RMS
Root mean square value of input or sequence of inputs
 Library:
DSP System Toolbox / Statistics
Description
The RMS block computes the root mean square (RMS) value of each row or column of the input, or along vectors of a specified dimension of the input. It can also compute the RMS value of the entire input. You can specify the dimension using the Find the RMS value over parameter. The RMS block can also track the RMS value in a sequence of inputs over a period of time. To track the RMS value in a sequence of inputs, select the Running RMS parameter.
Note
The Running mode in the RMS block will be removed in a future release. To compute the running RMS in Simulink^{®}, use the Moving RMS block instead.
Ports
Input
In
— Data input
vector  matrix  ND array
The block accepts realvalued or complexvalued multichannel and multidimensional inputs.
This port is unnamed until you select the Running
RMS parameter and set the Reset port
parameter to any option other than
None
.
Data Types: single
 double
Complex Number Support: Yes
Rst
— Reset port
scalar
Specify the reset event that causes the block to reset the running RMS. The sample time of the Rst input must be a positive integer multiple of the input sample time.
Dependencies
To enable this port, select the Running RMS
parameter and set the Reset port parameter to
any option other than None
.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
Output
Port_1
— RMS value along the specified dimension
scalar  vector  matrix  ND array
The data type of the output matches the data type of the input.
When you do not select the Running RMS parameter,
the block computes the RMS value in each row or column of the input, or
along vectors of a specified dimension of the input. It can also compute
the RMS value of the entire input at each individual sample time. Each
element in the output array y
is the RMS value of the
corresponding column, row, or entire input. The output array
y
depends on the setting of the Find
the RMS value over parameter. Consider a
threedimensional input signal of size
MbyNbyP.
When you set Find the RMS value over to:
Entire input
— The output at each sample time is a scalar that contains the RMS value of the MbyNbyP input matrix.Each row
— The output at each sample time consists of an Mby1byP array, where each element contains the RMS value of each vector over the second dimension of the input. For an MbyN matrix input, the output at each sample time is an Mby1 column vector.Each column
— The output at each sample time consists of a 1byNbyP array, where each element contains the RMS value of each vector over the first dimension of the input. For an MbyN matrix input, the output at each sample time is a 1byN row vector.In this mode, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
Specified dimension
— The output at each sample time depends on the value of the Dimension parameter. If you set the Dimension to1
, the output is the same as when you selectEach column
. If you set the Dimension to2
, the output is the same as when you selectEach row
. If you set the Dimension to3
, the output at each sample time is an MbyN matrix containing the RMS value of each vector over the third dimension of the input.
When you select Running RMS, the block tracks the RMS value of each channel in a time sequence of inputs. In this mode, you must also specify a value for the Input processing parameter.
Elements as channels (sample based)
— The block treats each element of the input as a separate channel. For a threedimensional input signal of size MbyNbyP, the block outputs an MbyNbyP array. Each element y_{ijk} of the output contains the RMS value of the element u_{ijk} for all inputs since the last reset.When a reset event occurs, the running RMS y_{ijk} in the current frame is reset to the element u_{ijk}.
Columns as channels (frame based)
— The block treats each column of the input as a separate channel. This option does not support input signals with more than two dimensions. For a twodimensional input signal of size MbyN, the block outputs an MbyN matrix. Each element y_{ij} of the output contains the RMS value of the elements in the jth column of all inputs since the last reset, up to and including the element u_{ij} of the current input.When a reset event occurs, the running RMS for each channel becomes the RMS value of all the samples in the current input frame, up to and including the current input sample.
Data Types: single
 double
Parameters
Main Tab
Running RMS
— Option to select running RMS
off (default)  on
When you select the Running RMS parameter, the block tracks the RMS value of each channel in a time sequence of inputs.
Find the RMS value over
— Dimension over which the block computes the RMS value
Each column
(default)  Entire input
 Each row
 Specified dimension
Each column
— The block outputs the RMS value over each column.Each row
— The block outputs the RMS value over each row.Entire input
— The block outputs the RMS value over the entire input.Specified dimension
— The block outputs the RMS value over the dimension specified in the Dimension parameter.
Dependencies
To enable this parameter, clear the Running RMS parameter.
Dimension
— Custom dimension
1
(default)  scalar
Specify the dimension (onebased value) of the input signal over which the RMS value is computed. The value of this parameter must be greater than 0 and less than the number of dimensions in the input signal.
Dependencies
To enable this parameter, set Find the RMS value
over to Specified
dimension
.
Input processing
— Method to process the input in running mode
Columns as channels (frame
based)
(default)  Elements as channels (sample
based)
Columns as channels (frame based)
— The block treats each column of the input as a separate channel. This option does not support input signals with more than two dimensions. For a twodimensional input signal of size MbyN, the block outputs an MbyN matrix. Each element y_{ij} of the output contains the RMS value of the elements in the jth column of all inputs since the last reset, up to and including the element u_{ij} of the current input.When a reset event occurs, the running RMS for each channel becomes the RMS value of all the samples in the current input frame, up to and including the current input sample.
Elements as channels (sample based)
— The block treats each element of the input as a separate channel. For a threedimensional input signal of size MbyNbyP, the block outputs an MbyNbyP array. Each element y_{ijk} of the output contains the RMS value of the element u_{ijk} for all inputs since the last reset.When a reset event occurs, the running RMS y_{ijk} in the current frame is reset to the element u_{ijk}.
VariableSize Inputs
When your inputs are of variable size, and you select the Running RMS parameter, then:
If you set the Input processing parameter to
Elements as channels (sample based)
, the state is reset.If you set the Input processing parameter to
Columns as channels (frame based)
, then:When the input size difference is in the number of channels (number of columns), the state is reset.
When the input size difference is in the length of channels (number of rows), there is no reset and the running operation is carried out as usual.
Dependencies
To enable this parameter, select the Running RMS parameter.
Reset port
— Reset event
None
(default)  Rising edge
 Falling edge
 Either edge
 Nonzero sample
The block resets the running RMS whenever a reset event is detected at the optional Rst port. The reset sample time must be a positive integer multiple of the input sample time.
When a reset event occurs while the Input
processing parameter is set to Elements as
channels (sample based)
, the running RMS for each
channel is initialized to the value in the corresponding channel of the
current input. Similarly, when the Input processing
parameter is set to Columns as channels (frame
based)
, the running RMS for each channel becomes the
RMS value of all the samples in the current input frame, up to and
including the current input sample.
Use this parameter to specify the reset event.
None
— Disables the Rst port.Rising edge
— Triggers a reset operation when the Rst input does one of the following:Rises from a negative value to either a positive value or zero.
Rises from zero to a positive value, where the rise is not a continuation of a rise from a negative value to zero.
Falling edge
— Triggers a reset operation when the Rst input does one of the following:Falls from a positive value to a negative value or zero.
Falls from zero to a negative value, where the fall is not a continuation of a fall from a positive value to zero.
Either edge
— Triggers a reset operation when the Rst input is aRising edge
orFalling edge
.Nonzero sample
— Triggers a reset operation at each sample time, when the Rst input is not zero.
Note
When running simulations in the Simulink multitasking mode, reset signals have a onesample latency. Therefore, when the block detects a reset event, there is a onesample delay at the reset port rate before the block applies the reset. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and TimeBased Scheduling and Code Generation (Simulink Coder).
Dependencies
To enable this parameter, select the Running RMS parameter.
Model Examples
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

More About
Root Mean Square (RMS)
The RMS value of a discretetime signal is the square root of the arithmetic mean of the squares of the signal sample values.
For an MbyN input matrix u, the RMS value of the jth column of the input is given by:
$${y}_{j}=\sqrt{\frac{{\displaystyle \sum _{i=1}^{M}{\left{u}_{ij}\right}^{2}}}{M}}\text{}1\le j\le N$$
Algorithms
Root Mean Square (RMS)
When you clear the Running RMS parameter in the block and
specify a dimension, the block produces results identical to the MATLAB^{®}
rms
function, when it is called as y =
rms(u,D)
.
u
is the data input.D
is the dimension.y
is the RMS value.
The RMS value along the entire input is identical to calling the
rms
function as y = rms(u(:))
.
When inputs are complex, the block computes the RMS value of the magnitude of the complex input.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
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