Fractal Sinusoidal Modelling For Low Bit-Rate Audio Coding

Transcription

1 Frctl Sinusoidl Modelling For Low Bit-Rte Audio Coding Author Mrks, Sturt, Gonzlez, Ruen Pulished 25 Conference Title Proceedings of the 8th Interntionl Symposium on DSP nd Communiction Systems, DSPCS'25 Copyright Sttement 25 IEEE. Personl use of this mteril is permitted. However, permission to reprint/ repulish this mteril for dvertising or promotionl purposes or for creting new collective works for resle or redistriution to servers or lists, or to reuse ny copyrighted component of this work in other works must e otined from the IEEE. Downloded from Griffith Reserch Online

2 FRACTAL SINUSOIDAL MODELLING FOR LOW BIT-RATE AUDIO CODING Sturt K. Mrks, Ruen Gonzlez School of Informtion Technology Griffith University PMB 5, Gold Cost Mil Centre, QLD, 9726, Austrli ABSTRACT This pper proposes frctl sinusoidl model tht is le to reduce the it-rte of sinusoidl model coders while chieving perceptully lossless qulity. This is chieved y removing the redundncy etween sinusoidl trcks through encoding similr trcks with the trnsformtion etween templte trck nd the originl trck. This pper proposes trnsform tht is le to cpture the perceptul nture of sinusoidl trcks, nd cn e encoded efficiently. The results from our experiments show tht the proposed frctl sinusoidl model coder is le to reduce the it-rte of the sinusoidl model y roughly 3% while remining perceptully lossless, while more ggressive modelling results in reduction of round 6%, with minor qulity degrdtion. INTRODUCTION Sinusoidl model udio coders [] hve een shown to e le to produce high-qulity udio t low it-rtes [2,3,4]. These efforts were driven y the inility of other coding techniques, e.g. trnsform coders, to chieve good qulity udio t these low it-rtes. In this pper we further reduce the it-rte of sinusoidl model coders y pplying frctl modelling to remove the self-similrities etween sinusoidl trcks. Frctl coding opertes on ojects; these ojects re referred to s frctls nd hve self-similrity. The gol of frctl coding is to recrete ojects y utilising the self-similrity to encode the dt. With frctl imge coding, pttern is found tht cn e used to itertively reconstruct the originl oject. This is clled n Iterted Function System (IFS), consisting of n ttrctor (pttern) nd collge ( specifiction of the required itertions). The collge consists of itertions of ffine trnsformtions tht re used to scle, rotte or stretch the [5]. Once suitle ttrctor cn e found frctl imge codes enle flexile coding schemes tht cn produce low it-rtes. These chrcteristics re lso eneficilly for udio coding, however frctl udio coding hs not een studied, except for the work of Wnnmker nd Vrscy [6] tht investigted the use of frctl coding to efficiently encode the wvelet coefficients for wvelet udio coder. This pper exmines how frctl modelling cn e pplied to the encoding of mid-level udio representtions to improve the performnce of model coders. In this work we use sinusoidl trcks s our mid-level udio representtion due to their high perceptul importnce in model udio coding. It should e noted, however, tht the sme pproch could e used with other mid-level representtions, such s those used to represent trnsient nd noise components of n udio signl. Sinusoidl modelling genertes sinusoidl trcks. Perceptully, trcks re ojects tht follow the evolution of single prtil or hrmonic. Trcks re used with sinusoidl model s they improve the reconstruction qulity while reducing the it-rte [7]. Sinusoidl trcks re highly similr, nd this similrity represents redundncy tht cn e removed to further reduce the it-rte of sinusoidl model coders. The pproch tken in this pper is to perform frctl modelling on sinusoidl trcks to reduce the itrte of udio coding. Frctl modelling encodes sinusoidl trcks s the trnsform from templte trck. This pproch hs high coding efficiency when the trnsform cn e encoded with significntly fewer its thn the originl trck. This pper proposes such trnsform. The pper will egin with description of the proposed frctl sinusoidl modelling technique, with prticulr emphsis on the trnsform tht fcilittes high coding efficiency. Then the results otined y encoding udio smples using the frctl sinusoidl model coder will e presented, with the finl section providing the conclusions of the pper.

3 2 FRACTAL SINUSOIDAL MODELLING Frctl sinusoidl modelling reduces the it-rte of udio coding y removing the redundncy tht is present due to the similrity etween sinusoidl trcks. This is chieved y encoding the trnsform from templte trck to the originl trck. We modelled the trnsform off sensile modifictions of sinusoidl trcks, sed on their perceptul nture. The trnsform provides mpping opertors for frequency shift, mplitude gin, phse offset, time trnsltion nd time diltion of sinusoidl trcks. Figure 2. demonstrtes how this cn e chieved for two similr trcks in the frequency-time plne, with trck eing replic of trck tht is delyed y Δ t smples nd is frequency shifted y Φ f. Similr mppings exist in the mplitude-time nd phse-time plnes, s well s for trck durtion. shift, which mps the difference etween trcks in the frequency plne. The rgument is clculted using the verge frequency estimte from ech trck s is shown in () where N x is the numer of estimtes in trck x, nd ˆ is the i th frequency estimte in trck x. Φf f i, x N fˆ ˆ N f i= men, = = () N fˆ men, fˆ N i= The time trnsltion opertor llows trcks to occur t different times. The rgument is clculted from the difference of the trck onset times. This is demonstrted in (2) where t, x is the time of the first estimte in trck x. Δt = t, t, = onset onset (2) The durtion of trcks cn lso vry; the time diltion opertor mps this vrition. The rgument is determined y the rtio of trck durtions, s is shown in (3). Φt ( t N t ),, ( t t ) = (3) N,, Figure 2.. Frctl modelling of two similr sinusoidl trcks in the time-frequency plne. These trnsform opertors cn e encoded cheply, ut do not provide perfect trck reconstruction. As will e shown in section 3 this is not detrimentl s sinusoidl trcks re not idel representtions themselves. They re sed off sequence of sinusoidl estimtes, nd smll mount of error will not e udile. It ws lso found tht the error etween the reconstructed trck nd the originl could e determined y the similrity etween the templte nd originl trcks, providing mens for mnging the modelling error. The reminder of this section will exmine the components of the frctl sinusoidl model in more detil. This includes the opertors tht define the trnsform nd similrity metric. 2. Trnsform The five trnsform opertors tke sclr rguments which re clculted from the difference etween the estimtes from the templte trck, trck, nd the originl trck, trck. The first opertor is frequency Work conducted for the MPEG-4 high qulity prmetric coder hs shown tht the phse trjectory is chrcterised from the initil phse estimte nd the sequence of frequency estimtes [8]. Therefore the vrition in phse trjectory etween trcks cn e determined from the initil phse offset. The phse offset opertor does this precisely, with the rgument eing clculted using (4) where ˆ θ, x is the first phse estimte of trck x. Δθ = θˆ θˆ (4),, The finl opertor ccounts for the vrition in mplitude etween trcks. The rgument for the mplitude gin opertor uses the verge mplitude estimte from ech trck to determine the rgument; this is shown in (5). ΦA N Aˆ ˆ N A i= men, = = (5) N Aˆ men, Aˆ N i= Using these opertors trck cn e recreted from templte trck (6).

4 trck T ( Φf, Δt, Φt, Δθ, A) Φ trck trck (6) Trcks re recreted from the templte trck y copying ech estimte nd djusting the prmeters using the opertor rguments. The mplitude estimtes re scled y Φ A, nd the frequency estimtes re scled y Φ f. The initil phse estimte is determined y dding the phse offset, Δ θ, to the initil phse estimte of the templte trck, then the sequence of phse estimtes is predicted using the frequency estimtes. The time of the estimtes is shifted y Δ t smples. This process continues until the trck grows to the desired durtion, s defined y Φ t. This ssumes tht the templte trck is longer thn the originl trck, so the time diltion must e in the rnge of < Φt. The recreted trck will e equivlent to the originl if the two trcks re highly similr; otherwise the recreted trck will not e equivlent to the originl trck. The next susection presents technique for determining the similrity etween trcks tht enles the trck recretion error to e mnged. Using this similrity metric the similrity etween trck comintions cn e mesured. Figure 2.2 provides the similrity coefficient mesured for every trck generted from pino chord ginst the 5 th trck. It shows tht trcks 5, 7 nd 6 re similr, nd thus cn e modeled off ech other. A similrity threshold, σ T, cn e used to determine when trck comintion hs dequte similrity, nd will result in low-error trck recretion. For this pper glol serch for similrities is employed, s our udio smples re reltively short t round 3 seconds ech. Oviously glol serch is not prcticl for longer udio smples; in this cse locl serch would e eneficil. From our experimenttion, it ppers tht this would not e detrimentl to performnce s similr trcks re loclised in time. 2.2 Similrity Metric We mesure the similrity etween two trcks y using the perceptul mesure proposed y Virtnen nd Klpuri [9]. It mesures the distnce etween normlised frequency nd mplitude trjectories. This is eneficil s it utomticlly ccounts for frequency shift nd mplitude gin. The distnce metric (7) mesures the difference etween frequency or mplitude estimtes over the durtion of the shortest trck. d x ( ) () t x () t T x, = (7) T t= xmen x, men, A similrity coefficient, σ, is then clculted from the distnce of the frequency nd mplitude trjectories, s is shown in (8). The similrity coefficient lies within the rnge of σ, with high coefficients indicting high similrity etween the trcks. The α, β nd ρ coefficients re used to djust the similrity mesurement performnce nd is. From experimenttion it ws found tht n unised similrity coefficient, with α =. 5, performed est s informtion from the frequency nd mplitude trcks re eqully s importnt. It ws lso found tht setting β = ρ = gve the est seprtion etween similr nd non-similr sinusoidl trcks. σ (, ) βd f (, ) ρd, = αe + α e (8) 2 ( ) ( ) Figure 2.2. Similrity plot for trck 5 of n udio smple of pino chord. This demonstrtes tht trcks 5, 7 nd 6 re similr. 3 RESULTS To determine the performnce of the frctl sinusoidl model coder numer of udio smples were encoded using the proposed coder. The coder uses multiresolution sinusoidl nlysis [] to generte the sinusoidl trcks. This includes the use of CFB filter nk, sinusoidl estimtion using qudrtic interpoltion, multiresolution sinusoidl trcking [] nd interpolting oscilltors for synthesis. The similrity metric is used to glolly serch ll trcks for similrity. When the similrity is ove similrity threshold, σ T, the trck is encoded using the frctl model t cost of ytes (6 its per opertor rgument). Otherwise the trck is encoded using DPCM techniques s presented in [2,3,2]. The similrity threshold is the prmeter tht defines the rte-distortion performnce of the frctl sinusoidl model coder, with high threshold vlues improving qulity ut providing little reduction in itrte, nd low threshold vlues decresing the qulity

5 while significntly reducing the it-rte. Our experiments investigted the performnce of the coder ginst this prmeter. Figure 3. shows the numer of trcks tht re encoded using frctl modelling s the similrity threshold is djusted. When more trcks re encoded using frctl modelling the reduction in it-rte increses, s is illustrted in the right plot of Figure 3.. Further reduction would e seen y entropy encoding the opertor rguments, nd remins s further work. The originl it-rte for the sinusoidl model coding is specified in Tle for ech smple used. Tle. The itrte (Kps per chnnel) for the originl sinusoidl modelled smples, nd the corresponding it-rtes for 3% nd 6% itrte reduction. The high vlues for the Led Zeppelin smple re due to the lrge mount of trnsient signl energy present in this smple. While it could e rgued tht similr reduction in it-rte could e chieved y limiting the numer of encoded trcks, from our experiments this pproch should e voided s it cretes udio which egins to sound synthetic due to the lost signl components. The enefit of the frctl sinusoidl model is tht it provides chep method for encoding trcks, insted of removing trcks completely. The frctl sinusoidl model is le to provide signl reconstruction tht hs perceptully lossless qulity t low it-rtes. Figure 3.. Percentge of trcks modelled (left) nd it-rte reduction (right) mesured ginst the similrity threshold. Four stereo udio smples were used, nd the error rs indicte the 95% confidence intervl of the mesurements. The smples were reconstructed fter frctl sinusoidl modelling to determine their perceptul qulity. Perceptul qulity experiments were conducted for ech of the four smples listed in Tle using the ITU-R BS.6- [3] test method. The reference signl ws the reconstructed signl fter sinusoidl modelling. The results for ten sujects re presented in Figure 3.2. The results indicte tht the frctl sinusoidl model is le to provide lossless qulity t σ T =. 9, with the sujects unle to differentite etween the originl sinusoidl modelled nd frctl modelled smples. The verge reduction t this threshold ws 28.9% cross the four smples. More ggressive modelling, σ T. 8, provides slight reduction is qulity, with the sujects eing le to perceive the difference etween the originl nd modelled smples. At these thresholds the it-rte reduction reches up to 6% on verge. Smple Originl 3% 6% Jck Johnson Jmiroqui Led Zeppelin Mozrt Figure 3.2. Men perceptul qulity of the reconstructed udio smples from the frctl sinusoidl model coder. The error rs represent the 95% confidence intervl. 4 CONCLUSION This pper presented frctl sinusoidl model coder tht is le to efficiently encode sinusoidl trcks y encoding the trnsformtion from templte trcks. A trnsform ws presented tht could e efficiently encoded, ut is lso cple of cpturing the perceptul chrcteristics of the sinusoidl trcks. This resulted in roughly 3% reduction in it-rte while providing perceptully lossless qulity for conservtive modelling. While more ggressive modelling results in round 6% it-rte reduction with minor qulity degrdtion. 5 ACKNOWLEDGEMENTS Austrlin Reserch Council s Spirt Scheme, ActiveSky Inc.

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