# Talk:Decimation (signal processing)

There should also be a part on the way decimation transformations work in physics. Meaning by applying the renormalization group to a crystal structure and then relabeling the points. --131.174.17.21 (talk) 18:48, 16 January 2008 (UTC)

The article refers to "eliminating every other sample without changing the sampling rate". This seems like a contradiction in terms; removing every other sample will by definition halve the sampling rate. I think the article means to say / should say "without changing the playback rate (in samples per time period)" or somesuch. 142.103.107.100 (talk) 23:35, 18 August 2008 (UTC)

## Decimation

This page contains the term decimation. Currently decimation has to do with the Roman army... 212.143.17.66

Removed the word. —Pangolin 06:27, 23 June 2006 (UTC)
Someone has now corrected the link to be decimation (signal processing) Jasen betts (talk) 06:16, 26 October 2011 (UTC)

## Circular definition

The first paragraph defines downsampling as "the process of reducing the sampling rate", so starting the next section "By downsampling, the sampling rate is also reduced . . ." doesn't work. Fredsie 15:03, 21 December 2006 (UTC)

## Phrase

"So in practice the cutoff frequency is placed far enough below the theoretical cutoff that the filter's skirt is contained below the theoretical cutoff."

Huh? O.o I think there is a below the theoretical cutoff surplus... --ANDROBETA 02:11, 27 December 2010 (UTC)
the skirt is the leakage of the filter, real world filters aren't [brick-wall filters] you don't want leakage crossing the threshold and coming back frequency inverted and corrupting the desired signal. Jasen betts (talk) 06:16, 26 October 2011 (UTC)

## Interpolation is a low pass filter?

really? suppose I interpolate using sinc() at the sample rate but yeah, In the real world it makes more sense to use some other convolution that is finite and does perform a low pass with the desired limit.

Jasen betts (talk) 06:16, 26 October 2011 (UTC)

## Merger proposal

I think the Decimation (signal processing) article is a good candidate for merging, since Decimation and Downsampling are used interchangeably (in my experience). Jcmcclurg (talk) 05:18, 19 March 2012 (UTC)

Downsampling means to reduce the number of bits of information for each sample. Decimation means to reduce the number of samples. Based upon this and because this merger proposal has been sitting dormant since March, I will make "not to be confused with" links and remove the template. --Mblumber (talk) 20:08, 17 August 2012 (UTC)
After further research, I am wrong and will complete the merge of decimation into downsampling --Mblumber (talk) 20:20, 17 August 2012 (UTC)

## Decimation by a factor of 1?

The section on effect on the Z transform made no sense, so I tried to improve it, starting from incrementing that 1 to 2. That section came in in this March 2012 edit, by an editor who seems to be inactive. I'd just get rid of it unless someone sees the point and wants to fix it up. Dicklyon (talk) 23:40, 29 June 2013 (UTC)

## Decimation (signal processing)

I have proposal to iclude in text this very importent fragment^

"In the easer case can be use the algorithm:[1]

${\displaystyle y[n]=\sum _{k=0}^{M-1}x[nM+k]\ e^{-i2\pi fkT},n=0,1,..,N}$,

where T is interval between samples of signal.

Decimation process of ADC samples of digital video signals

For example by ${\displaystyle 2\pi fkT=k\pi /2}$ we have ${\displaystyle e^{-i2\pi fkT}=1,e^{-i\pi /2},e^{-i\pi },...}$ and[1]

${\displaystyle Re(y[n])=\sum _{k=0}^{M-1}(Re(x[nM+k])cos{k\pi /2}+Im(x[nM+k])sin{k\pi /2})\,}$,
${\displaystyle Im(y[n])=\sum _{k=0}^{M-1}(Im(x[nM+k])cos{k\pi /2}-Re(x[nM+k])sin{k\pi /2})\,}$.

For ${\displaystyle Im(x[nM+k])=0}$ we have [2]

${\displaystyle Re(y[n])=\sum _{k=0}^{M-1}(Re(x[nM+k])cos{k\pi /2}\,}$,
${\displaystyle Im(y[n])=\sum _{k=0}^{M-1}(Re(x[nM+k])sin{k\pi /2})\,}$,

or

${\displaystyle Re(y[n])=x[nM]-x[nM+2]+x[nM+4]-...,}$,
${\displaystyle Im(y[n])=-x[nM+1]+x[nM+3]-x[nM+5]-...}$.

For video signals (${\displaystyle Im(x[nM+k])=0}$ and ${\displaystyle Re(x[nM+k])>=0}$)

${\displaystyle y[n]=\sum _{k=0}^{M-1}x[nM+k]\ }$.[3]

This Algorithm is only one filter of discrete Fourier transform and is very importent for decimation of ADC samples before digital beamforming in digital antenna arrays in radars and MIMO systems in communications."

It's very importent for Wiki-readers. Thank you for your understanding. Best regards,Swadim (talk) 10:32, 25 August 2017 (UTC)

References

1. ^ a b Slyusar V. I. Synthesis of algorithms for measurement of range to M sources with the use of additional gating of the ADC readings.// Radioelectronics and Communications Systems. - Vol. 39. - no. 5. - 1996. - P. 36 – 40. [1]
2. ^ T. Schilcher. RF applications in digital signal processing//” Digital signal processing”. Proceedings, CERN Accelerator School, Sigtuna, Sweden, May 31-June 9, 2007. - Geneva, Switzerland: CERN (2008). - P. 258. - DOI: 10.5170/CERN-2008-003. https://cds.cern.ch/record/1100538/files/p249.pdf
3. ^ Saska Lindfors, Aarno Pärssinen, Kari A. I. Halonen. A 3-V 230-MHz CMOS Decimation Subsampler.// IEEE transactions on circuits and systems— Vol. 52, No. 2, February 2005. – P. 110.
If current academic works on the article subject (which the referenced paper is not) include this information then (subject to WP:DUE weight), it could be included here. It seems more likely though, that if it belongs anywhere, it is in a more-specialised article (perhaps radio/MIMO/etc.).—Aquegg (talk) 12:38, 25 August 2017 (UTC)
--Bob K (talk) 20:05, 25 August 2017 (UTC)
Dear Bob K,

I'm sorry, but it's only your personal vision. Where you see in this article the frequency-shifting? This are only radio and video signals decimation methods.

If you don't know that ${\displaystyle \sum _{k=0}^{M-1}x[nM+k]\ e^{-i2\pi fkT},n=0,1,..,N}$ is performing a frequency-shift, then I have to ask what "science" is your degree in. And yes, I do have a PhD, in Electrical Engineering/Communication Theory. And my 40 years of experience beats your 30 years.
--Bob K (talk) 12:10, 26 August 2017 (UTC)

Concerning anti-alias filtering I should be tell that proposed algorithm is only one case of formula

${\displaystyle y[n]=\sum _{k=0}^{K-1}x[nM-k]\cdot h[k],}$

and have similare properties.

I know exactly what that algorithm is doing, apparently better than you do. As I have already explained, it combines two different concepts, which is not necessary or relevant to the explanation of decimation. So you are the one being disruptive. As Aquegg has said, you are trying to turn a basic tutorial on decimation into something more specialized. Take it somewhere else.
--Bob K (talk) 12:10, 26 August 2017 (UTC)
Dear Bob K,

In any case the term decimation is more bigger as your little and old experience in this field. Your concept of this term is very limited. I'm so sorry that Wikipedia has you as moderator of this article. The Wikipedia is not your personal site. You should consider all other points of vision and all theories. The time will show who is right. Swadim (talk) 15:16, 26 August 2017 (UTC)

If 40 years is "little" experience, then you still have a long way to go. I am sorry that we couldn't come to a better understanding. And I thank you for your patience. Good luck.
--Bob K (talk) 05:07, 27 August 2017 (UTC)
Dear Bob K,

Thank you, but I have additinal arguments.

You wrote, that "it (proposed algorithm)) combines two different concepts, which is not necessary or relevant to the explanation of decimation". But the anti-alias filtering is similary different concept regarding for decimation. The better anti-alias filtering give only the analog filtering. Old concept of decimation combined with digital equivalence of anti-alias filtering.

The same proposed algorithm combine 4 concept: decimation, anti-alias filtering (may be not very good), frequency-shift and I/Q-demodulation. Why one combined concept in your opinion is better as other? And what is your opinion about this algorithm of decimation:

${\displaystyle Re(y[n])=-6[nM+1]+32x[nM+3]-52x[nM+5]+32x[nM+7]-6x[nM+9].}$
${\displaystyle Im(y[n])=x[nM]-17x[nM+2]+46x[nM+4]-46x[nM+6]+17x[nM+8]-x[nM+10].}$

This is only one case of general formula:

${\displaystyle y[n]=\sum _{k=0}^{M-1}x[nM+k]\cdot h[k].}$

But this is decimation with anti-alias filtering, frequency-shift and I/Q-demodulation.

I have proposal regarding compronise solution of this discussion; Introduce the additional part for the article "decimation" with name "Combined nethods of decimation". I think that this not destroy article concept and expand termin "decimation" to practical solutions. Best regards,Swadim (talk) 06:45, 27 August 2017 (UTC)

"Destroy" is your word Swadim, but I agree that is what you were doing to the basic explanation of decimation. That is why you met such stiff resistance, not because "Swadim isn't very good with English, and doesn't know any good English-language sources for this". I have no objection to elaborating on a specific application in a subsequent section, because disinterested readers can simply stop reading at that point, without missing the basics. It is a standard approach seen over and over again in Wikipedia. --Bob K (talk) 04:29, 28 August 2017 (UTC)

Thank you, Bob K. I will do it with your help. Swadim (talk) 12:39, 28 August 2017 (UTC)

To reiterate, whether or not a WP article should include information depends on whether the authors of pertinent scholarly works include it. For example, if the referenced books by Milić and Harris (titled “Multirate … Processing …”) include it, then that could be an argument for including it here. (See WP:RS and WP:DUE.)—Aquegg (talk) 13:11, 27 August 2017 (UTC)

The biggest problem I see here (besides Bob K and Swadim dipping into personal attacks on each others' credentials) is that Swadim isn't very good with English, and doesn't know any good English-language sources for this. I agree that it's not uncommon to do something like this combined algorithm for decimated downconversion to baseband (modulator/mixer followed by sum-and-dump decimation, or integrate-and-dump in the old analog days); it's essentially what Goertzel's algorithm does, differently arranged with perhaps different opportunities for optimization. The more general case with the arbitrary FIR filter before resampling might be more interesting, and looks like the sort of thing one sees in multi-rate signal processing; or maybe it's less interesting, as it's clearly just a filter followed by a sum-and-dump decimator, using the obvious optimization. But let's work on this via sources, as Aquegg suggests. Once we find what we want in sources, we can see whether Decimation is the best place to cover it or not. It's not the most elegant treatment, but Freeny does discuss this sort of bandpass resampling in telephony, in 1980 (Freeny, S. "TDM/FDM translation as an application of digital signal processing." IEEE Communications Magazine 18.1 (1980): 5-15.) and even less explicitly in 1971 (Freeny, S., et al. "Systems analysis of a TDM-FDM translator/digital A-type channel bank." IEEE Transactions on Communication Technology 19.6 (1971): 1050-1059.). I've used it myself recently in audio, but I agree it's more important for radar and radio where efficient bandpass downconversion is more crucial. Dicklyon (talk) 13:59, 27 August 2017 (UTC)

A more recent (analog discrete-time) implementation of this combined filtering and decimation is in Karvonen, Sami, Thomas AD Riley, and Juha Kostamovaara. "A CMOS quadrature charge-domain sampling circuit with 66-dB SFDR up to 100 MHz." IEEE Transactions on Circuits and Systems I: Regular Papers 52.2 (2005): 292-304. It has lots of refs, some of which might be better sources on this. Dicklyon (talk) 14:09, 27 August 2017 (UTC)

Thank you Aquegg and Dicklyon for your compromise solution.

Regarding of sources for this method and "scholarly works" (to Aquegg) I should say that the paper [1] is the full "scholarly work". This paper was published ALLERTON PRESS INC. (USA) and included in SCOPUS. As the additional reference can proposed the article from PIC S&T’2016[2].

I will study other references, which was proposed of Dicklyon. Unfortunatelly I don't find now identical formulas. But I think that this process will be more faster with help from all WIKI-users after publication the text in Wiki-article. The problem is not only with english but with absence of free access to good English-language books. I proposed references with free access. Swadim (talk) 16:34, 27 August 2017 (UTC)

I found the formula

${\displaystyle y[n]=\sum _{k=0}^{M-1}x[nM+k]\ }$

in paper [3]

and for ${\displaystyle Im(x[nM+k])=0}$ the formula [4]

${\displaystyle Re(y[n])=\sum _{k=0}^{M-1}(Re(x[nM+k])cos{k\pi /2}\,}$,
${\displaystyle Im(y[n])=\sum _{k=0}^{M-1}(Re(x[nM+k])sin{k\pi /2})\,}$.

I think that all these references will be enough for publication of my text as part of article about decimation (as 1st step with the condition of future corrections)?Swadim (talk) 18:09, 27 August 2017 (UTC)

1. ^ Slyusar V. I. Synthesis of algorithms for measurement of range to M sources with the use of additional gating of the ADC readings.// Radioelectronics and Communications Systems. - Vol. 39. - no. 5. - 1996. - P. 36 – 40. [2]
2. ^ Sliusar I.I., Slyusar V.I., Voloshko S.V., Smolyar V.G. Next Generation Optical Access based on N-OFDM with decimation.// Third International Scientific-Practical Conference “Problems of Infocommunications. Science and Technology (PIC S&T’2016)”. – Kharkiv. - October 3 –6, 2016. [3]
3. ^ Saska Lindfors, Aarno Pärssinen, Kari A. I. Halonen. A 3-V 230-MHz CMOS Decimation Subsampler.// IEEE transactions on circuits and systems— Vol. 52, No. 2, February 2005. – P. 110.
4. ^ T. Schilcher. RF applications in digital signal processing//” Digital signal processing”. Proceedings, CERN Accelerator School, Sigtuna, Sweden, May 31-June 9, 2007. - Geneva, Switzerland: CERN (2008). - P. 258. - DOI: 10.5170/CERN-2008-003. [4]