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# peak2rms

Peak-magnitude-to-RMS ratio

## Description

example

y = peak2rms(x) returns the ratio of the largest absolute value in x to the root-mean-square (RMS) value of x.

example

y = peak2rms(x,dim) computes the peak-magnitude-to-RMS ratio of x along dimension dim.

## Examples

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Compute the peak-magnitude-to-RMS ratio of a 100 Hz sinusoid sampled at 1 kHz.

t = 0:0.001:1-0.001;
x = cos(2*pi*100*t);

y = peak2rms(x)
y = 1.4142

Create a complex exponential with a frequency of $\pi /4$ rad/sample. Find the peak-magnitude-to-RMS ratio.

n = 0:99;
x = exp(1j*pi/4*n);

y = peak2rms(x)
y = 1

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 peak-magnitude-to-RMS ratios of the columns.

t = 0:0.001:1-0.001;
x = cos(2*pi*100*t)'*(1:4);

y = peak2rms(x)
y = 1×4

1.4142    1.4142    1.4142    1.4142

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 = peak2rms(x,2)
y = 4×1

1.4142
1.4142
1.4142
1.4142

## Input Arguments

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Input signal, specified as a vector, matrix, N-D array, or gpuArray object.

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

Data Types: double | single
Complex Number Support: Yes

Dimension to operate along, specified as a positive integer scalar. By default, peak2rms operates along the first array dimension of x with size greater than 1. For example, if x is a row or column vector, y is a real-valued scalar. If x is an N-by-M matrix with N > 1, y is a 1-by-M row vector containing the peak-magnitude-to-RMS levels of the columns of y.

Data Types: double | single

## Output Arguments

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Peak-magnitude-to-RMS ratio, specified as a real-valued scalar, matrix, N-D array, or gpuArray object.

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### Peak-Magnitude-to-RMS Ratio

The peak-magnitude-to-RMS ratio is

$\frac{{‖X‖}_{\infty }}{\sqrt{\frac{1}{N}\sum _{n=1}^{N}{|{X}_{n}|}^{2}}},$

where the -infinity norm and RMS values are computed along the specified dimension.

## References

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