nt_bias_filter

[c0,c1]=nt_bias_filter(x,B,A) - covariance with and w/o filter bias

 x: data 
 B,A: filter coefficients

 NoiseTools
 see nt_filter_peak for a second-order resonator

0001 function [c0,c1]=nt_bias_filter(x,B,A)
0002 %[c0,c1]=nt_bias_filter(x,B,A) - covariance with and w/o filter bias
0003 %
0004 % x: data
0005 % B,A: filter coefficients
0006 %
0007 % NoiseTools
0008 % see nt_filter_peak for a second-order resonator
0009 
0010 if nargin<3;
0011     error('!');
0012 end
0013 
0014 c0=nt_cov(x);
0015 x=filter(B,A,x);
0016 c1=nt_cov(x);
0017 return
0018 
0019 
0020 
0021 % example:
0022 w=0.3;  % center frequency
0023 Q=10;
0024 bw=f/Q;
0025 [B,A]=secondorderPeak(w,bw);
0026 
0027 
0028 
0029 function [B,A] = secondorderPeak(Wo,BW)
0030 %second order resonator
0031 
0032 % Inputs are normalized by pi.
0033 BW = BW*pi;
0034 Wo = Wo*pi;
0035 
0036 Ab=(10*log10(2));
0037 
0038 Gb   = 10^(-Ab/20);
0039 beta = (Gb/sqrt(1-Gb.^2))*tan(BW/2);
0040 gain = 1/(1+beta);
0041 
0042 B  = (1-gain)*[1 0 -1];
0043 A  = [1 -2*gain*cos(Wo) (2*gain-1)];