To 'sinc' or not to 'sink'

Started by 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.
&#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;

```
```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.
--
%% 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
```
```Hello Richard,
Sinc stands for "sine cardinal." The following links have some pertinent

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.

> [...]
--
%% 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
```
```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.
--
%% 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
```
```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.

```
```Clay S. Turner wrote:

> Hello Richard,
> Sinc stands for "sine cardinal." The following links have some pertinent
>
> http://mathworld.wolfram.com/SincFunction.html
>
> http://ccrma-www.stanford.edu/~jos/waveguide/Theory_Ideal_Bandlimited_Interpolation.html
>

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

```