What is the equation used for taylor window function 'taylorwin'

I am unable to find which function is used in MATLAB for taylor window function taylorwin. I opened the function. THere are many if else blocks. But I am unable to identify which equation is used in it.

Answer 1

[David Goodmanson]

Hi Palguna,

The equations are in the attachment. rect(t) is a rectagle function, = 1 for -1/2<= t <= 1/2, 0 otherwise. That's intended to describe a continous function. For an N-point discrete window, the function is evaluated at N equally spaced points between and including

-1/2 +1/(2N) and 1/2 -1/(2N).

The reference is a freely available Sandia report, SAND2017-4042, Catalog of Window Taper Functions

for Sidelobe Control, Armin W. Doerry. You should be able to find these same expressions in taylorwin.

Answer 2

[Chunru]

The formulation of Taylor windown is a bit more complicated and not directly documented in "doc taylorwin". One reference is: H.L. Van Trees, Optimum Array Processing, Sec 3.4.3, John Wiley, 2002

Answer 3

[Palguna Gopireddy]

@David Goodmanson and @Chunru.

Are you sure the same function is used in matlab also.

In https://ieeexplore.ieee.org/document/9641381 it is mentioned as

I am confused to assume, which one to take.

[Chunru]

Yes. I checked the reference (van Tree) and the "taylowrwin.m" and the formulatons are the same as far as I know (except for different variable names).

[Palguna Gopireddy]

Ok. thankyou. @Chunru and @David Goodmanson

What about the above equation above equation posted. Is it wrong?

[Chunru]

The above equation is not complete as β is not specified so I have no idea whethe it is right or wrong. You are recommended to look for more reliable reference when in doubt (books and journal papers may be more reliable than conference articles in general). The formula given by @David Goodmanson above (with less details) and the van Tree's book (with detailed derivation and expanation) are similar. They also agree with MATLAB implementation.