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# rms

Root-mean-square level

Y = rms(X)
Y = rms(X,DIM)

## Description

Y = rms(X) returns the root-mean-square (RMS) level of the input, X. If X is a row or column vector, Y is a real-valued scalar. For matrices, Y contains the RMS levels computed along the first nonsingleton dimension. For example, if X is an N-by-M matrix with N>1, Y is a 1-by-M row vector containing the RMS levels of the columns of X.

Y = rms(X,DIM) computes the RMS level of X along the dimension, DIM.

## Input Arguments

 X Real or complex-valued input vector or matrix. By default, rms acts along the first nonsingleton dimension of X. DIM Dimension for RMS levels. The optional DIM input argument specifies the dimension along which to compute the RMS levels. Default: First nonsingleton dimension

## Output Arguments

 Y Root-mean-square level. For vectors, Y is a real-valued scalar. For matrices, Y contains the RMS levels computed along the specified dimension DIM. By default, DIM is the first nonsingleton dimension.

## Examples

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### RMS Level of Sinusoid

Compute the RMS level of a 100-Hz sinusoid sampled at 1 kHz.

```t = 0:0.001:1-0.001;
X = cos(2*pi*100*t);
Y = rms(X);```

### RMS Levels of 2-D Matrix

Create a matrix where each column is a 100-Hz sinusoid sampled at 1 kHz with a different amplitude. The amplitude is equal to the column index.

Compute the RMS levels of the columns.

```t = 0:0.001:1-0.001;
x = cos(2*pi*100*t)';
X = repmat(x,1,4);
amp = 1:4;
amp = repmat(amp,1e3,1);
X = X.*amp;
Y = rms(X);```

### RMS Levels of 2-D Matrix Along Specified Dimension

Create a matrix where each row is a 100-Hz sinusoid sampled at 1 kHz with a different amplitude. The amplitude is equal to the row index.

Compute the RMS levels of the rows specifying the dimension equal to 2 with the DIM argument.

```t = 0:0.001:1-0.001;
x = cos(2*pi*100*t);
X = repmat(x,4,1);
amp = (1:4)';
amp = repmat(amp,1,1e3);
X = X.*amp;
Y = rms(X,2);```

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### Root-Mean-Square Level

The root-mean-square level of a vector, X, is

${X}_{\text{RMS}}=\sqrt{\frac{1}{N}\sum _{n=1}^{N}|{X}_{n}{|}^{2}}$

with the summation performed along the specified dimension.

## References

[1] IEEE® Standard on Transitions, Pulses, and Related Waveforms, IEEE Std 181, 2003.