function [y, gain] = cic_filter(R, M, N, x)
% [y, gain] = cic_filter(R, M, N, x)

a_i = [1 -1];
b_i = 1;

a_c = 1;
b_c = [1 zeros(1, M-1) -1];

gain = (M*R)^N
k_i = 1/(M*R);

i_out = x;

% Integrator
for i=1:N,
    i_out = k_i*filter(b_i, a_i, i_out);
end;

% Decimate
c_out = i_out(R:R:length(i_out));

% Comb
for i=1:N,
    c_out = filter(b_c, a_c, c_out);
end;


y = c_out;