Returns the filter coefficients of the n-point Dolph-Chebyshev window
with a given attenuation.
Usage
chebwin(n, at)
Arguments
n
length of the filter; number of coefficients to generate.
at
dB of attenuation in the stop-band of the corresponding
Fourier transform.
Value
An array of length n with the filter coefficients.
Details
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.
References
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.
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