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SignalProcessing

  

RootMeanSquare

  

calculate the root mean square of a signal

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

RootMeanSquare( data )

Parameters

data

-

rtable of data

Description

• 

The RootMeanSquare command takes a 1-D rtable of data and returns the root mean square. Specifically,

RootMeanSquareA=i=1nAi2n

  

where n=numelemsA.

• 

The input is converted to an Array of either float[8] or complex[8] datatype, and an error will be thrown if this is not possible. For this reason, it is most efficient for the input to already be an Array having the appropriate datatype.

• 

As the underlying implementation of the SignalProcessing package is a module, it is also possible to use the form SignalProcessing:-RootMeanSquare to access the command from the package. For more information, see Module Members.

Examples

withSignalProcessing:

Simple Examples

XArray1,2I,3

X12I3

(1)

RootMeanSquareX

2.16024689946929

(2)

Y3sqrt2,4sqrt2

Y3242

(3)

RootMeanSquareY

5.

(4)

Parseval's Theorem

• 

Parseval's Theorem shows that the root mean square of the Discrete Fourier Transform (DFT) of a signal is the same as that of the original signal. For example:

ALinearAlgebra:-RandomVector5,datatype=complex8

A−94.58.I12.7.I21.53.I40.25.I43.+97.I

(5)

BVectorcolumnDFTA

B9.8386991009990720.5718253929981I−108.101349850469+32.8995037690910I−68.936178759761269.2123797669952I−38.078365733228469.3476788839996I−4.913194642520883.45956242008582I

(6)

rms__ARootMeanSquareA

rms__A76.3229978446864

(7)

rms__BRootMeanSquareB

rms__B76.3229978446864

(8)
• 

We can also compare the original signal with the Inverse Discrete Fourier Transform (IDFT) of its DFT:

CInverseDFTB

C−94.000000000000058.I12.00000000000007.00000000000001I21.000000000000053.0000000000000I40.000000000000025.I43.+97.I

(9)

RootMeanSquareAC

1.3598124730410610−14

(10)

Compatibility

• 

The SignalProcessing[RootMeanSquare] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

SignalProcessing

SignalProcessing[Norm]