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rms

Root-mean-square level

Description

example

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.

example

y = rms(x,dim) computes the RMS level of x along the dimension dim.

Examples

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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

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

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

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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 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

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

Data Types: single | double

Output Arguments

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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.

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