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[0.145868794568315\,\mathrm{-0.00210915179497513}\,\mathrm{-0.00195907093484975}\,\mathrm{-0.00178456275043985}\,\mathrm{-0.00158722980411414}\,\mathrm{-0.00136900770282320}\,\mathrm{-0.00113213114103329}\,\mathrm{-0.000879117860469178}\,\mathrm{-0.000612728337002422}\,\mathrm{-0.000335934882985858}\,\mathrm{-0.0000518692254780711}\,0.000236197894566890\,0.000524918783106926\,0.000810908944735137\,0.00109079348582164\,0.00136125181123326\,0.00161907099674613\,0.00186117873841483\,0.00208470189501710\,0.00228698456916877\,0.00246565146857683\,0.00261861935500171\,0.00274413853877985\,0.00284081143640224\,0.00290761023531460\,0.00294389873514194\,0.00294943045862267\,0.00292435610432583\,0.00286922116454361\,0.00278495304233068\,0.00267284751090953\,0.00253456065004724\,0.00237204750575610\,0.00218758606839580\,0.00198369895366116\,0.00176313242300242\,0.00152882137087378\,0.00128383473574653\,0.00103134012336170\,0.000774547127922147\,0.000516676272821649\,0.000260892398505104\,0.0000102815060765986\,\mathrm{-0.000232212530880705}\,\mathrm{-0.000463806017244215}\,\mathrm{-0.000681945077811294}\,\mathrm{-0.000884314056498269}\,\mathrm{-0.00106887245552824}\,\mathrm{-0.00123388950002882}\,\mathrm{-0.00137795715745588}\,\mathrm{-0.00150000246975094}\,\mathrm{-0.00159931423333334}\,\mathrm{-0.00167552962553407}\,\mathrm{-0.00172864563225693}\,\mathrm{-0.00175900613582381}\,\mathrm{-0.00176729411328992}\,\mathrm{-0.00175451642361860}\,\mathrm{-0.00172196622240710}\,\mathrm{-0.00167122556660086}\,\mathrm{-0.00160410857177940}\,\mathrm{-0.00152263941551208}\,\mathrm{-0.00142901280008666}\,\mathrm{-0.00132555056860061}\,\mathrm{-0.00121466676828613}\,\mathrm{-0.00109882185918331}\,\mathrm{-0.000980478123049814}\,\mathrm{-0.000862059001360759}\,\mathrm{-0.000745905238849139}\,\mathrm{-0.000634235629773529}\,\mathrm{-0.000529117007923929}\,\mathrm{-0.000432411558128851}\,\mathrm{-0.000345765540157761}\,\mathrm{-0.000270566499548717}\,\mathrm{-0.000207929579872687}\,\mathrm{-0.000158676692163918}\,\mathrm{-0.000123323299725022}\,\mathrm{-0.000102069285736715}\,\mathrm{-0.0000948082004563935}\,\mathrm{-0.000101109322005782}\,\mathrm{-0.000120250042790877}\,\mathrm{-0.000151199645476117}\,\mathrm{-0.000192693663470080}\,\mathrm{-0.000243201663876019}\,\mathrm{-0.000300946862758585}\,\mathrm{-0.000364038927860769}\,\mathrm{-0.000430369102907126}\,\mathrm{-0.000497762721037037}\,\mathrm{-0.000563960596181902}\,\mathrm{-0.000626678637375343}\,\mathrm{-0.000683638243110826}\,\mathrm{-0.000732653898292036}\,\mathrm{-0.000771600687445201}\,\mathrm{-0.000798505127169153}\,\mathrm{-0.000811615330369709}\,\mathrm{-0.000809342111138219}\,\mathrm{-0.000790358227671851}\,\mathrm{-0.000753671247528751}\,\mathrm{-0.000698496464787393}\,\mathrm{-0.000624482125358902}\,\mathrm{-0.000531518328123398}\,\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.