decimation and resolution

Hi Robert,

robert bristow-johnson <rbj@audioimagination.com> wrote:
[]
>> Ok, so there's no 'Nyquist frequency' violation if we are undersampling
>> information, no aliasing effect that needs to be taken into account, is
>> that correct?
>>
> 
> uhm, i think you mean "oversampling".  "undersampling" means that your 
> sample rate is not high enough and that Nyquist is below the signal 
> bandwidth.  "oversampling" means that your sample rate is higher than 
> absolutely necessary and there is a gap of empty band (or stuff you 
> don't care about) between the top bandedge and Nyquist.

I did mean 'undersampling'. The useful signal is around 1.2Hz and we 
have a table of values (a.k.a. profile) to be executed at 3KHz. Yet the 
position is known with a 25KHz rate. So the encoder position is 
'undersampled' w.r.t. the control loop and if there's noise it can be 
injected right where the signal is.

Now another question I have is about the bandwidth of my control loop. 
The simple fact that I'm supposed to drive it at 3 KHz, does it mean the 
loop bandwidth is 3 KHz? I don't really see the connection.

> the definition of Nyquist frequency i am using is Fs/2 .  some people 
> (even O&S, which is a damn shame), might define Nyquist as the bandwidth 
> of the continuous-time signal being sampled.

I follow the same definition as you and I'm aware of the confusion!
Is O&S Oppenheim and Schafer?

Al

On Mon, 03 Nov 2014 09:50:57 +0000, alb wrote:

> Hi Tim,
> 
> Tim Wescott <tim@seemywebsite.com> wrote:
> []
>>> That's very nice! So if I understood you correctly what I'm doing with
>>> undersampling is getting the noise density above my sampling frequency
>>> and aliasing it. That's what I thought in the first place.
>> 
>> I was being sarcastic and thought you'd pick it up.
> 
> I did pick up your sarcasm indeed, but I failed to emphasize it enough
> in my reply. The /best/ thing about this whole story is that now I have
> my microvibration environment on top of my set of bldc motors and
> undersampling may simply be a receipt for failure!
> 
>> As a concrete example, if you're sampling at 8kHz and you've got
>> significant noise at 8002Hz, then after sampling that noise will appear
>> at 2Hz.  2Hz is probably well within your control loop's bandwidth, so
>> your controller will dutifully make sure that the 2Hz signal is
>> eliminated from the position feedback -- by making the assembly flap
>> around at 2Hz.
>> 
>> This is NOT a problem of the control loop itself: it is an issue with
>> the control loop, the sampling, AND the noise.
> 
> Meaning, in order for the control loop to work properly, signal *must*
> be treated to avoid issues.
> 
> []
>>>> At this point you ARE decimating, and it may be worthwhile to
>>>> consider some very judicious filtering.  About the only kind that I'd
>>>> contemplate is a filter that decimates by N and averages (or sums) by
>>>> N -- you end up with a comb filter with nulls at all harmonics of the
>>>> sampling rate (so it totally undermines any noise aliasing), at the
>>>> best possible phase shift to attenuation ratio for anything that may
>>>> alias down.
>>> 
>>> I'm sorry but I think I lost you here. I understood that noise can be
>>> aliased down around DC where my signal is (~1.2Hz) but I haven't
>>> understood how the comb filter may undermine aliasing.
>> 
>> If you take my 8kHz sampling example above, an average-and-decimate
>> filter will have a frequency response of sinc(pi*f/8000Hz).  Its
>> response will be 1 at DC, nearly 1 at 2Hz, zero at 8kHz, and about
>> 0.00025 at 8002Hz.  Without the average-and-decimate filter the signal
>> at 8002Hz would come through at full strength.
> 
> Ok, so is the attenuation of the 8002 Hz component that helps us reduce
> the 2Hz aliased signal. Of course this means spectral information for
> the environment shall be available in order to correctly define sampling
> rate *and* filter definition.
> 
>> If you figure out the phase delay in the filter vs. the amount of
>> attenuation you for signals that will alias to within your loop
>> passband,
>> you'll find that the average-and-decimate filter tends to be more
>> favorable than just about any other kind of anti-aliasing filters.
> 
> Why not a low-pass filter? Is it a matter of 'complexity'?

Sort of.  Unless your sampling rate is exceedingly generous you need far 
more than a 1st-order low-pass, and the filter absolutely positively must 
be minimum phase.  You can implement all of this with a 5th- or 6th- or 
whatever-order IIR filter, but you end up with something that takes more 
time to implement, analyze, and verify than an average-and-dump.

The average-and-dump filter also has very favorable action on random ADC 
noise (which your encoder experiences, if it's what I think it is).

> What I can do is to show what's the effect of some type of noise on our
> system and warn our customer about the lack of a specification for the
> filtering stage. They ought to know the microvibration environment at
> instrument and platform level so they can specify what we should
> implement.
> 
> For the time being I only see a potential flaw in their specification
> (the lack of a filter).

It may just be a non-problem.  It's hard not to borrow trouble when you 
don't have information.  A warning about vibration or electrical noise 
close to your sampling rate may be a good idea, though.

> []

[]

> []
>>> Sometimes the problem isn't fixable. A spourious value can be there
>>> because of a heavy ion commuting the state of a register and here you
>>> go with your crazy value. Failure analysis usually leads to
>>> countermeasures to be implemented because you cannot get rid of the
>>> root cause.
>>> 
>>> 
>> True.  If root cause analysis is being done, and the root cause really
>> is unfixable, then of course you need to do something else.
> 
> A low-pass filter will definitely dump the spikes, I'm not sure about an
> average.

A moving average, or average-and-dump, _is_ a low-pass filter.  So it'll 
reduce the spike magnitude.

Be aware, however, that a low-pass filter is effective at filtering out 
noise that has zero mean and a mostly-Gaussian distribution.  Noise that 
spikes every once in a while doesn't meet that criterion -- in that case, 
some sort of a median detector, or other filter that identifies outliers 
and tosses them, is a good idea.

-- 

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