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To 'sinc' or not to 'sink'

Started by Richard Owlett January 11, 2004
What is 'sinc' function and why is it important.

First response of "google" is "Sisters in Crime Internet Chapter" ;{

OK, I did find a site with plot of 'sinc' which resembled a 'cosine 
with decreasing amplitude' -- The amplitude at 0 WAS 1 and decreased 
from there ;]

Actually I suspect I need to know more about "windowing".
Any references besides a book coming out in March ;>


Richard Owlett wrote:

> What is 'sinc' function and why is it important. > > First response of "google" is "Sisters in Crime Internet Chapter" ;{ > > OK, I did find a site with plot of 'sinc' which resembled a 'cosine with > decreasing amplitude' -- The amplitude at 0 WAS 1 and decreased from > there ;] > > Actually I suspect I need to know more about "windowing". > Any references besides a book coming out in March ;>
Sin(x)/x. Although direct substitution is indeterminate at x=0, there are at least two ways to show that the ratio approaches unity as x->0. The impulse of a perfect low-pass filter has the shape of a sinc. Since it has a response at t=-infinity, you can see that a real-time perfect ("brick-wall") low pass is very hard to build. :-) Since low-pass filters are the "prototypes" from which other filters are derived, sincs show up throughout filter theory. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Richard Owlett <rowlett@atlascomm.net> writes:

> What is 'sinc' function and why is it important. > > First response of "google" is "Sisters in Crime Internet Chapter" ;{ > > OK, I did find a site with plot of 'sinc' which resembled a 'cosine > with decreasing amplitude' -- The amplitude at 0 WAS 1 and decreased > from there ;] > > Actually I suspect I need to know more about "windowing". > Any references besides a book coming out in March ;>
Richard, The sinc() function is defined as sinc(x) = sin(pi*x)/(pi*x). It is very common in signal processing since it is the inverse Fourier transform of the proverbial brick-wall lowpass filter. You are quite right that it looks like a "cosine with decreasing amplitude" because, well, it is (only not a cosine). The definition above is the reason. If you really want to know more about the sinc() function, I would suggest the classic textbook "The Fourier Transform and its Applications" by Ronald Bracewell. -- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://home.earthlink.net/~yatescr
Hello Richard,
Sinc stands for "sine cardinal." The following links have some pertinent
stuff about this function:

http://mathworld.wolfram.com/SincFunction.html

http://ccrma-www.stanford.edu/~jos/waveguide/Theory_Ideal_Bandlimited_Interpolation.html

Basically the sinc function in DSP does two primary things. First it is the
Fourier transform of the rectangle[1] function, and second it is what is
used in ideal interpolation of sampled data. Now using the Fourier duality
of multiplication in one domain being convolution in the other. Then you can
see when ever you try to window data with a rectangle function in one domain
that in the other domain you will have a convolution with a sinc function.

IHTH,
Clay


[1] Rectangle function                  rect(x) = 1 when |x|<pi,
                                                              =1/2 when
|x|=pi
                                                              = 0 otherwise





"Richard Owlett" <rowlett@atlascomm.net> wrote in message
news:1003fhr6v2i5h73@corp.supernews.com...
> What is 'sinc' function and why is it important. > > First response of "google" is "Sisters in Crime Internet Chapter" ;{ > > OK, I did find a site with plot of 'sinc' which resembled a 'cosine > with decreasing amplitude' -- The amplitude at 0 WAS 1 and decreased > from there ;] > > Actually I suspect I need to know more about "windowing". > Any references besides a book coming out in March ;> > >
Jerry Avins <jya@ieee.org> writes:

> Richard Owlett wrote: > >> What is 'sinc' function and why is it important. >> First response of "google" is "Sisters in Crime Internet Chapter" ;{ >> OK, I did find a site with plot of 'sinc' which resembled a 'cosine >> with decreasing amplitude' -- The amplitude at 0 WAS 1 and decreased >> from there ;] >> Actually I suspect I need to know more about "windowing". >> Any references besides a book coming out in March ;> > > Sin(x)/x.
Jerry, I guess you could say that is sinc(x/pi). However, it may be confusing. sinc(x) = sin(pi*x)/(pi*x), by definition.
> [...]
-- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://home.earthlink.net/~yatescr
Randy Yates wrote:

> Jerry Avins <jya@ieee.org> writes: > > >>Richard Owlett wrote: >> >> >>>What is 'sinc' function and why is it important. >>>First response of "google" is "Sisters in Crime Internet Chapter" ;{ >>>OK, I did find a site with plot of 'sinc' which resembled a 'cosine >>>with decreasing amplitude' -- The amplitude at 0 WAS 1 and decreased >>>from there ;] >>>Actually I suspect I need to know more about "windowing". >>>Any references besides a book coming out in March ;> >> >>Sin(x)/x. > > > Jerry, > > I guess you could say that is sinc(x/pi). However, it may be confusing. > sinc(x) = sin(pi*x)/(pi*x), by definition.
Thanks for being specific. I oversimplified when, for simplicity's sake, I left out the details. Later I wrote "shape of a sinc". Richard might recognize that as a central cross section of the "Mexican hat" figure. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Jerry Avins <jya@ieee.org> writes:

> Randy Yates wrote: > >> Jerry Avins <jya@ieee.org> writes: >> >>>Richard Owlett wrote: >>> >>> >>>>What is 'sinc' function and why is it important. >>>>First response of "google" is "Sisters in Crime Internet Chapter" ;{ >>>>OK, I did find a site with plot of 'sinc' which resembled a 'cosine >>>>with decreasing amplitude' -- The amplitude at 0 WAS 1 and decreased >>>>from there ;] >>>>Actually I suspect I need to know more about "windowing". >>>>Any references besides a book coming out in March ;> >>> >>> Sin(x)/x. >> Jerry, I guess you could say that is sinc(x/pi). However, it may be >> confusing. >> sinc(x) = sin(pi*x)/(pi*x), by definition. > > Thanks for being specific. I oversimplified when, for simplicity's sake, > I left out the details.
Sometimes it is good to simplify, but I don't think this is one of them. It seems that Richard is trying to get the rudiments and in that case it's important (at least I have found it to be so for myself) to get them right. Learning something wrong the first time seems to take an inordinate amount of effort to unlearn. I could be all wet, though. -- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://home.earthlink.net/~yatescr
Randy Yates wrote:


> Sometimes it is good to simplify, but I don't think this is one > of them.
That's why I thanked you for calling me on it, and described myself as having "oversimplified". Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Jerry Avins wrote:

> Randy Yates wrote: > > >> Sometimes it is good to simplify, but I don't think this is one >> of them. > > > That's why I thanked you for calling me on it, and described myself as > having "oversimplified". > > Jerry
Mr. turner referenced http://mathworld.wolfram.com/SincFunction.html which shows that "authorities" have used both definitions. [ posted only to prove that I do follow links, even if I tend to fade in threads I've triggered ;]
Clay S. Turner wrote:

> Hello Richard, > Sinc stands for "sine cardinal." The following links have some pertinent > stuff about this function: > > http://mathworld.wolfram.com/SincFunction.html > > http://ccrma-www.stanford.edu/~jos/waveguide/Theory_Ideal_Bandlimited_Interpolation.html >
"Thanks for the Links" apologies to Robin/Rainger/Sinatra ;]
> Basically the sinc function in DSP does two primary things. First it is the > Fourier transform of the rectangle[1] function, and second it is what is > used in ideal interpolation of sampled data. Now using the Fourier duality > of multiplication in one domain being convolution in the other. Then you can > see when ever you try to window data with a rectangle function in one domain > that in the other domain you will have a convolution with a sinc function. > >
I think I have a problem which is about to rear it's ugly head. My "eventual" field of interest is 'speech recognition'. I am coming at this field from an "avocational/amateur" [ NOT 'professional' point of view ] My first task is to "characterize speech" [ Please give both words their most vague/general denotations/connotations/implications/etc ;] BTW I've (re)discovered formants. I'm currently looking at speech samples =/> one second. I do a FFT and plot amplitude vs frequency for > 100 Hz. I doubt there is a problem so far. However, I understand typical speech recognition applications tend to use samples in the ten's to hundred's of msec. I assume I must take account of the artifacts caused by sampling. Please point me in appropriate direction. thanks