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# peak2rms

Peak-magnitude-to-RMS ratio

## Syntax

``y = peak2rms(x)``
``y = peak2rms(x,dim)``

## 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 Computing Requirements (Parallel Computing Toolbox) for details on `gpuArray` (Parallel Computing Toolbox) 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.

## More About

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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.

## Version History

Introduced in R2012a