# bohmanwin

## Syntax

``w = bohmanwin(L)``

## Description

example

````w = bohmanwin(L)` returns an `L`-point Bohman window in `w`.```

## Examples

collapse all

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

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

## Input Arguments

collapse all

Window length, specified as a positive integer.

Data Types: `single` | `double`

## Output Arguments

collapse all

Bohman window, returned as a column vector.

## Algorithms

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.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.