# Documentation

Root-sum-of-squares level

## Syntax

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

## Description

`Y = rssq(X)` returns the root-sum-of-squares (RSS) level, `Y`, of the input, `X`. If `X` is a row or column vector, `Y` is a real-valued scalar. For matrices, `Y` contains the RSS levels computed along the first nonsingleton dimension. For example, if `Y` is an N-by-M matrix with N>1, `Y` is a 1-by-M row vector containing the RSS levels of the columns of `Y`.

`Y = rssq(X,DIM)` computes the RSS level of `X` along the dimension, `DIM`.

## Input Arguments

 `X` Real- or complex-valued input vector or matrix. By default, `rssq` acts along the first nonsingleton dimension of `X`. `DIM` Dimension for root-sum-of-squares (RSS) level. The optional `DIM` input argument specifies the dimension along which to compute the RSS level. Default: First nonsingleton dimension

## Output Arguments

 `Y` Root-sum-of-squares level. For vectors, `Y` is a real-valued scalar. For matrices, `Y` contains the RSS levels computed along the specified dimension, `DIM`. By default, `DIM` is the first nonsingleton dimension.

## Examples

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Compute the RSS level of a 100-Hz sinusoid sampled at 1 kHz.

```t = 0:0.001:1-0.001; X = cos(2*pi*100*t); Y = rssq(X);```

### RSS Level 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 RSS level 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 = rssq(X);```

### RSS Level 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 RSS level 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 = rssq(X,2);```

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### Root-Sum-of-Squares Level

The root-sum-of-squares (RSS) level of a vector, X, is

${X}_{\text{RSS}}=\sqrt{\sum _{n=1}^{N}|{X}_{n}{|}^{2}}$

with the summation performed along the specified dimension. The RSS is also referred to as the ℓ2 norm.

## References

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