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# std() - Signal Processing

```S = std(A) returns
the standard deviation of
the elements of A along the first array dimension
whose size does not equal 1. If A is a vector of observations,
then the standard deviation is a scalar. If A is a matrix whose columns
are random variables and whose rows are observations, then S is
a row vector containing the standard deviations corresponding to each
column.If A is a multidimensional array,
then std(A) operates along the first array dimension
whose size does not equal 1, treating the elements as vectors. The
size of this dimension becomes 1 while the sizes
of all other dimensions remain the same.By default, the standard deviation is normalized by N-1,
where N is the number of observations.exampleS = std(A,w) specifies
a weighting scheme for any of the previous syntaxes. When w
= 0 (default), S is normalized by N-1.
When w = 1, S is normalized
by the number of observations, N. w also
can be a weight vector containing nonnegative elements. In this case,
the length of w must equal the length of the dimension
over which std is operating. exampleS = std(A,w,dim) returns
the standard deviation along dimension dim for
any of the previous syntaxes. To maintain the default normalization
while specifying the dimension of operation, set w = 0 in
the second argument.exampleS = std(___,nanflag) specifies
whether to include or omit NaN values from the
calculation for any of the previous syntaxes. For example, std(A,'includenan') includes
all NaN values in A while std(A,'omitnan') ignores
them.```

### Syntax

`S = std(A) exampleS = std(A,w) exampleS = std(A,w,dim) exampleS = std(___,nanflag) example`

### Example

```Standard Deviation of Matrix ColumnsOpen This ExampleCreate a matrix and compute the standard deviation of each column.A = [4 -5 1; 2 3 5; -9 1 7];
S = std(A)

S =

7.0000    4.1633    3.0551

Standard Deviation of 3-D ArrayOpen This ExampleCreate a 3-D array and compute the standard deviation along the first dimension.A(:,:,1) = [2 4; -2 1];
A(:,:,2) = [9 13; -5 7];
A(:,:,3) = [4 4; 8 -3];
S = std(A)

S(:,:,1) =

2.8284    2.1213

S(:,:,2) =

9.8995    4.2426

S(:,:,3) =

2.8284    4.9497

Specify Standard Deviation WeightsOpen This ExampleCreate a matrix and compute the standard deviation of each column according to a weight vector w.A = [1 5; 3 7; -9 2];
w = [1 1 0.5];
S = std(A,w)

S =

4.4900    1.8330

Standard Deviation Along Matrix RowsOpen This ExampleCreate a matrix and calculate the standard deviation along each row.A = [6 4 23 -3; 9 -10 4 11; 2 8 -5 1];
S = std(A,0,2)

S =

11.0303
9.4692
5.3229

Standard Deviation Excluding NaNOpen This ExampleCreate a vector and compute its standard deviation, excluding NaN values.A = [1.77 -0.005 3.98 -2.95 NaN 0.34 NaN 0.19];
S = std(A,'omitnan')

S =

2.2797```