SignalProcessing - Maple Programming Help

Home : Support : Online Help : Science and Engineering : Signal Processing : Windowing Functions : SignalProcessing/KaiserWindow

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

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $a≔\mathrm{GenerateUniform}\left(10,-1,1\right)$
 $\left[\begin{array}{cccccccccc}-0.7852184921503079& 0.5884139649569997& -0.9931658226996676& 0.9215782885439708& -0.03878017095848924& 0.013605792541056892& -0.21075697289779816& 0.7496002158150088& 0.13896635780110977& 0.21228513401001725\end{array}\right]$ (1)
 > $\mathrm{KaiserWindow}\left(a,0\right)$
 $\left[\begin{array}{cccccccccc}-0.7852184921503079& 0.5884139649569997& -0.9931658226996676& 0.9215782885439708& -0.03878017095848924& 0.013605792541056892& -0.21075697289779816& 0.7496002158150088& 0.13896635780110977& 0.21228513401001725\end{array}\right]$ (2)
 > $\mathrm{KaiserWindow}\left(a,-0.23\right)$
 $\left[\begin{array}{cccccccccc}-0.6104574300056718& 0.5071484044058431& -0.9218367948951758& 0.8974465114479& -0.0386666236385379& 0.013565955138573425& -0.2052382444786991& 0.6957640351752219& 0.11977378312235437& 0.16503818826436684\end{array}\right]$ (3)
 > $\mathrm{KaiserWindow}\left(a,4.2\right)$
 $\left[\begin{array}{cccccccccc}-5.2625125978084747{}{10}^{-8}& 0.0006657868165480829& -0.04513057064307362& 0.32216040975144156& -0.034606077016365415& 0.012141336484784996& -0.07367529551287662& 0.03406267586005384& 0.0001572395872257112& 1.422729091613559{}{10}^{-8}\end{array}\right]$ (4)
 > $c≔\mathrm{Array}\left(1..10,'\mathrm{datatype}'={'\mathrm{float}'}_{8},'\mathrm{order}'='\mathrm{C_order}'\right):$
 > $\mathrm{KaiserWindow}\left(a,0.03,'\mathrm{container}'=c\right)$
 $\left[\begin{array}{cccccccccc}-0.7816530268139116& 0.5867969462801652& -0.9917728447849977& 0.9211128580382028& -0.03877799455886883& 0.013605028964182682& -0.21065053297217343& 0.7485488540770225& 0.13858446476423653& 0.2113212044868189\end{array}\right]$ (5)
 > $c$
 $\left[\begin{array}{cccccccccc}-0.7816530268139116& 0.5867969462801652& -0.9917728447849977& 0.9211128580382028& -0.03877799455886883& 0.013605028964182682& -0.21065053297217343& 0.7485488540770225& 0.13858446476423653& 0.2113212044868189\end{array}\right]$ (6)
 > $a≔\mathrm{GenerateTone}\left(100,1,\frac{1}{\mathrm{Pi}},\mathrm{Pi}\right):$
 > $\mathbf{use}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{plots}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{in}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{display}\left(\mathrm{Array}\left(\left[\mathrm{listplot}\left(a\right),\mathrm{listplot}\left(\mathrm{KaiserWindow}\left(a,0.2\right)\right)\right]\right)\right);\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{animate}\left(\mathrm{listplot},\left['\mathrm{KaiserWindow}'\left(a,\mathrm{α}\right)\right],\mathrm{α}=-1..1\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{end use}$   > 

Compatibility

 • The SignalProcessing[KaiserWindow] command was introduced in Maple 17.