Subsample Delay Estimation: [x_max y_max A]=crit_interp_p(y,x) - File Exchange

Code covered by the BSD License

Highlights from
Subsample Delay Estimation

[e f_e G P]=zzb(s,n1,n2, f_s,... calculates the modified Ziv-Zakai lower bound for time delay estimation.
[x_max y_max A]=crit_interp_p...
delay=delayest_3point(u2,u1,m... delay=delayest_3point(u2,u1,method,estimator,parameter);
delay=delayest_fft(y,u); delay=delayest_fft(y,u);
delayest_iterative(u2,u1,N_i_...
x=rand_white(N);
y=fft_circshift(u,d) y=fft_circshift(u,d)
y=fourier_series(Y,t);
compare_delay_methods_6_03.m
simple_example.m
View all files

from Subsample Delay Estimation by Travis Wiens
Demonstrates a number of methods of estimating the delay between two signals to subsample accuracy.

[x_max y_max A]=crit_interp_p(y,x)

function [x_max y_max A]=crit_interp_p(y,x)
%[x_max y_max A]=crit_interp_p(y,x)
%fits a parabola to three points: y=[y(x(1)) y(x(2)) y(x(3))]. 
%Returns the position (x_max) and value (y_max) of the
%interpolated critical point (peak or trough). 
%If x is omitted, it is assumed to be [-1 0 1]
%y=A(1)*x.^2+A(2)*x+A(3)

%    Copyright Travis Wiens 2009 travis.mlfx@nutaksas.com

if nargin<2
    x=[-1 0 1];
end


a = (x(3) * (y(2) - y(1)) + x(2) * (y(1) - y(3)) + x(1) * (y(3) - y(2)));
b = (x(3)*x(3) * (y(1) - y(2)) + x(2)*x(2) * (y(3) - y(1)) + x(1)*x(1) * (y(2) - y(3)));


x_max=-b/(2*a);%critical point position

if nargout>1
    d = (x(1) - x(2)) * (x(1) - x(3)) * (x(2) - x(3));%denominator
    c = (x(2) * x(3) * (x(2) - x(3)) * y(1) + x(3) * x(1) * (x(3) - x(1)) * y(2) + x(1) * x(2) * (x(1) - x(2)) * y(3));
    y_max=c/d-b^2/(4*a*d);%critical point value
end

if nargout>2
    A=[a b c]./d;%parabola coefficients
end

Highlights from Subsample Delay Estimation

Highlights from
Subsample Delay Estimation