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I am using Chebychev window for its narrow main lobe. The problem of chebychev window is that it has discontinuities at the edge, and it seems that Taylor window solves this issue.

More detail: http://de.mathworks.com/help/signal/ref/taylorwin.html http://en.wikipedia.org/wiki/Window_function#Dolph.E2.80.93Chebyshev_window

I've searched around but I can't find any information on how to implement a Taylor window. Any information on taylor window or suggestions on fixing this issue of edge discontinuities would be very appreciated.

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You've probably seen that at the bottom of the mathworks page on the Taylor window there are two references. But I guess it might be hard access these publications.

It's indeed difficult to find the formula online, but on the bottom of this page you can find a link to a (not yet released) Octave function implementing the Taylor window. I guess it's not too hard to distill the formula from the code. And here is a C implementation of the Matlab function taylorwin.m.

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A little Googling came up with this reference, which indicates that the impulse response for a Taylor window is:

$$ h[n] = 1 + 2 \sum_{m=1}^{\tilde{n}-1} F_m \cos\left(\frac{2\pi m}{N} \left(n-\frac{N}{2}+\frac{1}{2}\right)\right) $$

$\tilde{n}$ is a parameter for controlling how many equal-height sidelobes there are in the window. $F_m$ is a parameter that is related to the maximum sidelobe height; the references given in Matt L's answer give more detail on how it is calculated.

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