Documentation

Root-sum-of-squares level

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

collapse all

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 = 22.3607

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 = 1×4

22.3607   44.7214   67.0820   89.4427

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 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 = 4×1

22.3607
44.7214
67.0820
89.4427

collapse all

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 2 norm.

References

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