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# rssq

Root-sum-of-squares level

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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### RSS Level of Sinusoid

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);```

## More About

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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.

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