matlab - 如何在不使用任何工具包中的方法的情况下平滑 matlab 中的数据

Question

我试图在 Matlab 中平滑一些测量数据，我认为是这样，我遗漏了一些东西。我编写了自己的代码来创建高斯窗口。但是其余代码是从此链接复制的：

% Generate sample data.
vector = 5*(1+cosd(1:3:180)) + 2 * rand(1, 60);
hist (vector)  ;
plot(vector, 'r-', 'linewidth', 3);
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.

% Construct blurring window.
windowWidth = int16(11);
halfWidth = windowWidth / 2 ;
gaussFilter = Gaussain (-5:5, 0, 1 ) ;
gaussFilter = gaussFilter / sum(gaussFilter); % Normalize.

% Do the blur.
smoothedVector = conv(vector(halfWidth:end-halfWidth), gaussFilter) ;

% plot it.
hold on;
plot(smoothedVector, 'b-', 'linewidth', 3);

请帮我纠正我的错误。下面是生成高斯窗的代码：

function y = Gaussain ( window, mu, sigma) 
% y = exp (-((window - mu).^2)/(2*sigma^2)).* (1/(sigma * sqrt(2* pi)))  ;
y = exp (-((window - mu).^2)/(2*sigma^2)) ;
end

我正在寻找一种不使用任何 Matlab 工具包方法的解决方案。在修复了一些东西之后，我得到了这个输出：

Answer 1

看起来WindowWidth应该是int16(11)，以匹配您的过滤器。或者，您可以使用WindowWidth = int16(50)具有 50 个抽头而不是 11 个抽头的滤波器。使用当前值，您正在修剪过多的输出信号。

参见图：http WindowWidth = int16(11): //i.stack.imgur.com/WOnW9.png

Answer 2

我正在研究同一主题，创建了解决我的问题的这篇文章，进行了一些调整和概括。非常感谢之前回复的作者，这是我的通用代码，它也适用于 n 维点向量

% SMOOTH Simple gaussian smooth function
% vector = input vector
% width = width of the smoothing
% window = width of the window to be used in the convolution
% 
% Credits: Generalization of a post made by User1551892 and Louis Mendo on 
% StackOverflow
% Created by: Leonardo Daga, 2016
function smoothedVector = smooth(vector, width, window)

% Check arguments and fill with defaults
if nargin < 2,
    width = 2;
end

if nargin < 3,
    window = width * 5 + 1;
end

% Rotate vector to a column vector (if needed) to make the code easier
if size(vector,1) > size(vector,2)
    isColumn = true;
else
    isColumn = false;
    vector = vector';
end

% Construct blurring window.
windowWidthInt = int16(window);
halfWidth = double(windowWidthInt / 2);
gaussFilter = Gaussian(-(halfWidth-1):(halfWidth-1), 0, width/2 ) ;
gaussFilter = gaussFilter / sum(gaussFilter);

% Do the blur, enlarging the vector to blur from the start with a
% convenient value and cutting the vector back when the blurring is done
enlargedVector = [ones(window, 1)*vector(1,:);
    vector;
    ones(window, 1)*vector(end,:)];

smoothedVector = zeros(size(enlargedVector,1)-1,size(enlargedVector,2));

for i=1:size(vector,2),
    smoothedVector(:,i) = conv(enlargedVector(halfWidth:end-halfWidth,i), gaussFilter) ;
end

smoothedVector = smoothedVector(window:end-window,:);

% Rotate back the vector, if it was a row vector
if (isColumn == false)
    smoothedVector = smoothedVector';
end

end

%% Create a gaussian vector to be used for the convolution
function y = Gaussian ( window, mu, sigma)
y = exp (-((window - mu).^2)/(2*sigma^2)) ;
end

您可以使用以下示例代码运行此函数：

% Generate sample data.
vector = [5*(1+cosd(1:3:900)) + 2 * rand(1, 300);
    5*(1+sind(1:3:900)) + 2 * rand(1, 300)];

smoothedVector = smooth(vector, 5) ;

% plot it.
figure
plot(1:size(vector,2), vector, 'r-', 1:size(smoothedVector,2), smoothedVector, 'b-');
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.

得到下图：