rssq

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 array x. If x is a row or column vector, then y is a real-valued scalar. If x has more than one dimension, then rssq operates along the first array dimension with size greater than 1.

y = rssq(x,dim) computes the RSS level of x along dimension dim.

Examples

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)

y = 
22.3607

RSS Levels 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 levels of the columns.

t = 0:0.001:1-0.001;
x = cos(2*pi*100*t)'*(1:4);

y = rssq(x)

y = 1×4

   22.3607   44.7214   67.0820   89.4427

RSS Levels 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 levels of the rows by specifying the dimension with the dim argument.

t = 0:0.001:1-0.001;
x = (1:4)'*cos(2*pi*100*t);

y = rssq(x,2)

y = 4×1

   22.3607
   44.7214
   67.0820
   89.4427

Input Arguments

x — Input array

vector | matrix | N-D array

Input array, specified as a vector, matrix, or N-D array.

Example: cos(2*pi*100*(0:0.001:1-0.001)) specifies a sinusoid sampled at 1 kHz for 1 second.

Data Types: single | double
Complex Number Support: Yes

dim — Dimension to operate along

positive integer scalar

Dimension to operate along, specified as a positive integer scalar.

Data Types: single | double

Output Arguments

y — Root-sum-of-squares level

scalar | vector | matrix | N-D array

Root-sum-of-squares level, returned as a scalar, vector, matrix, or N-D array.

More About

Root-Sum-of-Squares Level

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

$$x_{\text{RSS}}=\sqrt{{\displaystyle \sum _{n=1}^N{\left|x_n\right|}^2}},$$

with the summation performed along the specified dimension. The RSS level is also referred to as the 2-norm.

References

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If you supply dim, then it must be constant.

• For limitations related to variable-size inputs, see Incompatibility with MATLAB for Default Dimension Selection (MATLAB Coder).

• Code generation does not support sparse matrix inputs for this function.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2012a

R2023a: Use gpuArray objects

The rssq function supports gpuArray objects. You must have Parallel Computing Toolbox™ to use this functionality.