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The InverseComplexCepstrum(A) command computes the inverse complex cepstrum of the real data A.

nd is the number of samples of delay and the second output of ComplexCepstrum.

A must be a one-dimensional Array and must contain real numbers only.

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

$\mathrm{f1}≔12.0\:$

$\mathrm{f2}≔20.0\:$

$\mathrm{Fs}≔1000\:$

$\mathrm{signal}≔\mathrm{Vector}\left(2^{10}\,i\mapsto \sin \left(\frac{2\cdot \mathrm{f1}\cdot \mathrm{\pi }\cdot i}{\mathrm{Fs}}\right)+1.5\cdot \sin \left(\frac{2\cdot \mathrm{f2}\cdot \mathrm{\pi }\cdot i}{\mathrm{Fs}}\right)\,'\mathrm{datatype}'='\mathrm{float}\left[8\right]'\right)\:$

$t≔\mathrm{Vector}\left(2^{10}\,i\mapsto \frac{1.0\cdot i}{\mathrm{Fs}}\,'\mathrm{datatype}'='\mathrm{float}\left[8\right]'\right)\:$

$\mathrm{plot}\left(t\,\mathrm{signal}\right)$

$c,\mathrm{nd}≔\mathrm{ComplexCepstrum}\left(\mathrm{signal}\right)$

$c,\mathrm{nd}≔\left[0.145868794173792\,\mathrm{-0.00210915168798808}\,\mathrm{-0.00195907093726305}\,\mathrm{-0.00178456251262971}\,\mathrm{-0.00158723017952092}\,\mathrm{-0.00136900717332506}\,\mathrm{-0.00113213142754671}\,\mathrm{-0.000879118072908171}\,\mathrm{-0.000612729102717034}\,\mathrm{-0.000335933915463403}\,\mathrm{-0.0000518691823107554}\,0.000236197734301829\,0.000524918812761570\,0.000810908811898884\,0.00109079292502308\,0.00136125268434150\,0.00161907059588614\,0.00186117902837144\,0.00208470231063766\,0.00228698447219434\,0.00246565099305505\,0.00261861940868970\,0.00274413870246442\,0.00284081098011017\,0.00290761046438723\,0.00294389885055819\,0.00294943024876162\,0.00292435619419080\,0.00286922106086203\,0.00278495314552658\,0.00267284797386721\,0.00253455961693968\,0.00237204818932661\,0.00218758640375127\,0.00198369840536475\,0.00176313330805648\,0.00152881995008784\,0.00128383550256278\,0.00103133976532250\,0.000774547844280710\,0.000516675152373880\,0.000260892806657957\,0.0000102824560461322\,\mathrm{-0.000232213242061019}\,\mathrm{-0.000463805993100649}\,\mathrm{-0.000681945519545453}\,\mathrm{-0.000884313517395977}\,\mathrm{-0.00106887267165126}\,\mathrm{-0.00123388936138316}\,\mathrm{-0.00137795717630294}\,\mathrm{-0.00150000258721810}\,\mathrm{-0.00159931402960196}\,\mathrm{-0.00167552987248902}\,\mathrm{-0.00172864560991289}\,\mathrm{-0.00175900613600081}\,\mathrm{-0.00176729402500319}\,\mathrm{-0.00175451651226302}\,\mathrm{-0.00172196587771865}\,\mathrm{-0.00167122550132807}\,\mathrm{-0.00160410892899810}\,\mathrm{-0.00152263987372212}\,\mathrm{-0.00142901221661929}\,\mathrm{-0.00132555026666183}\,\mathrm{-0.00121466690706223}\,\mathrm{-0.00109882216513331}\,\mathrm{-0.000980478371266343}\,\mathrm{-0.000862058757528156}\,\mathrm{-0.000745905237416894}\,\mathrm{-0.000634235236511967}\,\mathrm{-0.000529117340369938}\,\mathrm{-0.000432411500765361}\,\mathrm{-0.000345765643365697}\,\mathrm{-0.000270566440713330}\,\mathrm{-0.000207929553229660}\,\mathrm{-0.000158676599499967}\,\mathrm{-0.000123323295874221}\,\mathrm{-0.000102069444963467}\,\mathrm{-0.0000948080311568395}\,\mathrm{-0.000101109203842169}\,\mathrm{-0.000120250394845111}\,\mathrm{-0.000151200712538078}\,\mathrm{-0.000192692782703455}\,\mathrm{-0.000243201202117998}\,\mathrm{-0.000300946820924559}\,\mathrm{-0.000364039494975447}\,\mathrm{-0.000430368053738830}\,\mathrm{-0.000497763222279364}\,\mathrm{-0.000563960995852642}\,\mathrm{-0.000626678134905142}\,\mathrm{-0.000683638965810780}\,\mathrm{-0.000732653699080411}\,\mathrm{-0.000771600353449508}\,\mathrm{-0.000798504981886469}\,\mathrm{-0.000811615564975181}\,\mathrm{-0.000809342108015785}\,\mathrm{-0.000790358262020568}\,\mathrm{-0.000753671347473382}\,\mathrm{-0.000698496435810887}\,\mathrm{-0.000624482159229903}\,\mathrm{-0.000531518263933250}\,\dots \,\text{⋯ 924 Array entries not shown}\right],1$

$\mathrm{ic}≔\mathrm{InverseComplexCepstrum}\left(c\,\mathrm{nd}\right)$

$\mathrm{ic}≔\left[0.263326655972138\,0.523260420059322\,0.776457590071404\,1.01967209281618\,1.24980243119433\,1.46393642577006\,1.65939306615587\,1.83376083735144\,1.98493193982217\,2.11113188073380\,2.21094399373977\,2.28332852490774\,2.32763599187019\,2.34361463095949\,2.33141182728137\,2.29156952135328\,2.22501367772047\,2.13303798842851\,2.01728208319397\,1.87970460551530\,1.72255155405477\,1.54832043700567\,1.35972077390639\,1.15963158231109\,0.951056515727385\,0.737077356030473\,0.520806593012789\,0.305339826790114\,0.0937087391441920\,\mathrm{-0.111164636191634}\,\mathrm{-0.306511633323757}\,\mathrm{-0.489757998104968}\,\mathrm{-0.658561591855673}\,\mathrm{-0.810846233240466}\,\mathrm{-0.944831101655407}\,\mathrm{-1.05905529651493}\,\mathrm{-1.15239716916862}\,\mathrm{-1.22408815700280}\,\mathrm{-1.27372089570133}\,\mathrm{-1.30125154130903}\,\mathrm{-1.30699626131380}\,\mathrm{-1.29162198490227}\,\mathrm{-1.25613158066947}\,\mathrm{-1.20184371584128}\,\mathrm{-1.13036776385586}\,\mathrm{-1.04357411954015}\,\mathrm{-0.943560494810057}\,\mathrm{-0.832614690705040}\,\mathrm{-0.713174480046158}\,\mathrm{-0.587785250812875}\,\mathrm{-0.459056110220408}\,\mathrm{-0.329615138504499}\,\mathrm{-0.202064551581808}\,\mathrm{-0.0789364739614809}\,0.0373499523850901\,0.144529431671584\,0.240528693323063\,0.323501353636181\,0.391858940706872\,0.444297524200124\,0.479819565792629\,0.497750620050192\,0.497750619978777\,0.479819565355025\,0.444297523480013\,0.391858939717937\,0.323501352397258\,0.240528691857820\,0.144529430949541\,0.0373499516271599\,\mathrm{-0.0789364759216888}\,\mathrm{-0.202064553634305}\,\mathrm{-0.329615140608765}\,\mathrm{-0.459056112334420}\,\mathrm{-0.587785252893833}\,\mathrm{-0.713174480349207}\,\mathrm{-0.832614692591976}\,\mathrm{-0.943560496538103}\,\mathrm{-1.04357412107063}\,\mathrm{-1.13036776272583}\,\mathrm{-1.20184371905926}\,\mathrm{-1.25613158324077}\,\mathrm{-1.29162198171368}\,\mathrm{-1.30699626267200}\,\mathrm{-1.30125153918472}\,\mathrm{-1.27372089507198}\,\mathrm{-1.22408815638882}\,\mathrm{-1.15239716800858}\,\mathrm{-1.05905529243608}\,\mathrm{-0.944831101480395}\,\mathrm{-0.810846230899849}\,\mathrm{-0.658561586015105}\,\mathrm{-0.489757997138195}\,\mathrm{-0.306511630227417}\,\mathrm{-0.111164626789267}\,0.0937087410772002\,0.305339833073036\,0.520806590732982\,0.737077359550136\,0.951056525184228\,\dots \,\text{⋯ 924 Array entries not shown}\right]$

$\mathrm{plot}\left(t\,\mathrm{ic}\right)$

The SignalProcessing[InverseComplexCepstrum] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019 .