Fundamental proof of signal averaging noise reduction

3 ビュー (過去 30 日間)
Christopher Meehan
Christopher Meehan 2022 年 8 月 31 日
I am trying to experimentally show the mathematical proof of averaging n samples for a reduction of noise of sqrt(n)
my code is very simple, but the ratio of improvement does not converge towards a fixed ratio. I get random improvements even with very large numbers of averaging
In this example I am using a 16x sampling improvment, I was expecting a 4x reduction in noise according to the theory.
clear all
close all
L1 = 1000
L2 = round(L1*16);
Noise = randn(1,L2);
PNoise_1 = mean(Noise(1:L1))
PNoise_2 = mean(Noise(1:L2))
Noisereduction = PNoise_1/PNoise_2


Jeff Miller
Jeff Miller 2022 年 9 月 1 日
Your code doesn't really measure noise reduction in the right way. Noise reduction refers to variability across many repeated means, something like this (untested):
nIterations = 100;
sampleMns = zeros(nIterations,2);
for iIter=1:nIterations
Noise = randn(1,L2);
sampleMns(iIter,1) = mean(Noise(1:L1));
sampleMns(iIter,2) = mean(Noise(1:L2));
sd1 = std(sampleMns(:,1));
sd2 = std(sampleMns(:,2));
Noisereduction = sd1/sd2;
  1 件のコメント
Christopher Meehan
Christopher Meehan 2022 年 9 月 1 日
Thanks Jeff! I did test this code and it does converge towards the theoretical


その他の回答 (0 件)


Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by