
is performed in the frequency domain.
Use Triggered when you have a stable periodic signal with impressed random noise. Use Auto when the signal is
not periodic and a stable trigger is not available. When Auto is used (and averaging is done in the frequency
domain) endpoint errors will be smoothed as they will have different frequency content from frame to frame.
End-point errors are discussed under ‘Windowing’ above.