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SignalProcessing

 KaiserWindow
 multiply an array of samples by a Kaiser windowing function

 Calling Sequence KaiserWindow(A, alpha)

Parameters

 A - Array of real or complex numeric values; the signal alpha - numeric parameter for Kaiser windowing function

Options

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

Description

 • The KaiserWindow(A, alpha) command multiplies the Array A by the Kaiser windowing function with parameter alpha and returns the result in a Array having the same length. The length of A must be at least $1$.
 • The Kaiser windowing function $w$ with parameter $\mathrm{alpha}$ is defined as follows for a sample with $N$ points.

$w\left(k\right)=\frac{{I}_{0}\left(\mathrm{\alpha }\sqrt{{\left(\frac{N}{2}-\frac{1}{2}\right)}^{2}-{\left(k-\frac{N}{2}+\frac{1}{2}\right)}^{2}}\right)}{{I}_{0}\left(\frac{\mathrm{\alpha }\left(N-1\right)}{2}\right)}$

where ${I}_{0}$ is a modified Bessel function of the first kind (see BesselI).

 • For an Array with complex values, the real and imaginary parts are multiplied by the same windowing function.
 • 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[KaiserWindow] command is thread-safe as of Maple 17.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $a≔\mathrm{GenerateUniform}\left(10,-1,1\right)$
 ${a}{≔}\left[\begin{array}{cccccccccc}{-}{0.785218492150308}& {0.588413964957000}& {-}{0.993165822699668}& {0.921578288543971}& {-}{0.0387801709584892}& {0.0136057925410569}& {-}{0.210756972897798}& {0.749600215815009}& {0.138966357801110}& {0.212285134010017}\end{array}\right]$ (1)
 > $\mathrm{KaiserWindow}\left(a,0\right)$
 $\left[\begin{array}{cccccccccc}{-}{0.785218492150308}& {0.588413964957000}& {-}{0.993165822699668}& {0.921578288543971}& {-}{0.0387801709584892}& {0.0136057925410569}& {-}{0.210756972897798}& {0.749600215815009}& {0.138966357801110}& {0.212285134010017}\end{array}\right]$ (2)
 > $\mathrm{KaiserWindow}\left(a,-0.23\right)$
 $\left[\begin{array}{cccccccccc}{-}{0.610457430005672}& {0.507148404405843}& {-}{0.921836794895176}& {0.897446511447900}& {-}{0.0386666236385379}& {0.0135659551385734}& {-}{0.205238244478699}& {0.695764035175222}& {0.119773783122354}& {0.165038188264367}\end{array}\right]$ (3)
 > $\mathrm{KaiserWindow}\left(a,4.2\right)$
 $\left[\begin{array}{cccccccccc}{-}{5.26251259780847}{}{{10}}^{{-8}}& {0.000665786816548083}& {-}{0.0451305706430736}& {0.322160409751442}& {-}{0.0346060770163654}& {0.0121413364847850}& {-}{0.0736752955128766}& {0.0340626758600538}& {0.000157239587225711}& {1.42272909161356}{}{{10}}^{{-8}}\end{array}\right]$ (4)
 > $c≔\mathrm{Array}\left(1..10,'\mathrm{datatype}'={'\mathrm{float}'}_{8},'\mathrm{order}'='\mathrm{C_order}'\right):$
 > $\mathrm{KaiserWindow}\left(a,0.03,'\mathrm{container}'=c\right)$
 $\left[\begin{array}{cccccccccc}{-}{0.781653026813912}& {0.586796946280165}& {-}{0.991772844784998}& {0.921112858038203}& {-}{0.0387779945588688}& {0.0136050289641827}& {-}{0.210650532972173}& {0.748548854077023}& {0.138584464764237}& {0.211321204486819}\end{array}\right]$ (5)
 > $c$
 $\left[\begin{array}{cccccccccc}{-}{0.781653026813912}& {0.586796946280165}& {-}{0.991772844784998}& {0.921112858038203}& {-}{0.0387779945588688}& {0.0136050289641827}& {-}{0.210650532972173}& {0.748548854077023}& {0.138584464764237}& {0.211321204486819}\end{array}\right]$ (6)
 > $a≔\mathrm{GenerateTone}\left(100,1,\frac{1}{\mathrm{π}},\mathrm{π}\right):$
 > $\mathbf{use}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{plots}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{in}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{display}\left(\mathrm{Array}\left(\left[\mathrm{listplot}\left(a\right),\mathrm{listplot}\left(\mathrm{KaiserWindow}\left(a,0.2\right)\right)\right]\right)\right);\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{animate}\left(\mathrm{listplot},\left['\mathrm{KaiserWindow}'\left(a,\mathrm{α}\right)\right],\mathrm{α}=-1..1\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{end use}$   > 

Compatibility

 • The SignalProcessing[KaiserWindow] command was introduced in Maple 17.
 • For more information on Maple 17 changes, see Updates in Maple 17.