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.