# Oversampling for noise reduction

Started by March 16, 2007
```Hi,
I've been reading quite a bit about oversampling and it's apparent use
in noise reduction, but haven't been able to tie everything together.
As I probably can't explain my exact question clearly, I'll give an
example, I have a Analog Devices evaluation board with a 1MSPS A/D
with CPU hooked up to a gryo. The gyro has a raw BW of 1000Hz, I have
a single pole filter at 50Hz between it and the A/D (hooked up per the
datasheet).  I am sampling at 10X 50hz, or 500 Hz, since the single
pole filter is not great. The datasheet indicates that the gryo noise
is white Gaussian and I am seeing it as +/- 4 counts on the A/D, which
agrees with the datasheet estimate with a 50Hz filter.

So my attempt here is to use oversampling to bring the noise down, I
oversample at 4x,16x,32x, up to 256x and average the samples (every
500hz, or 2 mS). But I see no reduction in noise, still +/- 4 counts,
no matter what. Well, thinking about it for a moment I realize that
the data probably doesn't change much over a 2mS period (i.e., the
noise is slow), it's just averaging the same number 256 times.

Ok, so the only way to get around this is to add higher frequency
noise, which I can do by relaxing the output filter, I do this and the
oversampling now brings down the noise, but, and here is the rub, when
I relax the filter the overall noise increases, so the net result is I
have the same noise as I did in the beginning :(

Now I can average multiple 2mS samples over a second to bring the
noise down, but this obviously reduces the BW, which I don't want, and
that is what I consider a normal filter, not oversampling.

So the question is, how can I use oversampling to reduce noise without
signal loss? Or maybe I can't, that oversampling doesn't do what I
think it does. It did reduce my external filtering requirements, I can
see that, but I don't see any noise reduction capabilities without
loss of signal content.

thanks  for any help!

steve

```
```"stevepierson" <gkicomputers@yahoo.com> wrote in

> Hi,
> I've been reading quite a bit about oversampling and it's apparent use
> in noise reduction, but haven't been able to tie everything together.
> As I probably can't explain my exact question clearly, I'll give an
> example, I have a Analog Devices evaluation board with a 1MSPS A/D
> with CPU hooked up to a gryo. The gyro has a raw BW of 1000Hz, I have
> a single pole filter at 50Hz between it and the A/D (hooked up per the
> datasheet).  I am sampling at 10X 50hz, or 500 Hz, since the single
> pole filter is not great. The datasheet indicates that the gryo noise
> is white Gaussian and I am seeing it as +/- 4 counts on the A/D, which
> agrees with the datasheet estimate with a 50Hz filter.
>
> So my attempt here is to use oversampling to bring the noise down, I
> oversample at 4x,16x,32x, up to 256x and average the samples (every
> 500hz, or 2 mS). But I see no reduction in noise, still +/- 4 counts,
> no matter what. Well, thinking about it for a moment I realize that
> the data probably doesn't change much over a 2mS period (i.e., the
> noise is slow), it's just averaging the same number 256 times.
>
> Ok, so the only way to get around this is to add higher frequency
> noise, which I can do by relaxing the output filter, I do this and the
> oversampling now brings down the noise, but, and here is the rub, when
> I relax the filter the overall noise increases, so the net result is I
> have the same noise as I did in the beginning :(
>
> Now I can average multiple 2mS samples over a second to bring the
> noise down, but this obviously reduces the BW, which I don't want, and
> that is what I consider a normal filter, not oversampling.
>
> So the question is, how can I use oversampling to reduce noise without
> signal loss? Or maybe I can't, that oversampling doesn't do what I
> think it does. It did reduce my external filtering requirements, I can
> see that, but I don't see any noise reduction capabilities without
> loss of signal content.
>
> thanks  for any help!
>
> steve
>
>

You have to define "oversampling" for us.  The way I'm familiar with it,
its a valuable tool in signal reconstruction that allows one to
accurately reproduce the digitized signal without noise.  When you think
about it this way, noise present when the data was acquired is considered
"signal".  Oversampling deals with noise associated with analog playback,
not noise that has already been sampled.  FWIW, it does this by
compressing the recorded info in frequency, allowing the analog output
filters to have gentler rolloffs.

--
Scott
```
```stevepierson wrote:

> Hi,
> I've been reading quite a bit about oversampling and it's apparent use
> in noise reduction, but haven't been able to tie everything together.
> As I probably can't explain my exact question clearly, I'll give an
> example, I have a Analog Devices evaluation board with a 1MSPS A/D
> with CPU hooked up to a gryo. The gyro has a raw BW of 1000Hz, I have
> a single pole filter at 50Hz between it and the A/D (hooked up per the
> datasheet).  I am sampling at 10X 50hz, or 500 Hz, since the single
> pole filter is not great. The datasheet indicates that the gryo noise
> is white Gaussian and I am seeing it as +/- 4 counts on the A/D, which
> agrees with the datasheet estimate with a 50Hz filter.
>
> So my attempt here is to use oversampling to bring the noise down, I
> oversample at 4x,16x,32x, up to 256x and average the samples (every
> 500hz, or 2 mS). But I see no reduction in noise, still +/- 4 counts,
> no matter what. Well, thinking about it for a moment I realize that
> the data probably doesn't change much over a 2mS period (i.e., the
> noise is slow), it's just averaging the same number 256 times.
>
> Ok, so the only way to get around this is to add higher frequency
> noise, which I can do by relaxing the output filter, I do this and the
> oversampling now brings down the noise, but, and here is the rub, when
> I relax the filter the overall noise increases, so the net result is I
> have the same noise as I did in the beginning :(
>
> Now I can average multiple 2mS samples over a second to bring the
> noise down, but this obviously reduces the BW, which I don't want, and
> that is what I consider a normal filter, not oversampling.
>
> So the question is, how can I use oversampling to reduce noise without
> signal loss? Or maybe I can't, that oversampling doesn't do what I
> think it does. It did reduce my external filtering requirements, I can
> see that, but I don't see any noise reduction capabilities without
> loss of signal content.
>
ADCs with a high front-end bandwidth and relatively high bit counts have
lots of high-frequency noise.  This noise tends to be white after
sampling, no matter how fast you sample.  If you're sampling something
slow, then sampling fast and low-pass filtering will average out more of
the ADC noise.  If you're sampling something with low-frequency noise
that swamps out the ADC noise then no amount of post-sampling filtering
will help.

By the way:  you can often make a superior anti-aliasing filter in the
sampled-time world.  Oversampling at the ADC, then filtering and
decimating before you do the rest of your processing, can save you board
space and grief with analog filters.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```
stevepierson wrote:

[...]

> I've been reading quite a bit about oversampling and it's apparent use
> in noise reduction, but haven't been able to tie everything together.

1. You can get with the lower bit precision ADC, since the quantization
error is averaged out.

2. You can get with the simple analog filter for antialiasing, since the
sample rate is higher.

But, the oversampling can't clean your signal from the noise which is
present in the signal bandwidth.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

```
```On Mar 16, 1:08 pm, Scott Seidman <namdiestt...@mindspring.com> wrote:
> "stevepierson" <gkicomput...@yahoo.com> wrote innews:1174063927.072728.48=
>
>
>
>
>
> > Hi,
> > I've been reading quite a bit about oversampling and it's apparent use
> > in noise reduction, but haven't been able to tie everything together.
> > As I probably can't explain my exact question clearly, I'll give an
> > example, I have a Analog Devices evaluation board with a 1MSPS A/D
> > with CPU hooked up to a gryo. The gyro has a raw BW of 1000Hz, I have
> > a single pole filter at 50Hz between it and the A/D (hooked up per the
> > datasheet).  I am sampling at 10X 50hz, or 500 Hz, since the single
> > pole filter is not great. The datasheet indicates that the gryo noise
> > is white Gaussian and I am seeing it as +/- 4 counts on the A/D, which
> > agrees with the datasheet estimate with a 50Hz filter.
>
> > So my attempt here is to use oversampling to bring the noise down, I
> > oversample at 4x,16x,32x, up to 256x and average the samples (every
> > 500hz, or 2 mS). But I see no reduction in noise, still +/- 4 counts,
> > no matter what. Well, thinking about it for a moment I realize that
> > the data probably doesn't change much over a 2mS period (i.e., the
> > noise is slow), it's just averaging the same number 256 times.
>
> > Ok, so the only way to get around this is to add higher frequency
> > noise, which I can do by relaxing the output filter, I do this and the
> > oversampling now brings down the noise, but, and here is the rub, when
> > I relax the filter the overall noise increases, so the net result is I
> > have the same noise as I did in the beginning :(
>
> > Now I can average multiple 2mS samples over a second to bring the
> > noise down, but this obviously reduces the BW, which I don't want, and
> > that is what I consider a normal filter, not oversampling.
>
> > So the question is, how can I use oversampling to reduce noise without
> > signal loss? Or maybe I can't, that oversampling doesn't do what I
> > think it does. It did reduce my external filtering requirements, I can
> > see that, but I don't see any noise reduction capabilities without
> > loss of signal content.
>
> > thanks  for any help!
>
> > steve
>
> You have to define "oversampling" for us.  The way I'm familiar with it,
> its a valuable tool in signal reconstruction that allows one to
> accurately reproduce the digitized signal without noise.  When you think
> about it this way, noise present when the data was acquired is considered
> "signal".  Oversampling deals with noise associated with analog playback,
> not noise that has already been sampled.  FWIW, it does this by
> compressing the recorded info in frequency, allowing the analog output
> filters to have gentler rolloffs.
>
> --
> Scott
> Reverse name to reply- Hide quoted text -
>
> - Show quoted text -

the oversampling I am talking about concerns input sampling, I am

https://www.mysilabs.com/public/documents/tpub_doc/anote/Microcontrollers/P=
recision_Mixed-Signal/en/an118.pdf

Key Points
=B7 Oversampling and averaging can be used to
increase measurement resolution, eliminating
the need to resort to expensive, off-chip ADC's.
=B7 Oversampling and averaging will improve the
SNR and measurement resolution at the cost of
increased CPU utilization and reduced throughput.
=B7 Oversampling and averaging will improve signal-
to-noise ratio for "white" noise.

```
```"stevepierson" <gkicomputers@yahoo.com> wrote in

> the oversampling I am talking about concerns input sampling, I am
> reading articles like this one
>
>
> https://www.mysilabs.com/public/documents/tpub_doc/anote/Microcontrolle
> rs/Precision_Mixed-Signal/en/an118.pdf
>

noise, though, comes in before the ADC.

--
Scott
```
```On Mar 16, 1:20 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:

"But, the oversampling can't clean your signal from the noise which is
present in the signal bandwidth."

Ok, thinking about that statement, I think it makes sense now, my
oversampling WAS removing any high frequency noise outside the signal
bandwidth, but since there wasn't any HF noise, it wasn't removing
any, that's why my 256 averaged oversampled result was exactly the
same as 1 sample.
The low frequency noise can't be distinguished from my signal, so
really nothing I can do about that, unless I bring the bandwidth down.

thanks for the help

```
```stevepierson wrote:

...

> https://www.mysilabs.com/public/documents/tpub_doc/anote/Microcontrollers/Precision_Mixed-Signal/en/an118.pdf
>
> Key Points
> &#65533; Oversampling and averaging can be used to
> increase measurement resolution, eliminating
> the need to resort to expensive, off-chip ADC's.
> &#65533; Oversampling and averaging will improve the
> SNR and measurement resolution at the cost of
> increased CPU utilization and reduced throughput.
> &#65533; Oversampling and averaging will improve signal-
> to-noise ratio for "white" noise.

The noise being referred to is produced by the sampling process. The
increase in resolution allows you to better see the noise riding on the
input signal.

Consider an attempt to record speech in a boiler factory. Everything
coming into the microphone is signal in the DSP sense, despite its being
called noise by the recording engineer. Oversampling won't diminish it.

Jerry
--
Engineering is the art of making what you want from things you can get.
&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
```
```On Mar 16, 9:52 am, "stevepierson" <gkicomput...@yahoo.com> wrote:
> Hi,
> I've been reading quite a bit about oversampling and it's apparent use
> in noise reduction, but haven't been able to tie everything together.
> As I probably can't explain my exact question clearly, I'll give an
> example, I have a Analog Devices evaluation board with a 1MSPS A/D
> with CPU hooked up to a gryo. The gyro has a raw BW of 1000Hz, I have
> a single pole filter at 50Hz between it and the A/D (hooked up per the
> datasheet).  I am sampling at 10X 50hz, or 500 Hz, since the single
> pole filter is not great. The datasheet indicates that the gryo noise
> is white Gaussian and I am seeing it as +/- 4 counts on the A/D, which
> agrees with the datasheet estimate with a 50Hz filter.
>
> So my attempt here is to use oversampling to bring the noise down, I
> oversample at 4x,16x,32x, up to 256x and average the samples (every
> 500hz, or 2 mS). But I see no reduction in noise, still +/- 4 counts,
> no matter what. Well, thinking about it for a moment I realize that
> the data probably doesn't change much over a 2mS period (i.e., the
> noise is slow), it's just averaging the same number 256 times.
>
> Ok, so the only way to get around this is to add higher frequency
> noise, which I can do by relaxing the output filter, I do this and the
> oversampling now brings down the noise, but, and here is the rub, when
> I relax the filter the overall noise increases, so the net result is I
> have the same noise as I did in the beginning :(
>
> Now I can average multiple 2mS samples over a second to bring the
> noise down, but this obviously reduces the BW, which I don't want, and
> that is what I consider a normal filter, not oversampling.
>
> So the question is, how can I use oversampling to reduce noise without
> signal loss? Or maybe I can't, that oversampling doesn't do what I
> think it does. It did reduce my external filtering requirements, I can
> see that, but I don't see any noise reduction capabilities without
> loss of signal content.
>
> thanks  for any help!
>
> steve

I think you may be confusing the issues of "noise reduction" and
"signal estimation", the latter which may be more useful here. There
are numerous papers which deal with this; here is one:
http://tinyurl.com/2cqowo

Tom

```
```stevepierson wrote:

...

> Ok, so the only way to get around this is to add higher frequency
> noise, which I can do by relaxing the output filter, I do this and the
> oversampling now brings down the noise, but, and here is the rub, when
> I relax the filter the overall noise increases, so the net result is I
> have the same noise as I did in the beginning :(

When starting out on the wrong foot, it's easy to march off into
absurdity. Adding noise for the pleasure of eliminating it later is an
example.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
```