Returns the filter coefficients of the n-point Dolph-Chebyshev window with a given attenuation.
chebwin(n, at)An array of length n with the filter coefficients.
length of the filter; number of coefficients to generate.
dB of attenuation in the stop-band of the corresponding Fourier transform.
Original Octave version by André Carezia, acarezia@uol.com.br. Conversion to R by Tom Short.
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.
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.
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