chebwin | R Documentation |

Returns the filter coefficients of the n-point Dolph-Chebyshev window with a given attenuation.

```
chebwin(n, at)
```

`n` |
length of the filter; number of coefficients to generate. |

`at` |
dB of attenuation in the stop-band of the corresponding Fourier transform. |

The window is described in frequency domain by the expression:

` W(k) = \frac{Cheb(n-1, \beta * cos(pi * k/n))}{Cheb(n-1, \beta)}`

with

`\beta = cosh(1/(n-1) * acosh(10^{at/20}))`

and `Cheb(m,x)`

denoting the `m`

-th order Chebyshev polynomial calculated
at the point `x`

.

Note that the denominator in `W(k)`

above is not computed, and after
the inverse Fourier transform the window is scaled by making its
maximum value unitary.

An array of length `n`

with the filter coefficients.

Original Octave version by André Carezia, acarezia@uol.com.br. Conversion to R by Tom Short.

Peter Lynch, “The Dolph-Chebyshev Window: A Simple Optimal Filter”, Monthly Weather Review, Vol. 125, pp. 655-660, April 1997. http://mathsci.ucd.ie/~plynch/Publications/Dolph.pdf

C. Dolph, “A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level”, Proc. IEEE, 34, pp. 335-348.

Octave Forge https://octave.sourceforge.io/

`kaiser`

```
plot(chebwin(50, 100))
```

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