(m) ¶(m, at) ¶Return the filter coefficients of a Dolph-Chebyshev window of length m. The Fourier transform of the window has a stop-band attenuation of at dB. The default attenuation value is 100 dB.
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(m-1, beta * cos(pi * k/m))
W(k) = -------------------------------
Cheb(m-1, beta)
with
beta = cosh(1/(m-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.
Package: signal