chebwin                package:signal                R Documentation

_D_o_l_p_h-_C_h_e_b_y_s_h_e_v _w_i_n_d_o_w _c_o_e_f_f_i_c_i_e_n_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     Returns the filter coefficients of the n-point Dolph-Chebyshev
     window with a given attenuation.

_U_s_a_g_e:

     chebwin(n, at)

_A_r_g_u_m_e_n_t_s:

       n: length of the filter; number of coefficients to generate. 

      at: dB of attenuation in the stop-band of the corresponding
          Fourier transform. 

_D_e_t_a_i_l_s:

     The window is described in frequency domain by the expression:


      W(k) = [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.

_V_a_l_u_e:

     An array of length 'n' with the filter coefficients.

_A_u_t_h_o_r(_s):

     Original Octave version by André Carezia, acarezia@uol.com.br.
     Conversion to R by Tom Short.

_R_e_f_e_r_e_n_c_e_s:

     Peter Lynch, "The Dolph-Chebyshev Window: A Simple Optimal
     Filter", Monthly Weather Review, Vol. 125, pp. 655-660, April
     1997. <URL:
     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.

     Octave Forge <URL: http://octave.sf.net>

_S_e_e _A_l_s_o:

     'kaiser'

_E_x_a_m_p_l_e_s:

       plot(chebwin(50, 100))

