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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

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $\mathrm{f1}≔12.0:$
 > $\mathrm{f2}≔20.0:$
 > $\mathrm{Fs}≔1000:$
 > $\mathrm{signal}≔\mathrm{Vector}\left({2}^{10},i→\mathrm{sin}\left(\frac{\mathrm{f1}\cdot 2\mathrm{Pi}i}{\mathrm{Fs}}\right)+1.5\mathrm{sin}\left(\frac{\mathrm{f2}\cdot 2\mathrm{Pi}i}{\mathrm{Fs}}\right),'\mathrm{datatype}'='{\mathrm{float}}_{8}'\right):$
 > $t≔\mathrm{Vector}\left({2}^{10},i→\frac{1.0i}{\mathrm{Fs}},'\mathrm{datatype}'='{\mathrm{float}}_{8}'\right):$
 > $\mathrm{plot}\left(t,\mathrm{signal}\right)$
 > $c,\mathrm{nd}≔\mathrm{ComplexCepstrum}\left(\mathrm{signal}\right)$
 ${c}{,}{\mathrm{nd}}{≔}\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}{0.145868794568315}& {-}{0.00210915153424983}& {-}{0.00195907093568577}& {-}{0.00178456266462854}& {-}{0.00158722980572758}& {-}{0.00136900765256120}& {-}{0.00113213114331282}& {-}{0.000879117825724025}& {-}{0.000612728339790145}& {-}{0.000335934856947447}& {-}{0.0000518692285805590}& {0.000236197915118234}& {0.000524918779904637}& {0.000810908961643890}& {0.00109079348274120}& {0.00136125182569238}& {0.00161907099400066}& {0.00186117875125773}& {0.00208470189279642}& {0.00228698458099978}& {0.00246565146703437}& {0.00261861936625991}& {0.00274413853802192}& {0.00284081144739502}& {0.00290761023539309}& {0.00294389874606536}& {0.00294943045953131}& {0.00292435611527912}& {0.00286922116621864}& {0.00278495305332948}& {0.00267284751323420}& {0.00253456066103722}& {0.00237204750856878}& {0.00218758607926743}& {0.00198369895676667}& {0.00176313243360697}& {0.00152882137405683}& {0.00128383474591313}& {0.00103134012640191}& {0.000774547137475045}& {0.000516676275508860}& {0.000260892407280031}& {0.0000102815082253819}& {-}{0.000232212523021449}& {-}{0.000463806015781688}& {-}{0.000681945070966349}& {-}{0.000884314055822069}& {-}{0.00106887244974803}& {-}{0.00123388950018436}& {-}{0.00137795715273694}& {-}{0.00150000247072595}& {-}{0.00159931422961690}& {-}{0.00167552962725953}& {-}{0.00172864562943142}& {-}{0.00175900613817886}& {-}{0.00176729411119746}& {-}{0.00175451642643904}& {-}{0.00172196622085345}& {-}{0.00167122556969059}& {-}{0.00160410857054620}& {-}{0.00152263941865678}& {-}{0.00142901279894585}& {-}{0.00132555057158262}& {-}{0.00121466676701493}& {-}{0.00109882186179677}& {-}{0.000980478121445168}& {-}{0.000862059003425795}& {-}{0.000745905236741439}& {-}{0.000634235631148726}& {-}{0.000529117005187834}& {-}{0.000432411558720843}& {-}{0.000345765536720262}& {-}{0.000270566499318680}& {-}{0.000207929575717542}& {-}{0.000158676691130008}& {-}{0.000123323294893250}& {-}{0.000102069283972729}& {-}{0.0000948081950428682}& {-}{0.000101109319635815}& {-}{0.000120250036937223}& {-}{0.000151199642665849}& {-}{0.000192693657354289}& {-}{0.000243201660821141}& {-}{0.000300946856582390}& {-}{0.000364038924773243}& {-}{0.000430369096881504}& {-}{0.000497762718130480}& {-}{0.000563960590512271}& {-}{0.000626678634850097}& {-}{0.000683638237982436}& {-}{0.000732653896321379}& {-}{0.000771600683010236}& {-}{0.000798505125887401}& {-}{0.000811615326736553}& {-}{0.000809342110631514}& {-}{0.000790358224897619}& {-}{0.000753671247829358}& {-}{0.000698496462873906}& {-}{0.000624482126442998}& {-}{0.000531518327017009}& {\mathrm{...}}& {"... 924 Array entries not shown"}\end{array}\right]{,}{1}$ (1)
 > $\mathrm{ic}≔\mathrm{InverseComplexCepstrum}\left(c,\mathrm{nd}\right)$
 ${\mathrm{ic}}{≔}\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}{0.263326656101111}& {0.523260420096627}& {0.776457590194615}& {1.01967209313065}& {1.24980243126404}& {1.46393642635575}& {1.65939306650029}& {1.83376083760918}& {1.98493193974933}& {2.11113188185542}& {2.21094399497925}& {2.28332852606907}& {2.32763599316731}& {2.34361463223136}& {2.33141182829740}& {2.29156952332947}& {2.22501367935942}& {2.13303799035641}& {2.01728208534914}& {1.87970460731090}& {1.72255155526800}& {1.54832043819712}& {1.35972077512268}& {1.15963158302414}& {0.951056516624380}& {0.737077356905143}& {0.520806593587941}& {0.305339827356360}& {0.0937087395306547}& {-}{0.111164635804138}& {-}{0.306511632728988}& {-}{0.489757998557749}& {-}{0.658561591672619}& {-}{0.810846232986650}& {-}{0.944831102083287}& {-}{1.05905529637504}& {-}{1.15239717044663}& {-}{1.22408815751023}& {-}{1.27372089655184}& {-}{1.30125154158349}& {-}{1.30699626259241}& {-}{1.29162198559060}& {-}{1.25613158056652}& {-}{1.20184371653216}& {-}{1.13036776447712}& {-}{1.04357412041345}& {-}{0.943560495031750}& {-}{0.832614691044060}& {-}{0.713174480141898}& {-}{0.587785250837211}& {-}{0.459056110222249}& {-}{0.329615138208784}& {-}{0.202064551389618}& {-}{0.0789364735762283}& {0.0373499529382165}& {0.144529432442659}& {0.240528694143745}& {0.323501354830963}& {0.391858941910938}& {0.444297525073816}& {0.479819566426345}& {0.497750621359420}& {0.497750621480023}& {0.479819566579856}& {0.444297524366212}& {0.391858940431624}& {0.323501353383734}& {0.240528692815891}& {0.144529432136081}& {0.0373499523384172}& {-}{0.0789364752688140}& {-}{0.202064553190823}& {-}{0.329615140219101}& {-}{0.459056112058297}& {-}{0.587785252699792}& {-}{0.713174480347811}& {-}{0.832614692893752}& {-}{0.943560496841576}& {-}{1.04357412148283}& {-}{1.13036776362137}& {-}{1.20184372074904}& {-}{1.25613158386973}& {-}{1.29162198197573}& {-}{1.30699626307110}& {-}{1.30125154014867}& {-}{1.27372089521281}& {-}{1.22408815725696}& {-}{1.15239716928589}& {-}{1.05905529329371}& {-}{0.944831102985633}& {-}{0.810846232056475}& {-}{0.658561586811886}& {-}{0.489757997847372}& {-}{0.306511631169004}& {-}{0.111164627672920}& {0.0937087402344454}& {0.305339832256410}& {0.520806590086270}& {0.737077359026905}& {0.951056524871455}& {\mathrm{...}}& {"... 924 Array entries not shown"}\end{array}\right]$ (2)
 > $\mathrm{plot}\left(t,\mathrm{ic}\right)$
 > 

Compatibility

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