% Usage: chebwin (n, at) % % Returns the filter coefficients of the n-point Dolph-Chebyshev window % with at dB of attenuation in the stop-band of the corresponding % Fourier transform. % % For the definition of the Chebyshev window, see % % * Peter Lynch, 'The Dolph-Chebyshev Window: A Simple Optimal Filter', % Monthly Weather Review, Vol. 125, pp. 655-660, April 1997. % (http://www.maths.tcd.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. % % The window is described in frequency domain by the expression: % % Cheb(n-1, beta * cos(pi * k/n)) % W(k) = ------------------------------- % 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. % % See also: kaiser