Signal reconstruction in ANSDM decoder


 Julian Briggs
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1 Sgnal reconstructon n ANSDM decoder RYSZARD GOLAŃSKI, JACEK KOŁODZIEJ, STANISŁAW KUTA Department of Electroncs AGHUST Unversty of Scence and Technology Al. A. Mckewcza 3, 359 Kraków POLAND Abstract: The decodng problems of the Adaptve Nonunform Samplng Delta Modulaton (ANSDM) system was carred out. The bt error robustness of the delta systems wth samplng nstant and step sze adaptaton have been presented. The analytcal analyss of a parastc sgnal oscllatons, overloadng and dynamc regulaton of the dc level n the reconstructed sgnal, as a consequence of the resynchronzaton process, have been dscussed. All presented analytcal concluson was confrmed by smulaton observatons. In the ssue, the phenomena of mprovng the qualty of the decoded sgnal by Zhu algorthm was showed. KeyWords: Delta modulaton, nonunform samplng, Error compensaton, Robustness.. Introducton Delta modulaton s one of a analog to dgtal converson method that effcently reduces the data rate of a coded source. Contemporary there are same opnons suggested that t s possble achevng the better compresson results of speech sgnals, TV, vdeo real tme converson, realzed by delta converters wth two parameters adaptaton (samplng nstant and quantzaton step sze) [, 2, 3]. Earler analytcal nvestgatons theoretcally showed an mprovement of the qualty of nonstatonary nput process converson due to the applcaton of nonunform samplng [4]. The great advantage of the varablerate delta modulatons s hgh dataprotecton performance [5]. The ANSDM schemes have been proposed and have been studed n [3,6]. Today, many mltary and commercal transmsson systems of voce usng classcal delta modulaton [7]. Specfcatons of WPAN networks (e.g. Bluetooth TM []) employ the lowcost, 64kbps Contnuously Varable Slope Delta (CVSD) modulaton scheme. Several semconductor manufacturers produce specalzed telecommuncaton IC s based on ADM codecs too. A very spectacular applcaton of delta technque has been voce encodng system used n the Shuttle system. It has been chosen by NASA because of ts tolerance to channel errors []. An algorthmc behavor of ADM converters wth samplng and step sze (quantzaton) adaptaton (ANSDM) has not been the object of earler numerous Wreless Personal Area Network low power, low dstance wreless technology for communcaton wth applance( IEEE82.5 []). smulaton or analytcal analyss. The compresson propertes of DM systems are based on a rule that the A/D converson s accomplshed on the removed redundancy from nput process. The effcent samples decorrelaton s usually made usng the adaptaton procedures [, 2]. The step sze adaptaton s the smplest one. The unform samplng ADM systems allow achevng an essental dynamc range of the constant SNR max rato, however ts value s not hgher than n case of Lnear Delta Modulaton [, 2]. It s a result of ths that codng methods wth unform samplng do not utlze all compresson possbltes nvolved wthn the ADM systems []. Algorthmc robustness of ADM converters wth unform samplng already has been the object of numerous smulaton and analytcal nvestgatons [5,6]. The adaptaton decoders that used Jayant, Abate, Song algorthms have been characterzed n detal n the papers [8]. It has been proved that converters wth the syllabc [2] or the nstantaneous Zhu algorthm [3] own the greatest robustness. An mportant problem concernng the delta converter s the process of correct reconstructon of the coded sgnal after losng the synchronzaton. An ANSDM codec output data carres nformaton not only of the sgn dfference between consequence samples, but as well as the step sze value and the nstant value. Any bt error n recever mght cause a parastc sgnal oscllatons, overloadng or dynamc regulaton of the dc level n the reconstructed sgnal. All of menton phenomena has not been the object of numerous smulaton and analytcal nvestgatons so far. Specally the resynchronzaton process, ts end makes good condton to proper sgnals reconstructon. ISSN: ISBN:
2 The bt error robustness of the ANSDM converters wth the Zhu algorthm ("wth return to start values" [3]) has been presented n the paper. The overload and dynamc regulaton of the dclevel that appear n the reconstructed sgnal as an effect of the burst nose (the transmsson gap) have been analyzed. 2. Prncples of ANSDM converson technques The Adaptve Nonunform Samplng Delta Modulaton s a converson technque, where both nternal coder parameters: the step sze and the samplng nstant are adopted (Fg.). Input sgnal changes cause a approprate samplng nstant and step sze adaptve varaton. Ths modulaton has slghtly better codng qualty and SNR s closer to ts maxmum value then NSDM s. output data nput sgnal samplng nterval adaptaton step sze adaptaton approxmatng sgnal both parameters adaptaton Fg.. Tmngs of the ANSDM technque. The ANSDM scheme s smlar to NSDM, t has been proposed and studed n [2,3]. Actually the ANSDM algorthm dffers from conventonal lnear delta modulaton by the addton of the Modfed Interval Functon (MIF) and dffers from the NSDM, by addton the Modfed Stepsze Functon (MSF). As was shown the MIF functon (table) modfes the samplng nterval whle the MSF modfes the step sze accordng to the tmevaryng slope characterstcs of the nput process. In ths way a starcase waveforms ft to the source sgnal better by ANSDM than others delta modulaton (LDM, NSDM). For the nput sgnal x(t) the predcted sgnal s(t ) s gven by expresson: + n= s(t ) = s(t ) k d () where d [ x(t ) s(t )] = sgn and: k th step sze. The output code stream s descrbed by equaton (2). If s s the samplng nstant and s(t ) approxmates sgnal x(t) at th sampled tme t, the samplng nstant s s changed accordng to followng algorthm: P S  for MIF > = Q S  for MIF < s (2) for MIF = where: MIF functon s descrbed by Table ; P, Q are the constant factors of samplng nstant modfcaton, and ther values are: P < <Q. In ths case s s placed between the upper bound and the lower one S mn. The s start samplng nstant and ts value decdes about the average output bt rate (smlar to NSDM). A value of step sze k s gven by: R k for MSF > k = (3) k for MSF = where MSF functon s descrbed by Table ; R s the constant factors of step sze modfcaton and R>. The 3bt Zhu adaptaton algorthm  ANSDM modulaton, could be smply descrbed by the MIF and MSF functon (Table ). The symbols: <, >, mean: decreasng, ncreasng, and comng back to start value of coder parameters. Table. MIF and MSF Tables b b  b 2 S T S  T  MSF MIF < > > < > < H H H H > H H H H H H > H H < > > < > < The ANSDM output bt stream carres the nformaton of not only the changng up or down of the nput sgnal but also of the samplng nstants and the step sze value of the modulator. 3 Delta modulaton and nose mmunty A characterstc feature of classcal delta modulaton wth nonunform samplng s varable output bt stream, that cares nformaton about a samplng nstant. That s why, tme synchronzaton becomes very mportant. In LDM demodulaton process synchronzaton always occurs, because proper decodng process requres only the same ISSN: ISBN:
3 samplng frequency and the dentcal predcton crcut n coder and decoder. A ac component n the reconstructed sgnal s vald (except CFDM Jayant algorthm), wthout any consderaton of the demodulatng process orgn. An asynchronous start of demodulaton relatve to modulaton begnnng causes (lkewse to transmsson gap and bt errors one bt error or seres error) only napproprate dc level reconstructon. In modulaton systems wth nonunform samplng, n order to mmedately achevng vald reconstructon, the nstantaneous samplng tme must be know. Because majorty transmsson cases don t fulfll ths condton, the passng process that leads to tme synchronzaton should be descrbed. There are followng stuatons, that requre a sgnal renewal: after loose of tme synchronzaton, caused by: o errors ntroduce n presence of sgnal or durng slence 2 ; o transmsson gap; after asynchronous recever restart refers to transmtter. Based on smulaton [,5] and analytcal consderatons [,3,5] ware shown, that proper reconstructon s possble and appears when transmsson contans a start nstant 3. Testng the nstablty and nose mmunty of delta modulaton presented n papers [,3], allow to state, that modulatons wth saplng tme adaptaton are error senstve durng slence. The decoder produces then parastc oscllaton, but the processes of actvaton, generaton and fadng are the same n all tree mentoned cases. Next subsecton descrbes the nature of ths dstorton n delta decoder works wth ANSDM 3 bt algorthm. 4 ANSDM nstablty n presence of dsturbance Durng the perod of slence or very low sgnal actvtes, accordng to ANSDM adaptaton algorthm (refer to secton 2), samplng nstant acheves ts maxmum value, but step sze gets ts mnmum value (n ths modulaton step sze s equal the start value q ). It causes sgnfcant reducton of 2 slent the part of coded sgnal, when ts value doesn t changes or the changes are very small. 3 start nstant s a tme value between two followng samples, wthn accordng to Zhu algorthm, coder sets characterstc bt sequence,, appears on the comparator output, refers to subsecton 2 S average bt rate [], but t s a drect reason to come to beng exctaton of harmonc dstorton, after one bt error or transmsson renewal turn up exactly when the s transted (Fg.2). If moment of dsturbance takes place beyond the slence, tme of resynchronzaton s very short and fnshes when n receved data stream the start nstant appears. The sde effect on ts resynchronzaton process s dc level n decoded sgnal. If reconstructon starts wthn slence the probablty of temporary oscllaton s ncreasng. They exert an nfluence at qualty and mpressons of sgnal, but ts degree changes due to modulaton nternal parameters. Takng nto consderaton adaptaton algorthm, and result of spectrum analyss of the dsturbance, can be smply shown, that exctaton frequency f equals: osc f osc =. (4) 2 The peaktopeak value of oscllaton A pp s a functon of remanng modulator parameters: App = f ( P, Q, R,, S mn,, k, kmax ) (5) The process of dsturbance can be fractonze to 3 phase: actvaton, generaton and fadng, as follows (Fg.3): actvaton of oscllaton (transent state) ths s the process from error nstant (or moment of modulator start) to tme of stable generaton of parastc oscllaton. It s consequence of mproper bt recognton, because demodulator actvates adaptaton and changes samplng nstant form to S mn and quantze step form q to q max ; generaton (stable state) demodulator produces harmonc dstorton; fadng (transent state) the harmonc dstorton fade out, the modulator comes to proper trackng of sgnal changes, a agreement occurs drect after start nstant n decoded stream. Each of ths phase was n detal descrbed n [],where author showed that A pp equals: + nadp max = ( + ) + + nmn App q na lg P (6) =, when the adaptaton process hasn t fnshed yet, and: A = q n + + P q + pp namp = ( ) alg P q + ( nadp max + nmn namp ) qmax, (7) ISSN: ISBN:
4 when demodulator works wth ts the greatest value of step sze and samplng. The meanng of varable: n alg  s a number of bts takng nto consderaton by concdence adaptaton algorthm, n amp a number of ampltude adaptaton steps from q to q max, n adpmax number of steps wth samplng nstant adaptaton, n mn number of steps wth mnmum tme nstant. a) Input sgnal transmtter output transmsson lne {b } {Q } recever bnary reconstructed sgnal b) Input sgnal Fg.3. ANSDM modulaton nstablty wth dsturbance phases. The relaton (6) and (7) assgns the upper lmt of dsturbance ampltude, that can be generated by ANS DM decoder. Practcally the tme s long enough to acheved by the A pp maxmum values of reconstructed sgnal (smlar to NSDM decoder [5,]). Fadng phase s connected wth sgnal fluctuaton and starts, when the coder returns to ntal condton. Example: Let assume: a modulaton ANSDM wth S :.2 ms, S mn :.5 ms, :.8 ms, q : % q max : 2%, P:.8, Q:.2, R:.2, that codng sne curve f o = 8 Hz and ampltude A o = V. The converter acheves SNR 9,4 db and BR (bt rate): 5 kb/s, but the tme of full dc level compensaton s.2ms. However synchronzaton requres specal sgnal change lke a jump functon. transmtter output {b } transmsson lne {Q } recever reconstructed sgnal Fg.2. The ANSDM decoder behavor n presence of dsturbance durng slence a) and when sgnal flux are very small b). 3. ANSDM synchronzaton condtons Based on observaton and analyss of the NSDM decodng mechansm, t was affrmed, that resynchronzaton processes after start of the decodng n any poston relatve to the nput data begnnng, and after one bt dstorton n a data transmsson stream, has the runnng n a smlar way [,]. Dependng, whether the decodng begnnng n the slent or out of t, the great dfferences n the operatng of the ANSDM decoder appears. Synchronzaton procedures of the ANSDM decoders wth the Zhu algorthm [Table ] are determned by two basc features: The appearance n nput stream {b } of the tme nterval (for 3bts Zhu algorthm appears after each sequence of bts:,,, ) ISSN: ISBN:
5 At the begnnng of the decodng process the nput streams {b } and the sequence of bts {Q } are not synchronous, but because of the mentoned earler ANSDM decoder features, the synchronzaton between {b } and {Q } streams always comes up to. Generally, the resynchronzaton process conssts of two stages (Fg. 2): ) The appearance of the same sgn bt n the streams {Q } and {b }, and next 2) The begnnng of the bt n the {b } stream wth the opposte sgn to the {Q } sgn, what caused that decoder forces the tme nterval n {Q } stream. If the both stages appear, the tmngs {b } and {Q } come up to the full synchronzaton (Fg.2). 4 Transmsson error nfluence on the reconstructed sgnal qualty The behavor of delta modulator after a transmsson dsturbance durng slence s very smlar to transmsson gap. Ths stuaton should be treated as a partcular case of a channel bt errors, n whch a certan numbers of successve output bts assume the same value (t s smulated as a sequence of the mark "" only or of number "" ). Accordng to the MIF logc (Tab.), the value of the reconstructed sgnal (Fg.3) s decreasng (or ncreasng) durng the gap nstant. The rate of approxmaton slope s greater and greater because adaptaton ncreases the samplng frequency. After the tme perod dependng on the decoder parameters, the approxmatng curve (Fg.3) attans the mnmum (or maxmum) value. If the transmsson gap s contnued, the approxmatng curve keeps, all the tme, the boundary value. When the transmsson gap s termnated, the bts n the Transmsson lne have the values correspondng to the modulated sgnal. Next, the wellknown process of the dynamc shft of the dc level n the electronc crcuts begns and contnues untl the moment when a varable component (ac) of the reconstructed sgnal occurs wthout dstortons. The process of the dc level shftng can be smply explaned. Let us assume that a transmsson gap caused a shft of the approxmatng sgnal to the mnmum value (Fg.3). If now the new coder output bt has the logcal value, the subsequent value of the approxmatng sgnal wll reman equal to the mnmum value 4. If however, the subsequent bt has the logc value, than the value of approxmatng sgnal wll ncrease. As a result, the postve jumps of the output stream wll be converted correctly, whereas from among the negatves ones only those for whch the approxmatng sgnal does not exceed the mnmum value. Ths nonbalance n the proper convertng of the postve and the negatve jumps s contnued untl the moment when the dc level ncreased so much that all negatve jumps can be correctly reconstructed. In partcular case, when the maxmum ampltude of the nput sgnal has the ampltude equal to the half of the range, the dc level (n the establshed state) returns to the zero value. The descrbed behavor of the dc level (elmnatng the cuttng off the peaks of the sgnal) takes place n each method of the delta converson (wth negatve feedback loop). The rate of changes of the dc level beng a result of a transmsson gap depends manly on the sgnal parameters. The ANSDM decoder wth Zhu algorthm after dsappearance of bt errors always leads to resynchronzaton [3],.e. correct reconstructng varable component (ac) of the sgnal. The tme of the ANSDM decoder synchronzaton after the bt errors termnaton does not depend on the fact how long these errors lasted and whch bts were nterfered 5. It can be proved by the followng argumentaton: Algorthms wth return of the samplng nterval to the basc value cause that every equalzaton of the approxmatng and nput sgnals value forces the return of the samplng nterval to ts basc value (Tab.). Consequently, the process of the nput sgnal reconstructng conssts of many ndependent parts whose start and end are determned by the basc value of the samplng nterval. After the bt errors are termnated, each sequence of the bts ndcatng the return of the samplng nstant to the basc value begns the fragment of correct reconstructng, ndependent of the prevous fragments (Fg 3.b). Bt errors that appeared n the prevous fragments do not affect the correct decodng of the ac sgnal component n the new fragments. 4 Smlarly values smaller than the negatve supply voltage cannot be obtaned n the hardware verson. 5 Tme of reganng the synchronzaton by the decoder depends on the fact whch bt was nterfered. Ths tme depends, above all, on the sequence of bts {b },.e. also on the nput sgnal. ISSN: ISBN:
6 In a stuaton when the end of the transmsson gap occurs beyond the socalled slent gap the resynchronzaton tme s very short. The full synchronzaton takes place at the moment of the vald appearance n the Transmsson lne stream" (Fg.3.b). In the opposte case, resynchronzaton takes place only after the end of the slent gap. A detaled descrpton of the prncples of resynchronzaton has been presented n [3]. 5. Summary Analytcal and smulaton nvestgatons of the resynchronzaton procedures n the adaptve delta demodulators wth the nonunform samplng wth two parameters adaptaton have been carred out. The phenomena of overloadng and dynamc regulaton of the dc level n the reconstructed sgnal as a result of transmsson errors have been dscussed. The smulaton was showed that the ANSDM algorthm wth returnng to the basc samplng ntervals and step sze decreases slghtly the exactness of sgnal reconstructon, but reduces the dstortons caused by a channel errors occurred durng the transmsson. After the resynchronzaton, automatc regulaton of the dc level takes place, so that the varable component (ac sgnal) can be reconstructed wthout dstortons. The nature of ths phenomena s analogcal to the automatc regulaton of the quescent pont n amplfers, as well as to the systems wth the dynamc basng. Therefore a proper sgnal fltraton after decodng becomes an mportant task. Dstortons of the ac envelope go on untl the tme of establshng the approprate dc level. The nvestgatons executed so far do not fully solve out the problems concernng all features of the ANSDM modulators. Ths research would allow to state that the concept of returnng to the basc samplng nterval and step sze" mplemented n the ANSDM algorthm allows keepng the hgh qualty and hgh tolerance to channel errors. Monographs No 5, Cracow, 25, ISSN , Poland. [2] C. K. Un, D. H. Cho, Hybrd Compandng Delta Modulaton wth VarableRate Samplng, IEEE Trans. On Comm., vol. COM 3, No. 4, pp , Apr [3] Y. S. Zhu, W. Leung, C. M. Wong, Adaptve NonUnform Samplng Delta Modulaton for Audo/Image Processng, IEEE Trans.Consumer Electron, vol. 42, No.4, pp , Nov.996 [4] Jayant N.S.: Dgtal Codng of Speech Waveforms: DPCM and DM Quantzers. Proceedngs of the IEEE, Vol.62, No. 5, 974, 6632, [5] Golańsk R, Kołodzej J: Transmsson Gaps Influence on Sgnal Reconstructon n the NSDM Decoder, WSEAS TRANSACTIONS On COMMUNICATIONS, Issue 8, Volume 5, August 26, pp , ISSN [6] Golańsk R., Kołodzej J., Nonunform Samplng Delta ConvertersDesgn Methodology, PROCEEDINGS OF THE 5TH WSEAS Internatonal Conference on Electroncs, [7] CML Mcrocrcut, [8] Rheem J.Y., Km B.H., Ann S.G.: A nonunform samplng method of speech sgnal and ts applcaton to speech codng. Sgnal Processng 4, Elsever, 995, [9] Golańsk R, Kołodzej J., Adaptve Rate Delta Codec Desgn and Implementaton, WSEAS TRANSACTIONS ON ELECTRONICS, Issue 3, Volume 3, March 26, ISSN , [] Golańsk R.: Study on the dynamc range of delta modulatons wth tmevaryng samplng perods. IEEE Sgnal Processng Letters, vol., No.8, 24, , [] Kolodzej J.: Hardware mplementaton of delta converters wth adaptve rate samplng, PhD thess, Department of Electroncs, AGHUST Krakow, 27 [2] References: [] Golańsk R., A/D and D/A Delta Converters wth Adaptve Samplng  Methods Analyss and Performance Evaluaton, AGHUnversty of Scence and Technology Publshers, ISSN: ISBN:
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