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...hods are proposed to extract vocal’s melody from accompanied Karaoke tracks bysreducing the interference from the background accompaniments. In parallel, we applysBayesian Information Criterion (BIC) =-=[16]-=- to detect the onset time of each phrase insthe accompanied vocal channel, which enables the subsequent DTW-based similarityscomparison to be performed more efficiently. The proposed system further us...

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...s shown in Fig. 4(a), the computational complexity in terms of the number of thesnecessary distance computation D(⋅) for constructing a T×L table iss. 4 )( 2 2 2 2 22 LTTL LLTTLTComplexity +−= ×−×−×=s=-=(15)-=-sAs mentioned earlier, since L is usually set to be kT, where , thescomputational complexity can be rewritten ass22/1 ≤≤ k . 4 )14( 22 TkkComplexity −−=s(16)sAlthough the DTW recursion allows a docume...

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...al DTW.sSince the complexity is O(T 2 ), the most promising way to speed up the searchingsprocess is to reduce the value of T. Motivated by Keogh and Pazzani’ssPiecewisesAggregate Approximation (PAA) =-=[14]-=-, we propose a dimensionality reductionstechnique, called Multi-Level Data Abstraction (MLDA). Unlike PAA, which dividessa time series into equal-length frames, and then calculates the mean value of t...

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...ween mt and m′t. The optimal b can besfound by choosing one of the possible values within a pre-set range, B, that results insthe smallest estimation error, i.e.,s||minarg* * btbt BbB ab +≤≤− −= mc ,s=-=(1)-=-swheresis the optimal amplitude scaling factor given mt+b. Letting ∂|ct −sabmt+b|2/∂ab = 0, we have a minimum mean-square-error solution of ab ass* ba . |||| 2 * bt btt ba + +′= m mcs(2)sAccordingly, ...

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...nventory of possiblesnotes performed by a singer, and xt,j denote the signal’s energy with respect to FFTsindex j in frame t, where 1 ≤ j ≤ J. The sung note of a recording in frame t issdetermined bys=-=(3)-=- ,smaxarg 0 12 , 1 ⎟⎠ ⎞⎜⎝ ⎛= ∑ = +≤≤ C c cnt c t yho Nn where C is a pre-set number of harmonics concerned, h is a positive value less than 1sfor discounting higher harmonics, and yt,n is the signal’s...

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... L, wheresD(t, l) is the distance between note sequences {q1, q2,…, qt} and {u1, u2,…, ul},scomputed using:s,s),()2,1( ),()1,1( ),(2)1,2( min),( ⎪⎩ ⎪⎨ ⎧ +−− −+−− ×+−− = ll ll ll l tdtD tdtD tdtD tD εs=-=(9)-=-sandsd(t, l) = | qt − ul| ,s(10)swhere ε is a small constant that favors the mapping between notes qt and ul, given thesdistance between note sequences {q1, q2,…,qt-1} and {u1, u2,…, ul-1}.sTo compens...

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... dropout errors, note insertionserrors, etc. To handle these errors, various approximate matching methods, such assdynamic time warping (DTW) [5][11-12], hidden Markov model [13], and N-gramsmodel [8]=-=[10]-=-, have been studied, with DTW being the most popular. However, duesto the considerable time consumption for DTW, another key issue on designing asquery-by-singing MIR system is how to speed up the sim...

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...sted note sequence o′ =s{o′1, o′2,…, o′T } is obtained bys⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ ⎨ ⎧ −<−⎥⎦ ⎥⎢⎣ ⎢ −−×− >−⎥⎦ ⎥⎢⎣ ⎢ +−×− ≤− =′ , )2/(sif,s12 2/12s)2/(sif,s12 2/12 )2/(||ifs,sRooRooo RooRooo Rooo o t t t t t t tt ts=-=(6)-=-swhere R is the normal varying range of the sung notes in a sequence, say 22, and osissthe mean note computed by averaging all the notes in o. In Eq. (6), a note ot issconsidered as a wrong note and n...

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...ote dropout errors, note insertionserrors, etc. To handle these errors, various approximate matching methods, such assdynamic time warping (DTW) [5][11-12], hidden Markov model [13], and N-gramsmodel =-=[8]-=-[10], have been studied, with DTW being the most popular. However, duesto the considerable time consumption for DTW, another key issue on designing asquery-by-singing MIR system is how to speed up the...

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...rs,sa sung query may contain inevitable tempo errors, note dropout errors, note insertionserrors, etc. To handle these errors, various approximate matching methods, such assdynamic time warping (DTW) =-=[5]-=-[11-12], hidden Markov model [13], and N-gramsmodel [8][10], have been studied, with DTW being the most popular. However, duesto the considerable time consumption for DTW, another key issue on designi...

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...w phrase onset time t′os as tos-r/2, clone the subsequencesof notes of a music document starting from t′os with a length L of kT+r to u, andsdefine the boundary conditions for the DTW recursion as,s.s=-=(11)-=-s)2,3(2)1,1()2,3( 1, 12),,2()1,1( ),2( , 1),,1( ),1( 4,)2,( 2,)1,( )1,1()1,1( ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ ⎨ ⎧ ×+= ⎩⎨ ⎧ ≤<+∞ +≤≤+−= ⎩⎨ ⎧ ≤<∞ ≤≤= ≤≤∞= ≤≤∞= = ddD Llr rdd D Llr rd D TttD TttD dD llll lll After the...

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... number of harmonics concerned, h is a positive value less than 1sfor discounting higher harmonics, and yt,n is the signal’s energy on note en in frame t,sestimated bys,smax ,, )( , jtnnt xy ejUj =∀=s=-=(4)-=-sands, 5.69 440 )(log12)( 2 ⎥⎦ ⎥⎢⎣ ⎢ +⎟⎠ ⎞⎜⎝ ⎛⋅= jFjUs(5)swhere ⎣ ⎦sis a floor operator, F(j) is the corresponding frequency of FFT index j, andsU(⋅) represents a conversion between the FFT indices an...

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... +≤≤− −= mc ,s(1)swheresis the optimal amplitude scaling factor given mt+b. Letting ∂|ct −sabmt+b|2/∂ab = 0, we have a minimum mean-square-error solution of ab ass* ba . |||| 2 * bt btt ba + +′= m mcs=-=(2)-=-sAccordingly, the underlying vocal signal in frame t can be estimated bysst = ct − mt+b*. Fig. 2(c) shows the resulting waveform of the accompanied vocalschannel after background music reduction. We c...

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...+−= ⎩⎨ ⎧ ≤<∞ ≤≤= ≤≤∞= ≤≤∞= = ddD Llr rdd D Llr rd D TttD TttD dD llll lll After the distance matrix D is constructed, the similarity between q and u can besevaluated bys).,(min),( 2/ l l TDS LT ≤≤=uqs=-=(12)-=-s5.2 Multiple-Pass DTW to Improve Retrieval AccuracysSince a query may be sung in a different key or register than the target musicsdocument, i.e., the so-called transposition, the resulting note sequ...

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...ote Sequence GenerationsAfter reducing the undesired background accompaniments, the next step is to convertseach recording from its waveform representation into a sequence of musical notes.sFollowing =-=[7]-=-, the converting method begins by computing the short-term FastsFourier Transform (FFT) of a signal. Let e1, e2,…, eN be the inventory of possiblesnotes performed by a singer, and xt,j denote the sign...

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...vitable tempo errors, note dropout errors, note insertionserrors, etc. To handle these errors, various approximate matching methods, such assdynamic time warping (DTW) [5][11-12], hidden Markov model =-=[13]-=-, and N-gramsmodel [8][10], have been studied, with DTW being the most popular. However, duesto the considerable time consumption for DTW, another key issue on designing asquery-by-singing MIR system ...