Envelope(s) of the Sinc function

[greswd]

What is the envelope function(s) of the sinc function?

 

[blue_leaf77]

$\textrm{sinc}(x) = \frac{\sin x}{x}$, if you define the carrier oscillation to be $\sin x$, what would be the envelope?

 

[greswd]

I was thinking of a function that would also accommodate the central peak and the underside of the central peak?

Does such a function exist, or do I need to use a piece-wise function?

 

[blue_leaf77]

As far as I know, the envelope of a function comes along with the carrier, which is usually defined to be oscillating periodically. In the case of $\textrm{sinc} (x)$, the carrier according to that definition is the sine and hence the envelope is $1/x$. I don't think you can find another form for the envelope, without changing the carrier and hence changing the whole function.

 

[greswd]

alright thanks