Dolph-Chebyshev window coefficients
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) = [Cheb(n-1, β * cos(pi * k/n))] / Cheb(n-1, β)
with
β = 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 http://octave.sf.net
plot(chebwin(50, 100))
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