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SignalProcessing

 GaussianWindow
 multiply an array of samples by a Gaussian windowing function

 Calling Sequence GaussianWindow( A, alpha )

Parameters

 A - Array of real or complex numeric values; the signal alpha - numeric value greater than $2$

Options

 • container : Array, predefined Array for holding results
 • inplace : truefalse, specifies that output should overwrite input

Description

 • The GaussianWindow( A, alpha ) command multiplies the Array A by the Gaussian windowing function, with parameter $\mathrm{\alpha }$, and returns the result in an Array having the same length.
 • The Gaussian windowing function $w\left(k\right)$ with parameter $\mathrm{\alpha }$ is defined as follows for a sample with $N$ points.

$w\left(k\right)={ⅇ}^{\frac{{\mathrm{\alpha }}^{2}{\left(\frac{2k}{N}-1\right)}^{2}}{2}}$

 • Before the code performing the computation runs, A is converted to datatype float[8] or complex[8] if it does not have one of those datatypes already. For this reason, it is most efficient if A has one of these datatypes beforehand. This does not apply if inplace is true.
 • If the container=C option is provided, then the results are put into C and C is returned. With this option, no additional memory is allocated to store the result. The container must be an Array of the same size and datatype as A.
 • If the inplace or inplace=true option is provided, then A is overwritten with the results. In this case, the container option is ignored.

 • The SignalProcessing[GaussianWindow] command is thread-safe as of Maple 18.

Examples

 > with( SignalProcessing ):
 > N := 1024:
 > a := GenerateUniform( N, -1, 1 );
 ${{\mathrm{_rtable}}}_{{18446884016778293486}}$ (1)
 > GaussianWindow( a, 3.14 );
 ${{\mathrm{_rtable}}}_{{18446884016639387758}}$ (2)
 > c := Array( 1 .. N, 'datatype' = 'float'[ 8 ], 'order' = 'C_order' ):
 > GaussianWindow( Array( 1 .. N, 'fill' = 1, 'datatype' = 'float'[ 8 ], 'order' = 'C_order' ), 5.0, 'container' = c );
 ${{\mathrm{_rtable}}}_{{18446884016639376070}}$ (3)
 > u := log~( FFT( c ) ):
 > use plots in display( Array( [ listplot( Re( u ) ), listplot( Im( u ) ) ] ) ) end;

 >

Compatibility

 • The SignalProcessing[GaussianWindow] command was introduced in Maple 18.
 • For more information on Maple 18 changes, see Updates in Maple 18.