remes算法matlab

Remes算法是一种用于逼近函数的方法，可以用于实现曲线拟合、信号分析、滤波器设计等应用。以下是MATLAB实现Remes算法的示例代码：

function [b,a] = remes(wp,ws,gpass,gstop)
% REMES - Parks-McClellan Optimum FIR filter design algorithm
%
% REMES(WP,WS,Gpass,Gstop) returns the N+1 coefficients of a length N
% linear phase FIR filter which has the best approximation to the
% desired frequency response function described by WP and WS.
%
% WP is the passband frequency vector defined between 0 and 1.
% WS is the stopband frequency vector defined between 0 and 1.
% Gpass is the maximum passband gain allowed.
% Gstop is the minimum stopband gain required in linear units.
%
% Example:
% >> wp = [0.2 0.4]; ws = [0.3 0.5]; gpass = 1; gstop = 0.1;
% >> [b,a] = remes(wp,ws,gpass,gstop);

% Normalize the frequency bands to [0,pi].
wp = wp*pi;
ws = ws*pi;

% Check band specifications.
if length(wp) ~= length(ws)
    error('The WP and WS frequency vectors must have the same length.');
end

% Check the passband and stopband specifications.
if gpass <= 0
    error('The passband gain Gpass must be greater than 0.');
end
if gstop <= 0 || gstop >= 1
    error('The stopband gain Gstop must be between 0 and 1.');
end

% Determine the number of filter taps.
N = length(wp) - 1;

% Set up the optimization problem.
f = [ones(1,N+1) zeros(1,N+1)];
A = [cos(kron(wp',(0:N))) -cos(kron(ws',(0:N)))];
b = [gpass*ones(size(wp)) gstop*ones(size(ws))]';

% Solve the optimization problem.
w = linprog(f,[],[],A,b,[],[],[],optimset('Display','off'));
h = w(1:N+1)';
h = fliplr(h);

% Compute the transfer function coefficients using the FIR filter
% design equation.
a = 1;
b = h;

该代码使用线性规划函数linprog来求解优化问题。它需要传入一些参数：WP和WS是滤波器的通带和阻带频率范围；Gpass是通带最大增益；Gstop是阻带最小增益。函数返回滤波器的系数b和a。