function [b,a] = f_cheby1s (F_p,F_s,delta_p,delta_s,n)

%F_CHEBY1S: Design Chebyshev-I lowpass analog filter
%
%                                     b(1)
%              H(s) = ------------------------------------
%                     a(1)s^n + a(2)s^(n-1) + ... + a(n+1)
%
% Usage: [b,a] = f_cheby1s (F_p,F_s,delta_p,delta_s,n)
%
% Inputs: F_p     = passband cutoff frequency in Hz
%         F_s     = stopband cutoff frequency in Hz (F_s > F_p)
%         delta_p = passband ripple
%         delta_s = stopband attenuation
%         n       = an optional integer specifying the filter
%                   order.  If n is not present, the smallest
%                   order which meets the specifications is
%                   used.
%
% Outputs: b = numerator coefficient 
%          a = 1 by (n+1) coefficient vector of denominator 
%              polynomial 
%
% See also: F_BUTTERS, F_CHEBY1S, F_CHEBY2S,

% Initialize

F_p = f_clip (F_p,0,F_p);
F_s = f_clip (F_s,F_p,F_s);
delta_p = f_clip (delta_p,0,delta_p);
delta_s = f_clip (delta_s,0,delta_s);

% Find filter order

r = F_p / F_s;
d = sqrt(((1 - delta_p)^(-2) - 1)/(delta_s^(-2) - 1));
if nargin < 5
   n = ceil(acosh(d^(-1))/acosh(r^(-1)));
end

% Find poles

epsilon = sqrt((1-delta_p)^(-2)-1);
k = 0 : n-1;
theta = pi*(2*k+1+n)/(2*n);
F_0 = F_p;
alpha = epsilon^(-1)+ sqrt(epsilon^(-2)+1);
r_1 = pi*F_0*(alpha^(1/n) - alpha^(-1/n));
r_2 = pi*F_0*(alpha^(1/n) + alpha^(-1/n));
sigma = r_1*cos(theta);
omega = r_2*sin(theta);              
              
%sigma = 2*pi*F_0*sinh((1/n)*asinh(1/epsilon))*cos(theta);
%omega = 2*pi*F_0*cosh((1/n)*asinh(1/epsilon))*sin(theta);

p = sigma + j*omega;

% Compute coefficients

a = real(poly(p));
gamma = (-1)^n*prod(p);
if mod(n,2) == 0
   A0 = sqrt(1/(1 + epsilon^2));
else
   A0 = 1;
end
b = real(gamma*A0);

%-------------------------------------------------------------------