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SignalProcessing

 PoissonWindow
 multiply an array of samples by a Poisson windowing function

 Calling Sequence PoissonWindow( A, alpha )

Parameters

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

Options

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

Description

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

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

 • 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[PoissonWindow] command is thread-safe as of Maple 18.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $N≔1024:$
 > $a≔\mathrm{GenerateUniform}\left(N,-1,1\right)$
 ${a}{≔}\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}{-}{0.785218492150308}& {0.588413964957000}& {-}{0.993165822699668}& {0.921578288543971}& {-}{0.0387801709584892}& {0.0136057925410569}& {-}{0.210756972897798}& {0.749600215815009}& {0.138966357801110}& {0.212285134010017}& {-}{0.727212007157506}& {0.609271531458945}& {-}{0.746508821379394}& {-}{0.681121068540962}& {-}{0.815677223727108}& {0.920580454170705}& {-}{0.357731881551445}& {-}{0.315850691869855}& {0.120832127984613}& {0.0235598362050951}& {-}{0.528712330386043}& {-}{0.502768306992949}& {0.716167932841928}& {0.387918812688441}& {0.927826197817923}& {-}{0.535605234093965}& {-}{0.867390423081817}& {0.356968106236309}& {-}{0.683916721958668}& {0.324222652241588}& {-}{0.0536105097271503}& {-}{0.469822424929590}& {0.751377623062582}& {-}{0.484332469291986}& {0.674785583745689}& {0.936373751610519}& {-}{0.709695004858078}& {-}{0.315371678676457}& {0.786426438484342}& {0.877079485449941}& {-}{0.940901432652028}& {-}{0.651838099118323}& {-}{0.466202749870718}& {0.728111944627018}& {-}{0.693676937371493}& {0.446705075912178}& {0.402212079148740}& {-}{0.465064398013056}& {-}{0.149959974456579}& {-}{0.893211717717351}& {-}{0.533857398666442}& {0.785364017821850}& {0.794103573076428}& {-}{0.511805256363005}& {-}{0.699780572205783}& {0.390154657885433}& {-}{0.306801157072187}& {0.380043311044574}& {0.250223507639021}& {-}{0.112387157976628}& {0.213712436612696}& {-}{0.462156727444381}& {-}{0.748708907514812}& {-}{0.151586118619889}& {-}{0.108139840420336}& {-}{0.168242880143225}& {-}{0.525201478973032}& {0.480703854002059}& {-}{0.893447801005097}& {0.705915172118695}& {-}{0.922403736039998}& {-}{0.150907000061125}& {-}{0.552928699180485}& {-}{0.630023401696236}& {0.476304094772787}& {-}{0.520089327357710}& {0.383331325836480}& {0.853844197466971}& {-}{0.561684322543443}& {-}{0.392888241447509}& {0.805707171559335}& {-}{0.830475841183217}& {0.958363623823972}& {0.267084791325033}& {-}{0.934454344213010}& {0.600780255626888}& {0.499754573684187}& {0.663151745684446}& {0.481067702174187}& {-}{0.756487140897663}& {0.800444356631489}& {-}{0.510770577006043}& {0.292151435278357}& {0.0674125049263240}& {-}{0.305776782333851}& {-}{0.469037371221931}& {0.649966387543828}& {0.648178403731437}& {0.870920942630620}& {-}{0.361100737471134}& {\mathrm{...}}& {"... 924 Array entries not shown"}\end{array}\right]$ (1)
 > $\mathrm{PoissonWindow}\left(a,1.23\right)$
 $\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}{-}{0.230065570346015}& {0.172817376493729}& {-}{0.292394720800498}& {0.271971452359329}& {-}{0.0114721318497906}& {0.00403461017721606}& {-}{0.0626473942748618}& {0.223354181381847}& {0.0415066214440786}& {0.0635580575461157}& {-}{0.218250576344441}& {0.183294135036549}& {-}{0.225120970106859}& {-}{0.205896349290445}& {-}{0.247164442397176}& {0.279622897151720}& {-}{0.108921083491442}& {-}{0.0964005392368077}& {0.0369677807049643}& {0.00722531102499158}& {-}{0.162535055361161}& {-}{0.154931177812097}& {0.221222412928483}& {0.120115324896241}& {0.287983452578811}& {-}{0.166643753893246}& {-}{0.270521741866494}& {0.111598997230281}& {-}{0.214327266042984}& {0.101849964136931}& {-}{0.0168814904505811}& {-}{0.148298895891298}& {0.237741915376034}& {-}{0.153615277463398}& {0.214535884471570}& {0.298419161094686}& {-}{0.226721416988257}& {-}{0.100991962862771}& {0.252444290870495}& {0.282221259547252}& {-}{0.303485696352345}& {-}{0.210754648663894}& {-}{0.151096908077496}& {0.236549604817577}& {-}{0.225904380083090}& {0.145824873320172}& {0.131616141326916}& {-}{0.152549386015926}& {-}{0.0493078484073986}& {-}{0.294400423739364}& {-}{0.176381328568277}& {0.260100788056030}& {0.263627762111576}& {-}{0.170318592470022}& {-}{0.233433146092129}& {0.130461017960877}& {-}{0.102835789020637}& {0.127692005862481}& {0.0842756378917657}& {-}{0.0379431999394630}& {0.0723253236635003}& {-}{0.156780914686340}& {-}{0.254601078640894}& {-}{0.0516713724191494}& {-}{0.0369504398787703}& {-}{0.0576253939653024}& {-}{0.180321070996137}& {0.165440360002218}& {-}{0.308231039751782}& {0.244119812587107}& {-}{0.319753192746745}& {-}{0.0524380516040893}& {-}{0.192597044194596}& {-}{0.219978629224487}& {0.166706084045673}& {-}{0.182468709805569}& {0.134811858338217}& {0.301006407254272}& {-}{0.198487305247638}& {-}{0.139172295083746}& {0.286091076527618}& {-}{0.295595222424835}& {0.341935390579805}& {0.0955226176513187}& {-}{0.335010538187798}& {0.215903338146079}& {0.180029554941806}& {0.239465676002219}& {0.174132517976417}& {-}{0.274484960963767}& {0.291133027096462}& {-}{0.186221373424061}& {0.106771416031706}& {0.0246962360711997}& {-}{0.112289237770025}& {-}{0.172657082975444}& {0.239834234190337}& {0.239749747446773}& {0.322913097092265}& {-}{0.134208068485349}& {\mathrm{...}}& {"... 924 row vector entries not shown"}\end{array}\right]$ (2)
 > $c≔\mathrm{Array}\left(1..N,'\mathrm{datatype}'={'\mathrm{float}'}_{8},'\mathrm{order}'='\mathrm{C_order}'\right):$
 > $\mathrm{PoissonWindow}\left(\mathrm{Array}\left(1..N,'\mathrm{fill}'=1,'\mathrm{datatype}'={'\mathrm{float}'}_{8},'\mathrm{order}'='\mathrm{C_order}'\right),0.72,'\mathrm{container}'=c\right)$
 $\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}{0.487437232831397}& {0.488123173629150}& {0.488810079709706}& {0.489497952431447}& {0.490186793154670}& {0.490876603241584}& {0.491567384056315}& {0.492259136964911}& {0.492951863335339}& {0.493645564537494}& {0.494340241943196}& {0.495035896926199}& {0.495732530862186}& {0.496430145128778}& {0.497128741105537}& {0.497828320173962}& {0.498528883717499}& {0.499230433121539}& {0.499932969773426}& {0.500636495062451}& {0.501341010379864}& {0.502046517118873}& {0.502753016674644}& {0.503460510444308}& {0.504168999826962}& {0.504878486223672}& {0.505588971037474}& {0.506300455673381}& {0.507012941538382}& {0.507726430041445}& {0.508440922593521}& {0.509156420607549}& {0.509872925498454}& {0.510590438683151}& {0.511308961580553}& {0.512028495611565}& {0.512749042199096}& {0.513470602768054}& {0.514193178745354}& {0.514916771559918}& {0.515641382642679}& {0.516367013426585}& {0.517093665346599}& {0.517821339839704}& {0.518550038344904}& {0.519279762303230}& {0.520010513157739}& {0.520742292353521}& {0.521475101337697}& {0.522208941559426}& {0.522943814469906}& {0.523679721522376}& {0.524416664172124}& {0.525154643876480}& {0.525893662094829}& {0.526633720288610}& {0.527374819921316}& {0.528116962458500}& {0.528860149367780}& {0.529604382118835}& {0.530349662183417}& {0.531095991035345}& {0.531843370150515}& {0.532591801006897}& {0.533341285084544}& {0.534091823865590}& {0.534843418834254}& {0.535596071476846}& {0.536349783281765}& {0.537104555739507}& {0.537860390342663}& {0.538617288585927}& {0.539375251966094}& {0.540134281982067}& {0.540894380134857}& {0.541655547927590}& {0.542417786865503}& {0.543181098455955}& {0.543945484208424}& {0.544710945634513}& {0.545477484247952}& {0.546245101564602}& {0.547013799102457}& {0.547783578381644}& {0.548554440924435}& {0.549326388255239}& {0.550099421900612}& {0.550873543389261}& {0.551648754252039}& {0.552425056021957}& {0.553202450234183}& {0.553980938426044}& {0.554760522137031}& {0.555541202908801}& {0.556322982285183}& {0.557105861812174}& {0.557889843037951}& {0.558674927512866}& {0.559461116789456}& {0.560248412422441}& {\mathrm{...}}& {"... 924 row vector entries not shown"}\end{array}\right]$ (3)
 > $u≔{\mathrm{~}}_{\mathrm{log}}\left(\mathrm{FFT}\left(c\right)\right):$
 > $\mathbf{use}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{plots}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{in}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{display}\left(\mathrm{Array}\left(\left[\mathrm{listplot}\left(\mathrm{ℜ}\left(u\right)\right),\mathrm{listplot}\left(\mathrm{ℑ}\left(u\right)\right)\right]\right)\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{end use}$

 > 

Compatibility

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