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SignalProcessing

 InverseComplexCepstrum
 compute the inverse complex cepstrum of the signal

 Calling Sequence InverseComplexCepstrum(A, nd)

Parameters

 A - Array of real numeric values; the signal nd - integer the number of samples of delay

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $\mathrm{f1}≔12.0:$
 > $\mathrm{f2}≔20.0:$
 > $\mathrm{Fs}≔1000:$
 > $\mathrm{signal}≔\mathrm{Vector}\left({2}^{10},i↦\mathrm{sin}\left(\frac{2\cdot \mathrm{f1}\cdot \mathrm{\pi }\cdot i}{\mathrm{Fs}}\right)+1.5\cdot \mathrm{sin}\left(\frac{2\cdot \mathrm{f2}\cdot \mathrm{\pi }\cdot i}{\mathrm{Fs}}\right),'\mathrm{datatype}'='\mathrm{float}\left[8\right]'\right):$
 > $t≔\mathrm{Vector}\left({2}^{10},i↦\frac{1.0\cdot i}{\mathrm{Fs}},'\mathrm{datatype}'='\mathrm{float}\left[8\right]'\right):$
 > $\mathrm{plot}\left(t,\mathrm{signal}\right)$
 > $c,\mathrm{nd}≔\mathrm{ComplexCepstrum}\left(\mathrm{signal}\right)$
 ${c}{,}{\mathrm{nd}}{≔}\left[{0.145868794568315}{,}{-0.00210915153424963}{,}{-0.00195907093568552}{,}{-0.00178456266462847}{,}{-0.00158722980572774}{,}{-0.00136900765256142}{,}{-0.00113213114331287}{,}{-0.000879117825723876}{,}{-0.000612728339790005}{,}{-0.000335934856947660}{,}{-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}{,}{-0.000232212523021458}{,}{-0.000463806015781722}{,}{-0.000681945070966373}{,}{-0.000884314055822090}{,}{-0.00106887244974806}{,}{-0.00123388950018437}{,}{-0.00137795715273697}{,}{-0.00150000247072594}{,}{-0.00159931422961691}{,}{-0.00167552962725953}{,}{-0.00172864562943142}{,}{-0.00175900613817884}{,}{-0.00176729411119747}{,}{-0.00175451642643903}{,}{-0.00172196622085344}{,}{-0.00167122556969059}{,}{-0.00160410857054618}{,}{-0.00152263941865677}{,}{-0.00142901279894585}{,}{-0.00132555057158261}{,}{-0.00121466676701490}{,}{-0.00109882186179676}{,}{-0.000980478121445167}{,}{-0.000862059003425817}{,}{-0.000745905236741443}{,}{-0.000634235631148718}{,}{-0.000529117005187840}{,}{-0.000432411558720841}{,}{-0.000345765536720265}{,}{-0.000270566499318687}{,}{-0.000207929575717559}{,}{-0.000158676691130030}{,}{-0.000123323294893262}{,}{-0.000102069283972735}{,}{-0.0000948081950428617}{,}{-0.000101109319635814}{,}{-0.000120250036937225}{,}{-0.000151199642665856}{,}{-0.000192693657354294}{,}{-0.000243201660821129}{,}{-0.000300946856582380}{,}{-0.000364038924773236}{,}{-0.000430369096881509}{,}{-0.000497762718130473}{,}{-0.000563960590512264}{,}{-0.000626678634850111}{,}{-0.000683638237982438}{,}{-0.000732653896321378}{,}{-0.000771600683010226}{,}{-0.000798505125887405}{,}{-0.000811615326736579}{,}{-0.000809342110631509}{,}{-0.000790358224897612}{,}{-0.000753671247829356}{,}{-0.000698496462873895}{,}{-0.000624482126443007}{,}{-0.000531518327017009}{,}{\dots }{,}{\text{⋯ 924 Array entries not shown}}\right]{,}{1}$ (1)
 > $\mathrm{ic}≔\mathrm{InverseComplexCepstrum}\left(c,\mathrm{nd}\right)$
 ${{\mathrm{_rtable}}}_{{18446884617788503094}}$ (2)
 > $\mathrm{plot}\left(t,\mathrm{ic}\right)$
 > 

Compatibility

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