rms

Root-mean-square level

Syntax

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 array dimension of x with size greater than 1. For example, if x is an N-by-M matrix with N > 1, then 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.

Examples

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)

y = 0.7071

RMS Levels of 2-D Matrix

Create a matrix in which 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)'*(1:4);

y = rms(x)

y = 1×4

    0.7071    1.4142    2.1213    2.8284

RMS Levels of 2-D Matrix Along Specified Dimension

Create a matrix in which 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 = (1:4)'*cos(2*pi*100*t);

y = rms(x,2)

y = 4×1

    0.7071
    1.4142
    2.1213
    2.8284

Input Arguments

x — Input array

vector | matrix | N-D array | gpuArray object

Input array, specified as a vector, matrix, N-D array, or gpuArray object. By default, rms acts along the first array dimension of X with size greater than 1.

See Run MATLAB Functions on a GPU (Parallel Computing Toolbox) and GPU Support by Release (Parallel Computing Toolbox) for details on gpuArray (Parallel Computing Toolbox) objects.

Example: cos(pi/4*(0:159))+randn(1,160) is a single-channel row-vector signal.

Example: cos(pi./[4;2]*(0:159))'+randn(160,2) is a two-channel signal.

Data Types: single | double
Complex Number Support: Yes

dim — Dimension along which to compute RMS levels

integer scalar

Dimension along which to compute RMS levels, specified as an integer scalar.

Data Types: single | double

Output Arguments

y — Root-mean-square level

real-valued scalar | real-valued vector | real-valued N-D array

Root-mean-square level, returned as a real-valued scalar, vector, N-D array, or gpuArray object. If x is a vector, then y is a real-valued scalar. If x is a matrix, then y contains the RMS levels computed along dimension dim. By default, dim is the first array dimension of x with size greater than 1.

More About

Root-Mean-Square Level

The root-mean-square level of a vector x is

$$x_{\text{RMS}}=\sqrt{\frac{1}{N}{\displaystyle \sum _{n=1}^N{\left|x_n\right|}^2}},$$

with the summation performed along the specified dimension.

References

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

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If you supply dim, then it must be constant.

• For variable-size inputs, see the automatic dimension restriction in Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

• Code generation does not support sparse matrix inputs for this function.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).