Hi All,
My objective is to measure a DC response of a sensor which has
a measuring bandwidth of a few thousand Hz from true DC). (The sensor is an ADXL
xxx accelerometer.) The output of the sensor has a portion of Gaussian noise.
This comes from the physical characteristics of the sensor.
The amplitude of the signal which I want to measure is under
the amplitude of the noise floor set by the Gaussian noise.
There is further unidentified high frequency AC noise (band in
N*100Hz) with much larger amplitude than the signal of interest. This kind of
noise should be filtered out as well.
For those of you who know the ADXL sensors well: let's ignore
drifts, let's say they are compensated for. My main point here is
noise.
It's obvious that I have to filter the signal (low pass
filtering) to eliminate the presence of the unvanted high frequency AC noise.
It's also obvious that by applying a low pass filter the Gaussian noise is also
reduced. But I cannot reduce the bandwidth enough to lower the noise floor set
by Gaussian noise because I have a settling time limit of <= 5 seconds for
the final readouts of the whole measuring system. That's 0.2 Hz for the noise
free readouts. So I cannot reduce the Gaussian noise floor beyond a limit either
with an ideal low pass filter.
According to the datasheet, there is another techique to
reduce Gaussian noise: taking a lot of samples of the signal and than averaging
these together to get the result. They say that taking 100 samples reduces the
noise by a factor of ten. (I think it suggests to avarage 100 samples to give
one "noise reduced" sample, am I right?) I don't see why a factor of
ten. (?!?)
1.) Does the above still stand if I have a low pass filter
before the A/D converter with a cutoff at 10Hz or 1Hz or 0.1 Hz? (At what
frequency should I set the cutoff? This cutoff could serve as an anti aliasing
filter for the A/D and a filter for the unidentified AC noise.)
2.) If I take 100,000 samples, and
avarage them to get one sample, to what extent does the Gaussian noise diminish
with the lowpass filter / without the lowpass filter? (I take the 100,000
samples in a second or in a fraction of a second.)
If I want the measured results to keep up with the 5 second
settling time considering the "noise reduced" samples, and I want to
comply with the Nyquist Theorem, then the sampling frequency should be at
least (1/5seconds)*2 = 0.4 Hz for the "noise reduced"
samples.
3.) Am I right with my statements?
4.) What happens to Gaussian noise if I implement another kind
of averaging technique: moving averaging? I take 100,000 samples and then apply
a moving average algorithm to the samples. How could my averaging system
modelled in the time domain?
5.) Am I right saying that a low pass filter integrates the
Gaussian noise over time, while the averaging scheme summarizes over discrete
time?
6.) Can I get a better noise reduction with averaging than
with low pass filtering only? If I can, why?
7.) Do I need the low pass filter for reducing the
unidentified high frequency AC noise before the A/D converter? Some sort of
filter is needed anyway to prevent the Gaussian and other AC noise aliasing into
the DC.
8.) If I average the "noise free" samples to keep up
with the <=5seconds settling time after the first averaging, does that ease
something on the filter requirement?
Thanks for your help
Laszlo Cser