% 功能：1. 生成一標準差為1，均值為0,成正太分布（高斯分布）的隨機噪聲， % 2. 求其概率密度函數p，均值mu,方差sigmax2，標準差sigmax,均方值x2_，有效值RMS, % 3. 滿足高斯分布的隨機噪聲，采用示波器觀察時，用峰峰值估計標準差；對零均值為0時，標準差=有效值 % 對零均值的噪聲，均方值 = 方差+均值的平方=方差， % 又有效值= sqrt(均方值),標準差= sqrt(方差)，so 有效值=標準差% 各物理意義如下： % 方差：反映了隨機噪聲的起伏程度 % 均方值：反映了隨機噪聲的歸一化功率（隨機電壓或電流在1歐姆電阻上消耗的功率，單位 V2 or A2） % 編輯者：lily % 日期：2019,4,1clc; clear; close all; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% mu = 0; % 均值 sigmax = 1; % 標準差 m =1; n =1e4; x = normrnd(mu,sigmax,m,n);% 生成均值mu,標準差為sigmax，m行n列的正態分布的隨機噪聲 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 求均值mu n = length(x); mu = (1/n).*sum(x); % mu = mean(x);%調用MATLAB工具% 求方差sigmax2,除以n sigmax2 = (1/n).*sum((x-mu).^2); % sigmax2 = var(x,1);%調用MATLAB工具% 求方差sigmax2.除以n-1 % sigmax2 = (1/(n-1)).*sum((x-mu).^2); % sigmax2 = var(x);%調用MATLAB工具% 求標準差sigmax sigmax = sqrt(sigmax2);% 求均方值 x2_ = (1/n)*sum(x.^2);% 求有效值 RMS = sqrt(x2_ );% 求概率密度函數P P = 1/(sigmax2*sqrt(2*pi)).*exp(-(x-mu).^2/(2*sigmax2));%公式 p = normpdf(x);% 調用MATLAB工具 subplot(2,1,1);plot(x,P);title('公式'); subplot(2,1,2);plot(x,p);title('調用MATLAB工具');%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 驗證：當x = 均值mu時，p有最大值 = 1/(sigmax2*sqrt(2*pi)) p_max = 1/(sigmax2*sqrt(2*pi));%最大值 max(P); %最大值，與上式相等 [m,index]=max(P); % 找到p最大值時的索引,m最大值，index索引號 x_index = x(index); % 找到index對應的x值str=['x = ' num2str(x_index) ' 對應的最大值p = ' num2str(m)]; disp(str); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 采用示波器觀察時，用峰峰值估計標準差；對零均值為0時，標準差=有效值 Vpp = max(x)-min(x); % Vpp =range(x); % 調用MATLAB工具 sigmax_ = (Vpp)/6.6; % 估計標準差fprintf('Vpp估計標準差sigmax_ = %s \n 計算標準差sigmax = %d', sigmax_, sigmax);

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