container : Array, predefined Array for holding results

inplace : truefalse, specifies that output should overwrite input

The WelchWindow(A) command multiplies the Array A by the Welch windowing function and returns the result in an Array having the same length.

The ReiszWindow( A ) command is provided as an alias.

The Welch windowing function $w\left(k\right)$ is defined as follows for a sample with $N$ points.

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[WelchWindow] and SignalProcessing[ReiszWindow] commands are thread-safe as of Maple 18.

For more information on thread safety, see index/threadsafe.

$\mathrm{with}\left(\mathrm{SignalProcessing}\right)\:$

$N≔1024\:$

$a≔\mathrm{GenerateUniform}\left(N\,-1\,1\right)$

$a≔\left[0.995867573674919\,0.408337529411819\,0.167610888327636\,\mathrm{-0.246858837322246}\,0.432866472071836\,\mathrm{-0.439979858216147}\,0.432901310269353\,0.481379433115581\,\mathrm{-0.477697063372826}\,0.0288390346482901\,0.121298888322326\,\mathrm{-0.347901581305424}\,\mathrm{-0.417575321932189}\,\mathrm{-0.377487291266245}\,\mathrm{-0.957241696004090}\,\mathrm{-0.106224023010499}\,\mathrm{-0.153815988427697}\,\mathrm{-0.796037529927613}\,0.914456672624718\,\mathrm{-0.838266016849289}\,0.780798342992182\,0.264941104331734\,0.307568462467303\,0.759836566745563\,\mathrm{-0.0974062939840268}\,\mathrm{-0.738299079939469}\,\mathrm{-0.222411502459510}\,\mathrm{-0.790666567452535}\,0.479324116036899\,\mathrm{-0.926660717719720}\,0.158096275557107\,\mathrm{-0.270853780765762}\,0.662332445466727\,\mathrm{-0.744445672422478}\,\mathrm{-0.478385013373665}\,\mathrm{-0.0621887851286065}\,0.172013089695077\,\mathrm{-0.591466642712960}\,\mathrm{-0.671336703895487}\,0.621614486337707\,\mathrm{-0.571712331523940}\,0.729500236463803\,0.927596094164525\,\mathrm{-0.166740832401267}\,\mathrm{-0.232738235376916}\,0.747897344476724\,\mathrm{-0.390875342827815}\,\mathrm{-0.824422433563177}\,0.419102838543417\,0.519515359664100\,0.339253361707115\,0.544663757892689\,\mathrm{-0.790555218506194}\,\mathrm{-0.626662143370472}\,0.809291667387941\,0.112528634479680\,\mathrm{-0.594205220415586}\,\mathrm{-0.547543621943336}\,0.917705395677354\,\mathrm{-0.719336755784793}\,0.797753419286497\,\mathrm{-0.0410473111353908}\,\mathrm{-0.460116401375612}\,0.221890072130439\,\mathrm{-0.372704340753435}\,\mathrm{-0.0865302486005877}\,\mathrm{-0.958873433799482}\,0.104950403128197\,\mathrm{-0.960985163666299}\,\mathrm{-0.555279271724625}\,\mathrm{-0.728221283327371}\,\mathrm{-0.159194410764132}\,\mathrm{-0.0496779615156940}\,0.887333813842765\,0.955854138274286\,0.294842910032204\,0.727087873584634\,\mathrm{-0.941265508088898}\,\mathrm{-0.936975655971576}\,\mathrm{-0.761605592710214}\,\mathrm{-0.518730224597855}\,\mathrm{-0.338608480594198}\,\mathrm{-0.455934113149177}\,0.520442334745367\,0.154686897427569\,0.532024301217215\,0.0391812730885115\,\mathrm{-0.210772442317735}\,0.726914650621525\,0.832612093819426\,0.511782993769936\,\mathrm{-0.0407688232327275}\,\mathrm{-0.827512086732588}\,\mathrm{-0.429504782480848}\,\mathrm{-0.697198097083888}\,\mathrm{-0.0173380781534870}\,\mathrm{-0.335721179041430}\,0.843225187896704\,0.546950585326249\,0.590849398058455\,\dots \,\text{⋯ 924 Array entries not shown}\right]$

$\mathrm{WelchWindow}\left(a\right)$

$\left[0.00388630877635743\,0.00318390621230224\,0.00195843563441295\,\mathrm{-0.00384210226545244}\,0.00841314191896822\,\mathrm{-0.0102516058883065}\,0.0117562272178937\,0.0149255830091989\,\mathrm{-0.0166464335400038}\,0.00111552357228722\,0.00515607266454954\,\mathrm{-0.0161167785773204}\,\mathrm{-0.0209357927557173}\,\mathrm{-0.0203615962925137}\,\mathrm{-0.0552667734871746}\,\mathrm{-0.00653526704068500}\,\mathrm{-0.0100447689281225}\,\mathrm{-0.0549875167538804}\,0.0666105276633034\,\mathrm{-0.0642104401334141}\,0.0627363414705060\,0.0222792118220854\,0.0270124386268033\,0.0695651153636685\,\mathrm{-0.00928009869480540}\,\mathrm{-0.0730796223688863}\,\mathrm{-0.0228389558208754}\,\mathrm{-0.0841144913983013}\,0.0527606863717831\,\mathrm{-0.105411615762337}\,0.0185649019259431\,\mathrm{-0.0327987000146039}\,0.0826273268283782\,\mathrm{-0.0955888417577386}\,\mathrm{-0.0631687058942009}\,\mathrm{-0.00843784602910720}\,0.0239629593756658\,\mathrm{-0.0845377814070480}\,\mathrm{-0.0983787516790204}\,0.0933332297601782\,\mathrm{-0.0878971942802786}\,0.114774733553746\,0.149264473114556\,\mathrm{-0.0274271571851449}\,\mathrm{-0.0391131704693986}\,0.128350851949001\,\mathrm{-0.0684684939091127}\,\mathrm{-0.147333305998107}\,0.0763803028542013\,0.0965133591294925\,0.0642195494384467\,0.105016651073181\,\mathrm{-0.155198452796876}\,\mathrm{-0.125215770987493}\,0.164532468465577\,0.0232694710459689\,\mathrm{-0.124938955475184}\,\mathrm{-0.117026420784917}\,0.199316241084634\,\mathrm{-0.158715965097780}\,0.178765980183207\,\mathrm{-0.00933924036163042}\,\mathrm{-0.106265362886367}\,0.0520054856555715\,\mathrm{-0.0886250498995413}\,\mathrm{-0.0208707220402449}\,\mathrm{-0.234535239035755}\,0.0260262138616861\,\mathrm{-0.241562337340510}\,\mathrm{-0.141454886496622}\,\mathrm{-0.187964007163162}\,\mathrm{-0.0416252963692346}\,\mathrm{-0.0131561016933595}\,0.237959164097391\,0.259524987379731\,0.0810350112228402\,0.202249605765983\,\mathrm{-0.264946362727599}\,\mathrm{-0.266837759386284}\,\mathrm{-0.219407861181165}\,\mathrm{-0.151146586400825}\,\mathrm{-0.0997752131462791}\,\mathrm{-0.135840690762673}\,0.156761652952172\,0.0470975292899378\,0.163716645548211\,0.0121842124973388\,\mathrm{-0.0662265950348939}\,0.230751810651665\,0.266988268304676\,0.165755888061710\,\mathrm{-0.0133349684878044}\,\mathrm{-0.273317256948729}\,\mathrm{-0.143231613481429}\,\mathrm{-0.234722969276957}\,\mathrm{-0.00589223749747408}\,\mathrm{-0.115156985085397}\,0.291904446988106\,0.191066741375928\,0.208261430284886\,\dots \,\text{⋯ 924 Array entries not shown}\right]$

$c≔\mathrm{Array}\left(1..N\,'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\,'\mathrm{order}'='\mathrm{C\_order}'\right)\:$

$\mathrm{WelchWindow}\left(\mathrm{Array}\left(1..N\,'\mathrm{fill}'=1\,'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\,'\mathrm{order}'='\mathrm{C\_order}'\right)\,'\mathrm{container}'=c\right)$

$\left[0.00390243530273438\,0.00779724121093750\,0.0116844177246094\,0.0155639648437500\,0.0194358825683594\,0.0233001708984375\,0.0271568298339844\,0.0310058593750000\,0.0348472595214844\,0.0386810302734375\,0.0425071716308594\,0.0463256835937500\,0.0501365661621094\,0.0539398193359375\,0.0577354431152344\,0.0615234375000000\,0.0653038024902344\,0.0690765380859375\,0.0728416442871094\,0.0765991210937500\,0.0803489685058594\,0.0840911865234375\,0.0878257751464844\,0.0915527343750000\,0.0952720642089844\,0.0989837646484375\,0.102687835693359\,0.106384277343750\,0.110073089599609\,0.113754272460938\,0.117427825927734\,0.121093750000000\,0.124752044677734\,0.128402709960938\,0.132045745849609\,0.135681152343750\,0.139308929443359\,0.142929077148438\,0.146541595458984\,0.150146484375000\,0.153743743896484\,0.157333374023438\,0.160915374755859\,0.164489746093750\,0.168056488037109\,0.171615600585938\,0.175167083740234\,0.178710937500000\,0.182247161865234\,0.185775756835938\,0.189296722412109\,0.192810058593750\,0.196315765380859\,0.199813842773438\,0.203304290771484\,0.206787109375000\,0.210262298583984\,0.213729858398438\,0.217189788818359\,0.220642089843750\,0.224086761474609\,0.227523803710938\,0.230953216552734\,0.234375000000000\,0.237789154052734\,0.241195678710938\,0.244594573974609\,0.247985839843750\,0.251369476318359\,0.254745483398438\,0.258113861083984\,0.261474609375000\,0.264827728271484\,0.268173217773438\,0.271511077880859\,0.274841308593750\,0.278163909912109\,0.281478881835938\,0.284786224365234\,0.288085937500000\,0.291378021240234\,0.294662475585938\,0.297939300537109\,0.301208496093750\,0.304470062255859\,0.307723999023438\,0.310970306396484\,0.314208984375000\,0.317440032958984\,0.320663452148438\,0.323879241943359\,0.327087402343750\,0.330287933349609\,0.333480834960938\,0.336666107177734\,0.339843750000000\,0.343013763427734\,0.346176147460938\,0.349330902099609\,0.352478027343750\,\dots \,\text{⋯ 924 Array entries not shown}\right]$

$u≔\mathrm{`~`}\left[\log \right]\left(\mathrm{FFT}\left(c\right)\right)\:$

$\mathbf{use}\mathrm{plots}\mathbf{in}\mathrm{display}\left(\mathrm{Array}\left(\left[\mathrm{listplot}\left(\mathrm{\ℜ}\left(u\right)\right)\,\mathrm{listplot}\left(\mathrm{\ℑ}\left(u\right)\right)\right]\right)\right)\mathbf{end\; use}$

The SignalProcessing[WelchWindow] and SignalProcessing[ReiszWindow] commands were introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.