Why does the variance not coincide with the autocorrelation function in 0?

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Tommaso Ballantini
Tommaso Ballantini 2023-4-17
回答： Sharmin Kibria 2023-5-10
Ran in:
Hello everyone, I am a civil engineering student and I am practising some signal processing topics. I was wondering, why in my script the correlation function calculated in 0 does not agree with the variance of my signal? They are very close (within a factor of 1000).
Thanks to all of you who answer, your work is valuable.
clear all; close all; clc;
t = 0:1000;
x = randn(1,length(t));
subplot(2,1,1);
plot(t,x)
ylabel('Amplitude')
xlabel('Time sample')
title('Gaussian noise signal')
[y,lags]=xcorr(x);
subplot(2,1,2);
plot(lags,y);
ylabel('Correlation output')
xlabel('Delay')
title('Autocorrelation of AWGN')
y(lags==0)
ans = 1.0556e+03
var(x)
ans = 1.0529

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回答（1 个）

Sharmin Kibria
Sharmin Kibria 2023-5-10
var(x) = sum((x-mean(x)).^2)/1000 while y(lags==0) is just calculating sum(x.^2). Because of the normalization var does your result is off by a factor of 1000.

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