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29th July 2013
#1
Gear Nut

Sinc function confusion

Hey.
Recently i've started to dig deep into the aspects of digital audio.
The last few days iam reading some interesting papers at lavry's site.
At some point lavry is doing some tests with sinc functions.
I didn't have a clue what a sinc function was so i searched at wiki but things
got even more confusing!Wiki has a bunch of mathematical formulas as an explanation.I don't understand ****.
So if somenone have the patience to enligthten me with a slight simpler approach so i could move on i would be more than grateful.
29th July 2013
#2
The sinc function is defined as f(x)=sin(x)/x with sinc(0) defined as one.

The reason sinc functions are important in digital audio is because sinc functions are used to reconstruct a continuous bandlimited signal from its sample points. In particular, the reconstruction is simply the sum of shifted sinc functions each weighted by the sample point values.
30th July 2013
#3

One problem I have when people quote Nyquist's theorem, is that it only applies when DA conversion is done using the sinc function. No real-world DA converters use the sinc function.
30th July 2013
#4
Gear Guru

Quote:
Originally Posted by Kesh
One problem I have when people quote Nyquist's theorem, is that it only applies when DA conversion is done using the sinc function. No real-world DA converters use the sinc function.

Think of it as a place-holder for the math...

-tINY

30th July 2013
#5
Gear Nut

Quote:
Originally Posted by DaveTDC
The sinc function is defined as f(x)=sin(x)/x with sinc(0) defined as one.

The reason sinc functions are important in digital audio is because sinc functions are used to reconstruct a continuous bandlimited signal from its sample points. In particular, the reconstruction is simply the sum of shifted sinc functions each weighted by the sample point values.
hallelujah!
I've started to understand now.
So AD converters use the sinc function process in real life?
Last but not least regarding the equation,i know that is a function equation
and f(x) is the input and the x after the equal is the output,but what the sin actually means?
30th July 2013
#6
Gear Nut

Quote:
Originally Posted by Kesh
One problem I have when people quote Nyquist's theorem, is that it only applies when DA conversion is done using the sinc function. No real-world DA converters use the sinc function.
What is the process in DA converters?
30th July 2013
#7
Lives for gear

Quote:
Originally Posted by Stelios_Drk
but what the sin actually means?
sine wave
30th July 2013
#8
Gear Guru

Quote:
Originally Posted by Stelios_Drk
hallelujah!
,but what the sin actually means?

SOH-CAH-TOA

opposite over hypotenuse...

-tINY

Attached Thumbnails

30th July 2013
#9
Gear Nut

Quote:
Originally Posted by stinkyfingers
sine wave
I would have thought that.
Iam dumb!
It's time for study
30th July 2013
#10
Gear Nut

Quote:
Originally Posted by tINY

SOH-CAH-TOA

opposite over hypotenuse...

-tINY

Yes i got it!
But i have to get back to maths!
Thanks
30th July 2013
#11
Lives for gear

you can download this app.(wolfram cdf player) to view the linked page and use the interactive graphs.
sometimes i need a visual and the wolfram site is nice for that...
Wolfram Demonstrations Project
31st July 2013
#12
Quote:
Originally Posted by Kesh
One problem I have when people quote Nyquist's theorem, is that it only applies when DA conversion is done using the sinc function. No real-world DA converters use the sinc function.
I don’t understand why you have a problem describing sampling theory using sinc functions. That is the math of the theory. How to implement the math in practice is another issue. For example, you can implement the summing of shifted sinc functions using impulse samples feeding an ideal low pass filter. The math is the same. You can describe the filter in the time domain (i.e., impulse response) or the frequency domain (ideal cutoff filter). The impulse response of an ideal low pass filter is a sinc function.

Now in practice, you have to use approximations. Sinc functions are not practical (they theoretically go from –inf to +inf) and ideal low pass filters cannot be realized. There are also other practical issues including using flat-top samples with equalization compensation, oversampling to make the reconstruction filter simpler, etc… . But no matter how you implement it, the math involves sinc functions (or approximations to sinc functions).
31st July 2013
#13

Quote:
Originally Posted by DaveTDC
I don’t understand why you have a problem describing sampling theory using sinc functions. That is the math of the theory. How to implement the math in practice is another issue. For example, you can implement the summing of shifted sinc functions using impulse samples feeding an ideal low pass filter. The math is the same. You can describe the filter in the time domain (i.e., impulse response) or the frequency domain (ideal cutoff filter). The impulse response of an ideal low pass filter is a sinc function.

Now in practice, you have to use approximations. Sinc functions are not practical (they theoretically go from –inf to +inf) and ideal low pass filters cannot be realized. There are also other practical issues including using flat-top samples with equalization compensation, oversampling to make the reconstruction filter simpler, etc… . But no matter how you implement it, the math involves sinc functions (or approximations to sinc functions).
You misunderstood my point, but answered it anyway. I have no problem with describing sampling theory using sinc functions, that would be silly. Nyquist's applies to ideal converters, you cannot apply it to non-ideal (ie real world) conversion with filters. This non-ideal conversion is why 44.1kHz was chosen for CDs, not 40kHz.

You may call it pedantry.
1st August 2013
#14
Lives for gear

Quote:
Originally Posted by Stelios_Drk
So AD converters use the sinc function process in real life?
Last but not least regarding the equation,i know that is a function equation
and f(x) is the input and the x after the equal is the output,but what the sin actually means?
Hi, mathematical functions are used for modeling the physical world -- they're convenient for working out the theory/predictions/etc -- but they are not physical objects.

The symbols used to describe functions work like this:

When the value of some number y depends on the value of some other number x, we say that y is a function of x. We express this in symbols like so:
y = f(x)
where f is some rule for determining the value of y, given x. You can think of f as a black box: you put in some number x and out comes another number y. For example, if the rule in my black box is "add one to whatever comes in", I could notate it as
f(x) = x + 1
Putting actual numbers in place of x would give you:
2 = f(1)
3 = f(2)
11 = f(10)
and so on. This is a very simple blackbox, but we can make them as complicated and fancy as we require. For example, this blackbox
f(x) = 1/(x^2 + 1)
maps every input to the reciprocal of its square. If we plot all the outputs on a grid, we get an elegant looking bell-shaped curve (with the cool ass name Witch of Agnesi). These graphs of functions are incredibly valuable because they let us "see" the behavior of a function over a whole range of inputs in one picture.

You've almost certainly seen the graph of the sine function, a smooth up-down wave-like curve (there's one in my avatar picture in red, along with its cousin the cosine, in blue). The sine function belongs to a special group of periodic functions (i.e., those that forever repeat a pattern) that are so useful they've been given their own names: while most functions are anonymously labeled f(x), the sine function is labeled sin(x).

What exactly is inside the blackbox of sin(x)? Unfortunately this doesn't have a simple answer -- it is a so-called transcendental function -- but rest assured it is well-defined. And it turns out that when you multiply sin(x) by x itself, you get an explosive curve that is damped toward the origin (the middle of the graph). When you divide sin(x) by x itself, you get the opposite graph: a big curve at the origin that's damped as it gets farther out. This behavior proves useful in modeling many things, so we've given it its own name: sinc(x).

That so very many phenomena in nature can be modeled by relatively simple mathematical functions is, I think, one of the great and beautiful mysteries of the universe.
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