# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

# peak2rms

Peak-magnitude-to-RMS ratio

## Syntax

```Y = peak2rms(X) Y = peak2rms(X,DIM) ```

## Description

`Y = peak2rms(X)` returns the ratio of the largest absolute value in `X` to the root-mean-square (RMS) value of `X`. `peak2rms` operates along the first nonsingleton dimension of `X`. For example, if `X` is a row or column vector, `Y` is a real-valued scalar. If `Y` 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`.

`Y = peak2rms(X,DIM)` computes the peak-magnitude-to-RMS level of `X` along the dimension, `DIM`.

## Input Arguments

 `X` Real– or complex-valued input vector or matrix. By default, `peak2rms` acts along the first nonsingleton dimension of `X`. `DIM` Dimension for peak-magnitude-to-RMS ratio. The optional `DIM` input argument specifies the dimension along which to compute the peak-magnitude-to-RMS level. Default: First nonsingleton dimension

## Output Arguments

 `Y` Peak-magnitude-to-RMS ratio. For vectors, `Y` is a real-valued scalar. For matrices, `Y` contains the peak-magnitude-to-RMS levels computed along the specified dimension, `DIM`. By default, `DIM` is the first nonsingleton dimension.

## Examples

collapse all

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 ```

Compute the peak-magnitude-to-RMS ratio of a complex exponential with a frequency of rad/sample.

Create a complex exponential with a frequency of 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 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 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 = 1.4142 1.4142 1.4142 1.4142 ```

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 = (1:4)'*cos(2*pi*100*t); y = peak2rms(x,2)```
```y = 1.4142 1.4142 1.4142 1.4142 ```

collapse all

### Peak-magnitude-to-RMS Level

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.