The ComplexCepstrum(A) command uses the Fourier transform to compute the complex cepstrum of a signal and the number of samples of delay.

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

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

$\mathrm{f1}≔12.0\:$

$\mathrm{f2}≔20.0\:$

$\mathrm{Fs}≔1000\:$

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

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

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

$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$

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

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

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