Root mean square value of input or sequence of inputs
DSP System Toolbox / Statistics
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.
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.
In
— Data inputThe 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 portSpecify 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.
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
Port_1
— RMS value along the specified dimensionThe 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 to 1
, the
output is the same as when you select Each
column
. If you set the
Dimension to 2
, the
output is the same as when you select Each
row
. If you set the
Dimension to 3
, 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
Running RMS
— Option to select running RMSWhen 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 valueEach 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.
To enable this parameter, clear the Running RMS parameter.
Dimension
— Custom dimension1
(default)  scalarSpecify 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.
To enable this parameter, set Find the RMS value
over to Specified
dimension
.
Input processing
— Method to process the input in running modeColumns 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.
To enable this parameter, select the Running RMS parameter.
Reset port
— Reset eventNone
(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 a
Rising edge
or
Falling edge
.
Nonzero sample
— Triggers a
reset operation at each sample time, when the
Rst input is not zero.
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).
To enable this parameter, select the Running RMS parameter.
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

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:
$${y}_{j}=\sqrt{\frac{{\displaystyle \sum _{i=1}^{M}{\left{u}_{ij}\right}^{2}}}{M}}\text{}1\le j\le N$$
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.
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