Down Sampling Questions: Theoretical vs Practical

20*2/0.8 = 50.

VLV



gmcauley wrote:

> Vladimir,
> 
> Could you please explain how you arrive at 50Hz?
> 
> 
>>For the DSP downsampling, the passband up to 0.8...0.9 of Nyquist is
> 
> usually
> 
>>a good compromise value. So, for a passband of 20Hz you will need a
> 
> sample
> 
>>rate of  50Hz, which makes nice even values.
>>
> 
> 
> 
> Pardon me if I am missing something obvious, but I don't see the '20' in
> the calculation.  Is it that 2*30*0.8 ~= 50Hz (in round numbers, and where
> the '30' is chosen as described in my original post)?

"gmcauley" <gmcauley@llu.edu> writes:

> Vladimir,
>
> Could you please explain how you arrive at 50Hz?
>
>>For the DSP downsampling, the passband up to 0.8...0.9 of Nyquist is
> usually
>>a good compromise value. So, for a passband of 20Hz you will need a
> sample
>>rate of  50Hz, which makes nice even values.
>>
>
>
> Pardon me if I am missing something obvious, but I don't see the '20' in
> the calculation.  Is it that 2*30*0.8 ~= 50Hz (in round numbers, and where
> the '30' is chosen as described in my original post)?

0.8*X = 20. X = 20/0.8. X is the required sample rate.
-- 
%  Randy Yates                  % "Bird, on the wing,
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%%%% <yates@ieee.org>           % 'One Summer Dream', *Face The Music*, ELO
http://home.earthlink.net/~yatescr

Randy Yates <yates@ieee.org> writes:

> "gmcauley" <gmcauley@llu.edu> writes:
>
>> Vladimir,
>>
>> Could you please explain how you arrive at 50Hz?
>>
>>>For the DSP downsampling, the passband up to 0.8...0.9 of Nyquist is
>> usually
>>>a good compromise value. So, for a passband of 20Hz you will need a
>> sample
>>>rate of  50Hz, which makes nice even values.
>>>
>>
>>
>> Pardon me if I am missing something obvious, but I don't see the '20' in
>> the calculation.  Is it that 2*30*0.8 ~= 50Hz (in round numbers, and where
>> the '30' is chosen as described in my original post)?
>
> 0.8*X = 20. X = 20/0.8. X is the required sample rate.

I meant Nyquist rate. Sample rate is 2*X.
-- 
%  Randy Yates                  % "So now it's getting late,
%% Fuquay-Varina, NC            %    and those who hesitate
%%% 919-577-9882                %    got no one..."
%%%% <yates@ieee.org>           % 'Waterfall', *Face The Music*, ELO
http://home.earthlink.net/~yatescr

gmcauley wrote:
> 
> Thank you for your reply.
> 
> >You state that you categorizing traces visually which suggests shape is
> >important. That suggests that at least the 5th harmonic of your
> >fundamental is significant.
> 
> I am not exactly sure about the relationship of the harmonics to the shape
> - please enlighten.
> 
> There are perhaps two points related to the visual analysis to help
> clarify our case:  Much of EEG data is historically evaluated visually,
> and there are other data traces (eg, tissue oxygenation) that need to be
> visually (at least initially) related to the EEG.
> 
> >Another question to ask if your sampling system was particularly
> >design/chosen to measure the process of current interest.
> >
> >Why did original designer/specifier chose 200 samples/sec?
> >
> 
> One of the data types (my involvement) is EEG.  The so called gamma band
> ranges from 26-100Hz.  So I guess this is why 200Hz seems to be used
> often.
> 
> >
> >Are you sure that 20 Hz is actually the highest frequency of interest?
> 
> In our case, we are not really interested in the gamma band.  I will
> probably choose 25Hz - 30Hz as the maximum frequency to be sure to get
> good fidelity of the beta band with max 20-30Hz (it seems that people
> define it differently???)
> 
> So I am really wanting to know I guess for a low-pass cut off of 30Hz,
> what is a reasonable resample rate.

You haven't provided any specific details of what exactly you are trying
to do or how you are going to do it. But I'm guessing that what you are
talking about is writing software so that a pair of human eyeballs can
look at the data on a computer screen or perhaps look at 2 sets of data
for comparison. At any rate I wouldn't modify your  data at all. I would
just let the user select the resolution that they wish to view at and do
the resampling on the fly. For the quantity of data that one pair of
eyeballs can digest at any one moment you should be able to do the
conversion in a blink. That way if there is any question about whether
some high frequency information is being lost the user can always zoom
in to a higher resolution to see.

-jim

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gmcauley wrote:

   ...

> I am not exactly sure about the relationship of the harmonics to the shape
> - please enlighten.

Plot on the same axes y = sin(x) + sin(5x)  and y = sin(x) - sin(5x). 
Compare the shapes.

   ...

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Aug 15, 9:31 am, "gmcauley" <gmcau...@llu.edu> wrote:
> Thank you for your reply.
>
> >You state that you categorizing traces visually which suggests shape is
> >important. That suggests that at least the 5th harmonic of your
> >fundamental is significant.
>
> I am not exactly sure about the relationship of the harmonics to the shape
> - please enlighten.

For a periodic waveform, any shape other than an absolutely
pure sine wave is composed of perhaps the fundamental
frequency plus some (possibly very large) number of harmonics.
Remove the harmonics, and the shape reverts to a pure sine
wave (or some intermediate form, depending on the number of
harmonics remaining vs. removed).  The sharpest rise/fall
deviations from a sine wave are likely produced by the
highest frequency harmonics.  Remove those and you get a
"softer" looking waveform.  Note that it is possible for
a periodic waveform to contain no spectral content at the
reciprocal of the period (for instance sin(2w)+sin(3w)).

If the shape of the beta signals is important, you will
alter that shape by simply filtering out the gamma band
spectrum.



IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

>
>20*2/0.8 = 50.
>

Thanks Vladimir (and Randy).

Thanks Jerry, I will try it.

Thank you for your (above) explanation.

>
>If the shape of the beta signals is important, you will
>alter that shape by simply filtering out the gamma band
>spectrum.
>

I appreciate you bringing this to my attention.  In our case I don't think
it will be an issue though since, based on power spectra I've seen, there
is very little power in the gamma band.

Thanks Jim for your reply.

>But I'm guessing that what you are
>talking about is writing software so that a pair of human eyeballs can
>look at the data on a computer screen or perhaps look at 2 sets of data
>for comparison.

Don't give them in any ideas!! They have not asked me for this yet!!<j>


>You haven't provided any specific details of what exactly you are trying
>to do or how you are going to do it. 

Other group members wanted smaller data sets for visually 'epoching' and
comparing trends between data different data types (eg, eeg vs tissue
oxygen).  I just wanted to be sure that down sampling would not lead to
significant information loss in the 'interesting' parts of the data.