ComplexCepstrum - Maple Help

SignalProcessing

 ComplexCepstrum
 compute the complex cepstrum of the signal

 Calling Sequence ComplexCepstrum(A)

Parameters

 A - Array of real numeric values; the signal

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $\mathrm{f1}≔12.0:$
 > $\mathrm{f2}≔20.0:$
 > $\mathrm{Fs}≔1000:$
 > $\mathrm{signal}≔\mathrm{Vector}\left({2}^{10},i↦\mathrm{sin}\left(\frac{2\cdot \mathrm{f1}\cdot \mathrm{\pi }\cdot i}{\mathrm{Fs}}\right)+1.5\cdot \mathrm{sin}\left(\frac{2\cdot \mathrm{f2}\cdot \mathrm{\pi }\cdot i}{\mathrm{Fs}}\right),'\mathrm{datatype}'='\mathrm{float}\left[8\right]'\right):$
 > $t≔\mathrm{Vector}\left({2}^{10},i↦\frac{1.0\cdot i}{\mathrm{Fs}},'\mathrm{datatype}'='\mathrm{float}\left[8\right]'\right):$
 > $c,\mathrm{nd}≔\mathrm{ComplexCepstrum}\left(\mathrm{signal}\right)$
 ${c}{,}{\mathrm{nd}}{≔}\left[{0.145868794568315}{,}{-0.00210915179497513}{,}{-0.00195907093484975}{,}{-0.00178456275043985}{,}{-0.00158722980411414}{,}{-0.00136900770282320}{,}{-0.00113213114103329}{,}{-0.000879117860469178}{,}{-0.000612728337002422}{,}{-0.000335934882985858}{,}{-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}{,}{-0.000232212530880705}{,}{-0.000463806017244215}{,}{-0.000681945077811294}{,}{-0.000884314056498269}{,}{-0.00106887245552824}{,}{-0.00123388950002882}{,}{-0.00137795715745588}{,}{-0.00150000246975094}{,}{-0.00159931423333334}{,}{-0.00167552962553407}{,}{-0.00172864563225693}{,}{-0.00175900613582381}{,}{-0.00176729411328992}{,}{-0.00175451642361860}{,}{-0.00172196622240710}{,}{-0.00167122556660086}{,}{-0.00160410857177940}{,}{-0.00152263941551208}{,}{-0.00142901280008666}{,}{-0.00132555056860061}{,}{-0.00121466676828613}{,}{-0.00109882185918331}{,}{-0.000980478123049814}{,}{-0.000862059001360759}{,}{-0.000745905238849139}{,}{-0.000634235629773529}{,}{-0.000529117007923929}{,}{-0.000432411558128851}{,}{-0.000345765540157761}{,}{-0.000270566499548717}{,}{-0.000207929579872687}{,}{-0.000158676692163918}{,}{-0.000123323299725022}{,}{-0.000102069285736715}{,}{-0.0000948082004563935}{,}{-0.000101109322005782}{,}{-0.000120250042790877}{,}{-0.000151199645476117}{,}{-0.000192693663470080}{,}{-0.000243201663876019}{,}{-0.000300946862758585}{,}{-0.000364038927860769}{,}{-0.000430369102907126}{,}{-0.000497762721037037}{,}{-0.000563960596181902}{,}{-0.000626678637375343}{,}{-0.000683638243110826}{,}{-0.000732653898292036}{,}{-0.000771600687445201}{,}{-0.000798505127169153}{,}{-0.000811615330369709}{,}{-0.000809342111138219}{,}{-0.000790358227671851}{,}{-0.000753671247528751}{,}{-0.000698496464787393}{,}{-0.000624482125358902}{,}{-0.000531518328123398}{,}{\dots }{,}{\text{⋯ 924 Array entries not shown}}\right]{,}{1}$ (1)
 > $\mathrm{plot}\left(t,c\right)$
 > 

Compatibility

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