WARPED LINEAR PREDICTION FOR IMPROVED PERCEPTUAL QUALITY IN THE SCELP LOW DELAY AUDIO CODEC (W-SCELP)

Transcription

1 ARPED LINEAR PREDICION FOR IMPROVED PERCEPUAL QUALIY IN HE SCELP LO DELAY AUDIO CODEC (-SCELP) Hauke Krüger and Peter Vary Insttute of Communcaton Systems and Data Processng RH Aachen Unversty, D-5256 Aachen, Germany ABSRAC he SCELP (Sphercal Code Excted Lnear Predcton) audo codec, whch has recently been proposed for low delay audo codng [5], s based on lnear predcton (LP). It apples closed-loop vector quantzaton employng a sphercal code whch s based on the Apple Peelng code constructon rule. Frequency warped sgnal processng s known to be benefcal especally n the context of wdeband audo codng based on warped lnear predcton (LP). In ths contrbuton, LP s ncorporated nto the SCELP low delay audo codec. he overall audo qualty of the resultng -SCELP codec benefts from an mproved perceptual maskng of the quantzaton nose. Compared wth exstng standardzed audo codecs wth an algorthmc delay below 1 ms, the -SCELP codec at a data rate of 48 kbt/ outperforms the IU- G.722 codec at a data rate of 56 kbt/ n terms of the achevable audo qualty. 1. INRODUCION Most of the popular audo codecs, e.g. the Advanced Audo Codec (AAC), [1], are based on perceptual audo codng. In perceptual audo codng n general an audo sgnal s at frst transformed by an analyss flter bank. he resultng representaton n the transform doman s quantzed whereas a perceptual model controls the adaptve bt allocaton. Large transform lengths cause a hgh algorthmc delay. Consderng moble communcatons, the approach of lnear predctve codng (LPC) has been followed for many years n speech codng. In LPC, an all-pole flter models the spectral envelope of an nput sgnal. he sgnal s fltered wth the nverse of that all-pole flter to produce the LP resdual whch s quantzed. In the most recently standardzed speech codecs, vector quantzaton (VQ) based on a sparse codebook s appled, followng the CELP (Code Excted Lnear Predcton) analyss-by-synthess prncple, [2]. A well-known example for ths approach s the adaptve mult rate speech codec (AMR), [3]. Due to the sparseness of the codebook and modelng of the speakers nstantaneous ptch perod, speech coders can not compete wth perceptual audo codng for non-speech nput sgnals. he algorthmc delay s n general lower than that n perceptual codng. he new SCELP audo codec targets applcaton scenaros whch requre hgh audo qualty and a very low algorthmc delay, for example dgtal audo transmsson for a wreless headphone. It employs the prncple of combned lnear predcton and vector quantzaton (LP VQ) as known from speech codng. In order to acheve a better perceptual audo qualty than speech coders, a sphercal codebook s employed. he sphercal codebook s constructed accordng to the Apple Peelng prncple. hs prncple was ntroduced n [4] for the purpose of channel codng. In [5] we have proposed an effcent vector search procedure for the sphercal codebook for lnear predctve quantzaton, and n [6] a representaton of the avalable Apple Peelng code vectors as codng trees has been ntroduced. Both technques enable very effcent encodng and decodng wth respect to computatonal complexty and memory consumpton. In [7] t was shown that warped sgnal processng technques are suted to decrease the requred data rate for wdeband audo codng whle retanng the same subjectve audo qualty. LP s employed n a smulated codng system wth D*PCM n that contrbuton. In contrast to that, n ths contrbuton LP wll be ncorporated nto the closed-loop analyss-by-synthess framework of the SCELP codec whch was ntroduced for conventonal LP prmarly. he prncple of the SCELP audo codec and warped lnear predcton wll be ntroduced n Secton 2 and 3 respectvely. he modfcatons requred for the applcaton of LP n analyss-by-synthess VQ n general and the SCELP framework for hghly effcent encodng n partcular are descrbed n Secton 4. Results are presented n Secton 5, ncludng a comparson of the -SCELP codec wth the IU- G.722 [8] low delay audo codec. 2. PRINCIPLE OF HE SCELP AUDIO CODEC he SCELP low delay audo codec s based on block adaptve combned lnear predcton and vector quantzaton: he correlaton mmanent to an nput sgnal s exploted DAFX-1

2 n order to acheve a hgh quantzaton sgnal-to-nose-rato (SNR). For ths purpose, a wndowed segment of the nput sgnal of length L LP s analyzed n order to obtan the N tme-varant flter coeffcents a 1 a N. Based on these LP coeffcents the LP analyss flter wth system functon H A (z) = 1 + N =1 a z converts the nput sgnal nto the LP resdual sgnal d(k) whch s segmented nto N V = L LP /L V N non overlappng sgnal vectors d = [ d d 1 d LV 1] of length LV. Each LP resdual vector s quantzed and transmtted to the decoder as placements Buffer uto code vector ndex Q. For sgnal reconstructon, also the LP laton coeffcents must be transmtted to the decoder. In general nson ths can be realzed wth only small addtonal bt rate as rbn shown for example n [9]. In the decoder, the transmtted code vector ndex Q s the bass for the reconstructon of the quantzed LP resdual vector d whch s fltered by the LP synthess flter H S (z) = (H A (z)) 1. he output of the LP synthess flter s the decoded sgnal vector x and hence [ ] the sgnal [1]. a1 a N he prncple of the encoder of a CELP codec s depcted n Fgure 1. he decoder s part of the encoder. Accordng to P Analyss Decoder nthess VQ codebook d MMSE H s (z) e w, (z) Fgure 1: Scheme SCELP Audo Codec, Encoder. the analyss-by-synthess prncple, the LP resdual vector d for each codebook ndex s generated frst. hs exctaton vector s fltered by the LP synthess flter H S (z) to obtan the correspondng decoded sgnal vector canddates x. he error dstance between the nput sgnal and the decoded sgnal, e = x x, s determned for each vector canddate correspondng to ndex. he goal s to fnd the ndex Q for whch the mnmum mean square error s acheved: Q = arg mn {D = e 2 = (x x ) (x x ) }. (1) he error weghtng flter (z) controls the spectral shape of the quantzaton nose nherent to the decoded sgnal for perceptual maskng of the quantzaton nose. he analyss-by-synthess vector search can be exhaustve for a large vector codebook Sphercal Vector Codebook In the SCELP audo codec, vector quantzaton s appled n a gan-shape approach to encode the LP resdual. Each LP x - x e resdual vector d s decomposed nto a radus for the gan and a vector on the surface of a unt sphere for the shape component. hle the radus R s quantzed by means of logarthmc scalar quantzaton, the vald code vectors for the quantzaton of the shape component are based on the Apple Peelng code constructon rule. hs rule was descrbed and demonstrated for the specal case of a 3-dmensonal sphere n [5]. he desgn target of the Apple Peelng code s to place all codebook vectors on the surface of a unt sphere as unformly as possble. he decoder n CELP codng n general s not very complex. For a low computatonal encodng complexty, the analyss-by-synthess approach n Fgure 1 was modfed n the SCELP encoder as descrbed n [5]. he result s a low complexty vector search framework. Addtonally, the technologes called Pre-Selecton and Canddate-Excluson, combned wth an effcent metrc computaton, enable a very effcent code vector search. Furthermore the representaton of the Apple Peelng code vectors as codng trees was explaned n [6] for the sake of hghly effcent encodng and decodng. 3. ARPED LINEAR PREDICION he prncple and propertes of warped lnear predcton are dscussed n [7]. In ths contrbuton only those aspects that are relevant for the analyss-by-synthess vector search of the SCELP wll be brefly presented. In conventonal lnear predcton the approxmaton of the spectral envelope of a sgnal s based on a unform resoluton of the frequency scale. Consderng the perceptual propertes of human hearng, a unform resoluton s known to be nferor compared to a non-unform resoluton of the frequency scale. For ths purpose, a non-unform resoluton of the frequency scale s acheved by applyng LP. Consderng the z-transform of a sgnal, ths can be realzed by replacng all unt delay elements by an allpass flter, z 1 = z 1 1 z 1 < 1; R (2) For postve values of warpng constant, the spectral resoluton s ncreased for lower and decreased for hgher frequences compared to conventonal LP arped LP Analyss In the SCELP codec the LP analyss s based on the auto correlaton method, as for example descrbed n [1]. In [7], t was shown that for the warped LP analyss, n the auto correlaton method all unt delay elements must be replaced by the frst order allpass flter accordng to (2). Hence the warped auto correlaton coeffcents ϕ w x,x () ϕw x,x (N) are determned as demonstrated for the frst three coeffcents n Fgure 2. arped auto correlaton coeffcents can DAFX-2

3 be transformed nto warped LP coeffcents a w 1 a w N by means of the Levnson Durbn algorthm as n conventonal LP. replacements ϕw x,x() ϕ w x,x (1) Fgure 2: arped LP Analyss. ϕ w x,x(2) 4. LP IN HE SCELP CODEC he propertes of the warped lnear predcton prohbt a straght forward ncorporaton nto the SCELP audo codec. herefore the followng modfcatons must be consdered frst Zero-Delay Path n Feedback Loop A zero-delay path n the feedback loop makes the mplementaton of the LP synthess flter accordng to equaton (3) mpractcal. In contrast to the mplementaton of the warped LP synthess flter n [7], n ths contrbuton [12] the substtuton of C(z) = + (6) 3.2. LP Analyss/Synthess flter For the warped LP analyss and synthess flter, all unt delay elements of the conventonal LP analyss/synthess flter are replaced by allpass flters : N HA w (z) = Hw A () = 1+ a w = (HS w (z)) 1. =1 (3) he flter coeffcents a w are calculated accordng to Secton Error eghtng Flter PSfrag replacements he SCELP audo codec employs an error weghtng flter as proposed n [11]. In conventonal lnear predcton ths error weghtng flter can be calculated from the LP analyss flter: 1/ s appled to the frst allpass flter n the allpass chan of the warped LP synthess flter to remove the zero-delay path. he resultng flter structure s employed for warped LP analyss and synthess flter as depcted n Fgure 3, and also for the error weghtng flter (5). (1 2 ) PSfrag replacements d(k) d(k) C(z) 1 2 (a) LP Analyss Flter - C(z) 1 2 1/ (1 2 ) (b) LP Synthess Flter (z) = H A(z/γ 2 ) H A (z/γ 1 ). (4) he coeffcents γ 1 and γ 2 are wthn the range of γ 1 γ 2 1. and control the degree of nose shapng. th the applcaton of the error weghtng flter, the quantzaton nose nherent to the decoded output sgnal s spectrally shaped accordng to the system functon of the nverse of the error weghtng flter, ( (z)) 1. Consderng LP, all unt delay elements n equaton (4) must be replaced by n the warped error weghtng flter: w (z) = Hw A ( γ 2) H w A ( γ 1). (5) Fgure 3: Modfed Structure for arped LP Flters. As a consequence of the appled substtuton, modfed flter coeffcents N are used n the new LP analyss and synthess flter structure. hese can be calculated from the orgnal coeffcents a w aw N recursvely as N = a w N = a w +1 ; = N 1, ; aw = 1.(7) 4.2. Zero-Mean Property Decorrelaton of an nput sgnal wthout any addtonal amplfcaton s connected to the well-known zero-mean property n conventonal LP [13]. LP does not provde ths DAFX-3

4 property. It can be shown, however, that the LP flters have zero-mean property f the modfed flter coeffcents (7) are normalzed accordng to a w = / = N,,. (8) Consderng Fgure 3, the flter coeffcents must be replaced by the normalzed coeffcents a w, wth the frst coeffcent resultng to a w = Spectral lt Compensaton Due to the non unform resoluton of the frequency scale n warped sgnal processng, the warped LP resdual sgnal s not perfectly flat but contans a spectral tlt [14]. hs spectral tlt nherent to the LP resdual must be compensated pror to quantzaton to acheve the hghest quantzaton SNR n closed-loop LP VQ. For ths purpose the flters accordng to (3), n the structure as depcted n Fgure 3, employng the normalzed coeffcents a w (8), are operated n the cascade wth the tlt compensaton flter Ht w (z) = 1 z 1 (9) replacements to form the overall LP analyss/synthess flter 1 A (z) = Hw A (z) Hw t (z) = (Hw,t S (z)) 1. (1) 4.4. SCELP Low Complexty Vector Search Consderng the analyss-by-synthess prncple, a low complexty vector search procedure s employed n the SCELP codec. It enables to search the large sphercal vector code- n a very effcent way to acheve the low computa- book tonal complexty of the codec. he prncple was ntro- n [5] and s depcted n Fgure 4. duced h 1 h ecursve flter ulse response (z) S/ S= x A (z) C D d flter rngng h w,t B (z) S A search loop codebook d R d MMSE h w,t h w,t E e w Fgure 4: Modfed Analyss-by-synthess. 1 No tlt compensaton s requred for the error weghtng flter because the same warpng factor s used for numerator and denomnator part. x - x Consderng Fgure 4, those functonal blocks whch must be adapted for the applcaton of LP wll be dentfed n the followng: he bass for an effcent vector search n the SCELP s the determnaton of sgnal d pror to the actual analyss-bysynthess vector search procedure. In order to determne ths sgnal, the flter rngng sgnal, marked by the label A, must be obtaned frst. Latter s the flter output resultng from the hstory related to prevously quantzed sgnal frames. Before a new sgnal nput vector x s quantzed, ths hstory s stored as the flter states S. In order to get the vector related to the flter rngng, the flter (z) s fed wth a zero nput sgnal vector of length L V. For the -SCELP, ths flter s dentfed as the cascade of the warped LP synthess flter accordng to (1) and the error weghtng flter accordng to (5): (z) = Hw,t S (z) w (z). (11) In order to obtan sgnal vector d, the flter rngng sgnal vector must be transformed nto the resdual sgnal doman. hs s done n Fgure 4 by means of convoluton, marked as the block h w,t at poston B. h w,t s dentfed as the truncated mpulse response of the nverse of flter (z) (11): h w,t = [h ] w,t, h w,t,(l V ; h w,t 1),k (H w,t (z)) 1 (12) he convolved flter rngng s added to the warped LP resdual d. he LP resdual d s obtaned by flterng x n the warped LP analyss flter A (z), poston C. he resultng sgnal vector d, poston D, s analyzed to determne the correspondng radus R whch s quantzed as R. In the analyss-by-synthess vector search procedure, code vectors d are generated by multplyng the sphercal shapecomponent vector canddates wth the quantzed radus R. Consderng the metrc (1) to fnd the optmal exctaton vector d Q, the unquantzed and the quantzed resdual vector canddate, d and d, both must be transformed from the LP resdual nto the sgnal doman. For ths purpose, the two blocks h w,t, poston E, represent the transform for both sgnals by means of convoluton wth the truncated mpulse response of flter (z) (11): [ ] h w,t = h w,t, hw,t,(l V 1) ; h w,t,k (z) (13) Now that all functonal blocks, whch were ntroduced for the SCELP codec, have been dentfed also for the -SCELP codec, the prncples of Pre-Selecton, the effcent metrc computaton and the Canddate-Excluson explaned n [5] for hghly effcent encodng can be appled also n the - SCELP. th the determnaton of quantzed LP resdual vector d Q, DAFX-4

5 the dfferental sgnal d d Q must be processed by flter H w (z) to fnally determne the update for the flter states S restored for the quantzaton of the next sgnal frame. codec (below 1 ms) 2. he result of the formal comparson of the new codec wth the G.722 reference codec s lsted n able 1 n the order of descendng perceptual qualty. he 4.5. Complexty he computatonal complexty of the warped LP analyss, synthess and error weghtng flter n the -SCELP codec s hgher than that of the same flters realzed for conventonal LP n the SCELP codec. he bggest part of the overall complexty of the SCELP codec, however, s spent on the analyss-by-synthess vector search. Snce the -SCELP benefts from the same prncples targetng low complexty encodng as the SCELP, the overall complexty s only margnally ncreased. he complexty of the encoder of the conventonal SCELP codec was estmated as 2-25 MOPS n [5], that of the encoder of the -SCELP codec as MOPS. he decoder of the -SCELP codec has an estmated complexty of 2-3 MOPS. 5. RESULS For the comparson of the acheved qualty of the -SCELP and the SCELP codec, both codecs have been confgured dentcally for a sample rate of f s = 16 khz. he resultng overall data rate s approxmately 48 kbt/, and the nose shapng coeffcents have been set to γ 1 =.6 and γ 2 =.94. he order of the lnear predcton n both cases s N = 1 and the algorthmc delay L LP ˆ=9 ms. For the -SCELP codec, the hghest performance has been determned for a warpng factor =.46 n nformal lstenng tests. Comparng the predcton gan n -SCELP and SCELP as a measure of sgnal decorrelaton, LP provdes only an nsgnfcantly hgher value. Consderng perceptual maskng of the quantzaton nose, t was observed n nformal lstenng tests that the hgher spectral resoluton of LP for lower frequences provdes sgnfcant benefts. Especally for audo sgnals wth a sparse spectrum, for example the sound of a flute, LP provdes clearly better perceptual results than conventonal LP. Consderng a formal assessment of the qualty, speech was processed by the -SCELP and the SCELP codec. he decoder output was rated wth the B-PESQ measure [15] whch s wdely used n the speech codng communty. As result, the -SCELP outperformed the SCELP by.2 on the MOS scale. Comparable results may also be obtaned usng the PEAQ qualty measure [16]. For a comparson of the -SCELP codec wth a standardzed audo codec, the same speech sgnal was also processed by the IU- G.722 low delay audo codec at 48, 56 and 64 kbt/. hs reference codec was chosen because of ts algorthmc delay n the magntude of that of the -SCELP Codec Data rate B-PESQ (MOS-LQO) G.722 mode 1 64 kbt -SCELP 48 kbt G.722 mode 2 56 kbt G.722 mode 3 48 kbt able 1: Results Formal Qualty Assessment. performance of the G.722 codecs was rated wth 4.2, 4.39 and 4.47 MOS for the three codec modes respectvely. he -SCELP at a data rate of roughly 48 kbt/ reached a value of 4.4 MOS. Consderng ths result, the qualty of the -SCELP codec at 48 kbt/ can be classfed as slghtly better than that of the G.722 at 56 kbt/. 6. CONCLUSION In ths contrbuton the prncple of warped sgnal processng was ncorporated nto the new SCELP low delay audo codec to form the -SCELP codec. hle the overall complexty of the -SCELP s only nsgnfcantly hgher than that of the SCELP codec, the achevable audo qualty s clearly better. In a comparson wth a standardzed codec that has a smlar algorthmc delay, the -SCELP at a data rate of 48 kbt/ outperforms the IU- G.722 audo codec at a data rate of 56 kbt/. 7. REFERENCES [1] ISO/IEC , Advanced Audo Codng (AAC), [2] M. Schroeder and B. Atal, Code-excted Lnear Predcton (CELP): Hgh-qualty Speech at very low Bt Rates, Proc. ICASSP, [3] Rec. GSM 6.9 ESI, Adaptve Mult-Rate (AMR) Speech ranscodng, [4] E. Gamal, L. Hemachandra, I. Spherlng, and V. e, Usng Smulated Annealng to Desgn Good Codes, IEEE rans. Inform. heory, vol. t-33, [5] H. Krüger and P. Vary, SCELP: Low Delay Audo Codng wth Nose Shapng based on Sphercal Vector Quantzaton, EUSIPCO, Florence, Italy, An alternatve codec wth a comparable algorthmc delay s the ULD codec [17]. hs codec, however, s not freely avalable and was thus not consdered. DAFX-5

6 [6] H. Krüger and P. Vary, An Effcent Codebook for the SCELP Low Delay Audo Codec, MMSP, Vctora, Canada, 26. [7] A. Härmä and U. Lane, A Comparson of arped and Conventonal Lnear Predctve Codng, IEEE rans. Speech and Audo Processng, vol. 9, no.5, 21. [8] IU- Rec. G.722, 7 khz Audo Codng wthn 64 kbt/s, [9] K. Palwal and B. Atal, Effcent Vector Quantzaton of LPC Parameters at 24 Bts/Frame, IEEE rans. Speech and Sgnal Proc., vol. 1, no.1, pp. 3 13, [1] N. Jayant and P. Noll, Dgtal Codng of aveforms, Prentce-Hall, Inc., [11] M. Schroeder, B. Atal, and J. Hall, Optmzng Dgtal Speech Coders by Explotng Maskng Propertes of the Human Ear, Journal of the Acoustcal Socety of Amerca, pp , [12] K. Stegltz, A Note on Varable Recursve Dgtal Flters, IEEE rans. Acc., Speech, and Sgnal Processng, vol. 28, 198. [13] J. Markel and A.Gray, Lnear Predcton of Speech, Sprnger, [14] H.. Strube, Lnear Predcton on a arped Frequency Scale, Journal of the Acoustcal Socety of Amerca, vol. 68, pp , 198. [15] IU- Rec. P.862.2, deband Extenson to Recommendaton P.862 for the Assessment of deband elephone Networks and Speech Codecs, 25. [16] Recommendaton IU-R BS.1387, Method for objectve measurements of perceved audo qualty, 21. [17] Audo Codng wth Ultra Low Encodng/Decodng Delay, 27. DAFX-6