# Talk:Raised-cosine filter

## Analogue or digital

PAR said on Oli Filth's talk page:

"The raised cosine filter is listed on the linear analog filter template, but it is a linear DIGITAL filter. This should be fixed. PAR 21:29, 25 August 2006 (UTC)"

I wasn't even aware that the "analog filter" template had been added, but according to the history, you added it!!
Don't change the subject! My bungled edits are not the subject of this discussion! Please put all such discussions on the Wikipedia page [[Bungled edits of PAR]] unless that page has been deleted for excessive length. PAR 22:56, 25 August 2006 (UTC)
As to whether raised-cosine is analogue or digital, it's an interesting question. Technically, "raised-cosine filter" as presented in this article is just a mathematical expression that operates in continuous-time, continuous-frequency; this would imply an analogue implementation. However, it happens to be implemented digitally in pretty much all applications. However, the digital implementation requires discrete-time equations. So it's probably best to not call it either. Oli Filth 22:12, 25 August 2006 (UTC)
Perhaps a template for linear digital filters? PAR 22:56, 25 August 2006 (UTC)
Perhaps, however there's currently nothing in the raised-cosine article that even hints at the digital implementation - the equations would be different, as they'd be discrete-time (obviously).
Actually, I'm not sure what specific types of digital filters there are. Because the designer has so much more flexibility in their design than in the analogue domain, generally digital filters are custom-designed according to requirements, using the Parks-McLellan algorithm, etc., or designed and then multiplied by an appropriate window. I'm not sure how many specific digital filters there out there with names. Oli Filth 23:04, 25 August 2006 (UTC)
It's mathematically defined as a linear analog filter that would ideally be used to convert a digital dirac-pulse signal to an analog continuous-time signal. Typically root-raised-cosine filters are used, however, as stated in the article. Strstrep (talk) 17:47, 2 April 2008 (UTC)

## Alpha or beta?

It seems that the roll-off parameter is more commonly known as alpha. Temblast (talk) 11:29, 24 June 2011 (UTC)

## The Raised-cosine-impulse.svg picture has label bugs on the time axis.

The bug can be found in the python code:

ax.set_xticks([-3,-2,-1,0,3,2,1])

ax.set_xticklabels(["-3T","-2T","-T","0","T","2T","3T"])

It should probably be:

ax.set_xticks([-3,-2,-1,0,1,2,3])

ax.set_xticklabels(["-3T","-2T","-T","0","T","2T","3T"]) — Preceding unsigned comment added by 81.230.178.57 (talk) 10:44, 12 August 2011 (UTC)

Corrected. Thanx. --ElectroKid (talkcontribs) 22:00, 28 August 2011 (UTC)

## The Raised-Cosine Square Waves

I use transmitting, on a voice channel, digital data [high/low] as 'raised-cosine square waves' to eliminate the high harmonics. The transitions (edges) of these square waves follow the cosine function. I do this wave shaping by an analog circuit (using diodes or transistors, as done in some old sine-wave generator ICs). My question is: Could I find this technique on a Wikipedia page? Searching the expression 'raised-cosine square wave' leads me always to pages related to 'raised-cosine filter' instead. Thank you. KerimF (talk) 18:21, 19 November 2016 (UTC) , Edited KerimF (talk) 16:41, 2 December 2016 (UTC)

## Scaling and dimensional issue...

This is a matter of consistency within Wikipedia and even within this article.

There are textbooks that present the Nyquist–Shannon sampling theorem with misleading scaling by leaving off the sample period ${\displaystyle T}$ scaler from the sampling function

${\displaystyle T\cdot \mathrm {III} _{T}(t)=T\sum _{n=-\infty }^{\infty }\delta (t-nT)}$

which requires them to put the ${\displaystyle T}$ factor in the passband gain of the reconstruction filter. But we normally consider the gain of the filter, ${\displaystyle H(f)}$, to be dimensionless. This requires the impulse response ${\displaystyle h(t)}$ to have dimension of 1/time, and this is confirmed when examining the convolution integral.

As ${\displaystyle \beta }$ approaches 0, the roll-off zone becomes infinitesimally narrow, hence:
${\displaystyle \lim _{\beta \rightarrow 0}H(f)=\mathrm {rect} (fT)}$
where ${\displaystyle \mathrm {rect} (.)}$ is the rectangular function, so the impulse response approaches ${\displaystyle \mathrm {sinc} \left({\frac {t}{T}}\right)}$. Hence, it converges to an ideal or brick-wall filter in this case.
This is actually dimensionally correct, but disagrees with earlier expressions of ${\displaystyle H(f)}$ having passband gain ot ${\displaystyle T}$.