# diric

Dirichlet or periodic sinc function

## Syntax

`y = diric(x,n)`

## Description

`y = diric(x,n)` returns a vector or array `y` the same size as `x`. The elements of `y` are the Dirichlet function of the elements of `x`. `n` must be a positive integer.

The Dirichlet function, or periodic sinc function, is

$D\left(x\right)=\left\{\begin{array}{ll}\frac{\mathrm{sin}\left(Nx/2\right)}{N\mathrm{sin}\left(x/2\right)}\hfill & x\ne 2\pi k,\text{ }k=0,±1,±2,±3,...\hfill \\ {\left(-1\right)}^{k\left(N-1\right)}\hfill & x=2\pi k,\text{ }k=0,±1,±2,±3,...\hfill \end{array}$

for any nonzero integer `n`. This function has period 2π for `n` odd and period 4π for `n` even. Its peak value is 1, and its minimum value is -1 for `n` even. The magnitude of this function is (`1/n`) times the magnitude of the discrete-time Fourier transform of the `n`-point rectangular window.

## Diagnostics

If `n` is not a positive integer, `diric` gives the following error message:

```Requires n to be a positive integer. ```