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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

with( SignalProcessing ):

Simple Examples

X := Array( [ 1, 2*I, 3 ] );

X12I3

(1)

RootMeanSquare( X );

2.16024689946929

(2)

Y := < 3 * sqrt(2), 4 * sqrt(2) >;

Y3242

(3)

RootMeanSquare( Y );

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:

A := LinearAlgebra:-RandomVector( 5, datatype = complex[8] );

A−94.58.I12.7.I21.53.I40.25.I43.+97.I

(5)

B := Vector[column]( DFT( A ) );

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

(6)

rms__A := RootMeanSquare( A );

rms__A76.3229978446864

(7)

rms__B := RootMeanSquare( B );

rms__B76.3229978446864

(8)
• 

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

C := InverseDFT( B );

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

(9)

RootMeanSquare( A - C );

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]