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# Discussion Groups | Comp.DSP | Decimation / downsampling

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# Decimation / downsampling - pardon_232000 - 2004-02-14 13:28:00

```Hello,

I have problem puting the rigth name on the rigth thing:

--> In "Discrete-time signal processing" of Oppenheim and schafer :
"In general, the operation of reducing the sampling rate (including
any prefiltering) will be called downsampling" section 4.6.1

--> In "An overview of sigma-delta converters" in IEEE signal
processing of january 1996 vol 13, no 1 it is say
"The collective operation of low-pass filtering and downsampling is
know as decimation"

What is the exact word for just take one sample among N ? Decimation
or downsampling
What is the exact word for take one sample among N after prefiltering
? Decimation or downsampling
```
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# Re: Decimation / downsampling - Clay S. Turner - 2004-02-14 14:35:00

```I think of of them as almost the same thing but with decimation being a part
of downsampling. "Decimation" comes from the Roman method of punishment
where a group of men were selected at random and every tenth one was
killed - hence the "deci" part of the word. So I think of decimation in
signal processing as the keeping of some of the original samples and
throwing others away in some orderly fashion. I think of downsampling as the
whole process of resampling at a lower sample rate which generally includes
some kind of antialias filter followed by a decimation. Also downsampling
may involve some interpolation followed by decimation to get to the desired
rate. Imagine if you wanted the data sampled at 2/3 of its original rate. So
here the overall down sampling can be done by a 3x upsampling, lowpass
filtering and then decimation by two. Of course these steps can be combined
into a poly phase method where the decimation becomes the orderly picking of
outputs from different filters.

IHTH,

--
Clay S. Turner, V.P.
Wireless Systems Engineering, Inc.
Satellite Beach, Florida 32937
(321) 777-7889
www.wse.biz
c...@wse.biz

"pardon_232000" <p...@yahoo.fr> wrote in message
> Hello,
>
> I have problem puting the rigth name on the rigth thing:
>
> --> In "Discrete-time signal processing" of Oppenheim and schafer :
> "In general, the operation of reducing the sampling rate (including
> any prefiltering) will be called downsampling" section 4.6.1
>
> --> In "An overview of sigma-delta converters" in IEEE signal
> processing of january 1996 vol 13, no 1 it is say
> "The collective operation of low-pass filtering and downsampling is
> know as decimation"
>
>
> What is the exact word for just take one sample among N ? Decimation
> or downsampling
> What is the exact word for take one sample among N after prefiltering
> ? Decimation or downsampling

```
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# Re: Decimation / downsampling - Clay S. Turner - 2004-02-14 14:38:00

```"Clay S. Turner" <C...@WSE.Biz> wrote in message
news:TIuXb.21136\$B...@bignews3.bellsouth.net...
> I think of of them as almost the same thing but with decimation being a
part
> of downsampling. "Decimation" comes from the Roman method of punishment
> where a group of men were selected at random and every tenth one was
> killed - hence the "deci" part of the word. So I think of decimation in
> signal processing as the keeping of some of the original samples and
> throwing others away in some orderly fashion. I think of downsampling as
the
> whole process of resampling at a lower sample rate which generally
includes
> some kind of antialias filter followed by a decimation. Also downsampling
> may involve some interpolation followed by decimation to get to the
desired
> rate. Imagine if you wanted the data sampled at 2/3 of its original rate.
So
> here the overall down sampling can be done by a 3x upsampling, lowpass
> filtering and then decimation by two.

Really I meant 2x interpolation followed by 3x decimation. Sorry about the
transposition.

Of course these steps can be combined
> into a poly phase method where the decimation becomes the orderly picking
of
> outputs from different filters.
>
> IHTH,
>
> --
> Clay S. Turner, V.P.
> Wireless Systems Engineering, Inc.
> Satellite Beach, Florida 32937
> (321) 777-7889
> www.wse.biz
> c...@wse.biz
>
>
>
> "pardon_232000" <p...@yahoo.fr> wrote in message
> > Hello,
> >
> > I have problem puting the rigth name on the rigth thing:
> >
> > --> In "Discrete-time signal processing" of Oppenheim and schafer :
> > "In general, the operation of reducing the sampling rate (including
> > any prefiltering) will be called downsampling" section 4.6.1
> >
> > --> In "An overview of sigma-delta converters" in IEEE signal
> > processing of january 1996 vol 13, no 1 it is say
> > "The collective operation of low-pass filtering and downsampling is
> > know as decimation"
> >
> >
> > What is the exact word for just take one sample among N ? Decimation
> > or downsampling
> > What is the exact word for take one sample among N after prefiltering
> > ? Decimation or downsampling
>
>

```
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# Re: Decimation / downsampling - Fred Marshall - 2004-02-14 20:14:00

```"pardon_232000" <p...@yahoo.fr> wrote in message
> Hello,
>
> I have problem puting the rigth name on the rigth thing:
>
> --> In "Discrete-time signal processing" of Oppenheim and schafer :
> "In general, the operation of reducing the sampling rate (including
> any prefiltering) will be called downsampling" section 4.6.1
>
> --> In "An overview of sigma-delta converters" in IEEE signal
> processing of january 1996 vol 13, no 1 it is say
> "The collective operation of low-pass filtering and downsampling is
> know as decimation"
>
>
> What is the exact word for just take one sample among N ? Decimation
> or downsampling

It's always correct to say that one is sampling at the reduced rate because
it is as if the original sampling had been done at that lower rate.  Whether
it is proper to do this or not / i.e. whether it causes frequency aliasing
or not / would be a matter of concern.

> What is the exact word for take one sample among N after prefiltering
> ? Decimation or downsampling

I would probably say "sample rate reduction by a factor of N" (with the
assumption that the prefiltering was done as was done properly).  I believe
that decimation (by a factor of N) is also a common term.

Downsampling might connotes something different although it might also be
used and understood in the context you've given.  Downsampling could also
mean sampling where the objective is to do a frequency translation of a
bandpass signal to a lower frequency.  For example:
A bandpass signal with <1kHz bandwidth centered at 10kHz is sampled at 1kHz
in quadrature with I and Q clocks.
There results I and Q sample streams at 1kHz each.
The signal has been downsampled to the lowest possible frequency and rate at
the same time.

So, the essential differences are:
Was the original signal bandlimited to <fs/2 or was it bandlimited to
<fs/2N?
If the former, then sampling at a lower rate would be problematic.
If the former, then filtering so that the bandwidth is limited to fs/2N is
necessary.
If the latter, then sampling at a lower rate would be OK.
If the latter, then prefiltering is unnecessary.

Fred

```
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