How to normalize a signal to zero mean and unit variance?

Question

I am new to MATLAB and I am trying to built a voice morphing system using MATLAB.

So I would like to know how to normalize a signal to zero mean and unit variance using MATLAB?

possible duplicate of [normalize mat file in matlab](http://stackoverflow.com/questions/7729880/normalize-mat-file-in-matlab) — Jonas, Jan 03 '12 at 19:05

score 87 · Accepted Answer · answered Jan 03 '12 at 19:00

87

if your signal is in the matrix X, you make it zero-mean by removing the average:

X=X-mean(X(:));

and unit variance by dividing by the standard deviation:

X=X/std(X(:));

answered Jan 03 '12 at 19:00

Oli

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one remark/question @Oli, in your code, you're actually computing the `std` of the aligned/zero-mean data (x-mu), i.e: `std(x-mu)`, but it should be: `std(x)`, right? – Tin Mar 25 '14 at 16:18
19

\forall scalar a, std(x) == std(x+a) – Oli Mar 27 '14 at 04:47

score 13 · Answer 2 · answered Dec 29 '12 at 06:25

13

If you have the stats toolbox, then you can compute

Z = zscore(S);

answered Dec 29 '12 at 06:25

jon

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score 11 · Answer 3 · 2012-01-03T19:05:45.187

11

You can determine the mean of the signal, and just subtract that value from all the entries. That will give you a zero mean result.

To get unit variance, determine the standard deviation of the signal, and divide all entries by that value.

edited Jan 03 '12 at 19:05

answered Jan 03 '12 at 18:50

Kavka · Answer 4 · 2012-01-05T22:28:52.103

6

It seems like you are essentially looking into computing the z-score or standard score of your data, which is calculated through the formula: z = (x-mean(x))/std(x)

This should work:

%% Original data (Normal with mean 1 and standard deviation 2)
x = 1 + 2*randn(100,1);
mean(x)
var(x)
std(x)

%% Normalized data with mean 0 and variance 1
z = (x-mean(x))/std(x);
mean(z)
var(z)
std(z)

edited Jan 05 '12 at 22:28

answered Jan 03 '12 at 19:05

Kavka

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score 1 · Answer 5 · answered Nov 21 '17 at 15:00

To avoid division by zero!

function x = normalize(x, eps)
    % Normalize vector `x` (zero mean, unit variance)

    % default values
    if (~exist('eps', 'var'))
        eps = 1e-6;
    end

    mu = mean(x(:));

    sigma = std(x(:));
    if sigma < eps
        sigma = 1;
    end

    x = (x - mu) / sigma;
end

How to normalize a signal to zero mean and unit variance?

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