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# 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

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### Peak-magnitude-to-RMS Ratio of Sinusoid

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);```

### Peak-magnitude-to-RMS Ratio of Complex Exponential

Compute the peak-magnitude-to-RMS ratio of a complex exponential with a frequency of π/4 radians/sample.

Create a complex exponential with a frequency of π/4 radians/sample. Find the peak-magnitude-to-RMS ratio.

```n = 0:99;
X = exp(1j*pi/4*n);
Y = peak2rms(X);```

### Peak-magnitude-to-RMS ratio of 2-D Matrix

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 ratio of the columns.

```t = 0:0.001:1-0.001;
x = cos(2*pi*100*t)';
X = repmat(x,1,4);
amp = 1:4;
amp = repmat(amp,1e3,1);
X = X.*amp;
Y = peak2rms(X);```

### Peak-magnitude-to-RMS ratio of 2-D Matrix Along Specified Dimension

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 peak-magnitude-to-RMS ratio of the rows specifying the dimension equal to 2 with the DIM argument.

```t = 0:0.001:1-0.001;
x = cos(2*pi*100*t);
X = repmat(x,4,1);
amp = (1:4)';
amp = repmat(amp,1,1e3);
X = X.*amp;
Y = peak2rms(X,2);```

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### 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 l-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.