## Savgol萨维基购耳滤波方法-MATLAB

SAVGOL function returns the coefficients of a Savitzky-Golay smoothing filter, which can then be applied using the CONVOL function. The Savitzky-Golay smoothing filter, also known as least squares or DISPO (digital smoothing polynomial), can be used to smooth a noisy signal.

The filter is defined as a weighted moving average with weighting given as a polynomial of a certain degree. The returned coefficients, when applied to a signal, perform a polynomial least-squares fit within the filter window. This polynomial is designed to preserve higher moments within the data and reduce the bias introduced by the filter. The filter can use any number of points for this weighted average.

function g = savgol2(f, nl, nr, M)

% SAVGOL SavGol smoothes the data in the vector f by means of a
%        Savitzky-Golay smoothing filter.
%        Input: f : noisy data
%        nl: number of points to the left of the reference point
%        nr: number of points to the right of the reference point
%        M : degree of the least squares polynomial
%        Output: g: smoothed data
%        W. H. Press and S. A. Teukolsky,
%        Savitzky-Golay Smoothing Filters,
%        Computers in Physics, 4 (1990), pp. 669-672.

% matrix A
A = ones (nl+nr+1, M+1);
for j = M:-1:1,
A (:, j) = [-nl:nr]' .* A (:, j+1);
end

% filter coefficients c
[Q, R] = qr (A);
c = Q (:, M+1) / R (M+1, M+1);

% smoothing of the noisy data
% Note that there are two equivalent ways to apply the Savitzky-Golay
% filter to the vector f.  In the first case we use a for-loop whereas
% in the second case we use the faster built-in function filter.
n = length (f);
g = filter (c (nl+nr+1:-1:1), 1, f);
g (1:nl) = f (1:nl);
g (nl+1:n-nr) = g (nl+nr+1:n);
g (n-nr+1:n) = f (n-nr+1:n);

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