# Documentation

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# bohmanwin

## Syntax

```w = bohmanwin(L) ```

## Description

`w = bohmanwin(L)` returns an `L`-point Bohman window in column vector `w`. A Bohman window is the convolution of two half-duration cosine lobes. In the time domain, it is the product of a triangular window and a single cycle of a cosine with a term added to set the first derivative to zero at the boundary. Bohman windows fall off as 1/w4.

## Examples

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Compute a 64-point Bohman window. Display the result using `wvtool`.

```L = 64; bw = bohmanwin(L); wvtool(bw)```

## Algorithms

The equation for computing the coefficients of a Bohman window is

`$w\left(x\right)=\left(1-|x|\right)\mathrm{cos}\left(\pi |x|\right)+\frac{1}{\pi }\mathrm{sin}\left(\pi |x|\right),\text{ }-1\le x\le 1$`

where x is a length-L vector of linearly spaced values generated using `linspace`. The first and last elements of the Bohman window are forced to be identically zero.

## References

[1] Harris, Fredric J. “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform.” Proceedings of the IEEE®. Vol. 66, January 1978, pp. 51–83.