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SignalProcessing

 BohmanWindow
 multiply an array of samples by a Bohman windowing function

 Calling Sequence BohmanWindow(A)

Parameters

 A - Array of real or complex numeric values; the signal

Options

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

Description

 • The BohmanWindow(A) command multiplies the Array A by the Bohman windowing function and returns the result in an Array having the same length.
 • The Bohman windowing function $w\left(k\right)$ is defined as follows for a sample with $N$ points.

$w\left(k\right)=\left(1-\left|\frac{2k}{n}-1\right|\right)\mathrm{cos}\left(\mathrm{\pi }\left|\frac{2k}{n}-1\right|\right)+\frac{\mathrm{sin}\left(\mathrm{\pi }\left|\frac{2k}{n}-1\right|\right)}{\mathrm{\pi }}$

 • Before the code performing the computation runs, A is converted to datatype float or complex 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[BohmanWindow] command is thread-safe as of Maple 18.

Examples

 > with( SignalProcessing ):
 > N := 1024:
 > a := GenerateUniform( N, -1, 1 );
 ${{\mathrm{_rtable}}}_{{18446883885100806382}}$ (1)
 > BohmanWindow( a );
 ${{\mathrm{_rtable}}}_{{18446883884961999438}}$ (2)
 > c := Array( 1 .. N, 'datatype' = 'float'[ 8 ], 'order' = 'C_order' ):
 > BohmanWindow( Array( 1 .. N, 'fill' = 1, 'datatype' = 'float'[ 8 ], 'order' = 'C_order' ), 'container' = c );
 ${{\mathrm{_rtable}}}_{{18446883884961987750}}$ (3)
 > u := log~( FFT( c ) ):
 > use plots in display( Array( [ listplot( Re( u ) ), listplot( Im( u ) ) ] ) ) end;  >

Compatibility

 • The SignalProcessing[BohmanWindow] command was introduced in Maple 18.