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{-0.00210915153424963}\,\mathrm{-0.00195907093568552}\,\mathrm{-0.00178456266462847}\,\mathrm{-0.00158722980572774}\,\mathrm{-0.00136900765256142}\,\mathrm{-0.00113213114331287}\,\mathrm{-0.000879117825723876}\,\mathrm{-0.000612728339790005}\,\mathrm{-0.000335934856947660}\,\mathrm{-0.0000518692285804922}\,0.000236197915118545\,0.000524918779904569\,0.000810908961643773\,0.00109079348274112\,0.00136125182569231\,0.00161907099400061\,0.00186117875125773\,0.00208470189279648\,0.00228698458099987\,0.00246565146703445\,0.00261861936625998\,0.00274413853802196\,0.00284081144739503\,0.00290761023539303\,0.00294389874606528\,0.00294943045953124\,0.00292435611527904\,0.00286922116621859\,0.00278495305332947\,0.00267284751323420\,0.00253456066103730\,0.00237204750856884\,0.00218758607926747\,0.00198369895676671\,0.00176313243360700\,0.00152882137405687\,0.00128383474591317\,0.00103134012640193\,0.000774547137475038\,0.000516676275508851\,0.000260892407280020\,0.0000102815082253654\,\mathrm{-0.000232212523021458}\,\mathrm{-0.000463806015781722}\,\mathrm{-0.000681945070966373}\,\mathrm{-0.000884314055822090}\,\mathrm{-0.00106887244974806}\,\mathrm{-0.00123388950018437}\,\mathrm{-0.00137795715273697}\,\mathrm{-0.00150000247072594}\,\mathrm{-0.00159931422961691}\,\mathrm{-0.00167552962725953}\,\mathrm{-0.00172864562943142}\,\mathrm{-0.00175900613817884}\,\mathrm{-0.00176729411119747}\,\mathrm{-0.00175451642643903}\,\mathrm{-0.00172196622085344}\,\mathrm{-0.00167122556969059}\,\mathrm{-0.00160410857054618}\,\mathrm{-0.00152263941865677}\,\mathrm{-0.00142901279894585}\,\mathrm{-0.00132555057158261}\,\mathrm{-0.00121466676701490}\,\mathrm{-0.00109882186179676}\,\mathrm{-0.000980478121445167}\,\mathrm{-0.000862059003425817}\,\mathrm{-0.000745905236741443}\,\mathrm{-0.000634235631148718}\,\mathrm{-0.000529117005187840}\,\mathrm{-0.000432411558720841}\,\mathrm{-0.000345765536720265}\,\mathrm{-0.000270566499318687}\,\mathrm{-0.000207929575717559}\,\mathrm{-0.000158676691130030}\,\mathrm{-0.000123323294893262}\,\mathrm{-0.000102069283972735}\,\mathrm{-0.0000948081950428617}\,\mathrm{-0.000101109319635814}\,\mathrm{-0.000120250036937225}\,\mathrm{-0.000151199642665856}\,\mathrm{-0.000192693657354294}\,\mathrm{-0.000243201660821129}\,\mathrm{-0.000300946856582380}\,\mathrm{-0.000364038924773236}\,\mathrm{-0.000430369096881509}\,\mathrm{-0.000497762718130473}\,\mathrm{-0.000563960590512264}\,\mathrm{-0.000626678634850111}\,\mathrm{-0.000683638237982438}\,\mathrm{-0.000732653896321378}\,\mathrm{-0.000771600683010226}\,\mathrm{-0.000798505125887405}\,\mathrm{-0.000811615326736579}\,\mathrm{-0.000809342110631509}\,\mathrm{-0.000790358224897612}\,\mathrm{-0.000753671247829356}\,\mathrm{-0.000698496462873895}\,\mathrm{-0.000624482126443007}\,\mathrm{-0.000531518327017009}\,\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.