Implementation of IMDCT Block of an MP3 Decoder through Optimization on the DCT Matrix

Transcription

1 22 M. GALABOV, IMPLEMENTATION OF IMDCT BLOCK OF AN MP DECODER THROUGH OPTIMIZATION... Implementaton of IMDCT Block of an MP Decoder through Optmzaton on the DCT Matr Mroslav GALABOV Dept. of Computer Systems and Technologes, Unversty of Velko Turnovo, T. Tarnovsk 2, 5 V. Turnovo, Bulgara plam@val.bg Abstract. The paper descrbes an attempt to create an effcent dedcated MP-decoder, accordng to the MPEG- Layer III standard. A new method of Inverse Modfed Dscrete Cosne Transform by optmzaton on the Dscrete Cosne Transform (DCT matr s proposed and an assembler program for Dgtal Sgnal Processor s developed. In addton, a program to calculate DCT usng Lee's algorthm for any matr of the sze 2 M s created. The epermental results have proven that the decoder s able to stream and decode MP n real tme. Keywords IMDCT, MP decoder, btstream, DSP.. Introducton MPEG- Layer III s a hghly compressed dgtal audo format. The Movng Pctures Epert Group standardzed t n 99. MPEG was formed n 988 by ISO/IEC organzatons to develop generc codng standards of movng pctures, audo and systems contanng both [] [2]. 2. Functonalty The nput to the MP decoder s a btstream and the decodng process turns ths nto samples whch are sent to a dgtal to analog converter (DAC add-on board. The MP stream s dvded nto frames where each frame contans 27 ms of musc data. The decodng process can be dvded nto s blocks and these are mplemented ndependent each other (Fg.. The frst three blocks Huffman decodng, descalng and reorderng convert the orgnal MP btstream nto 576 frequency lnes dvded nto 2 subbands wth 8 frequency lnes n each. Ths s the format whch the last three blocks antalas, Inverse Modfed Dscrete Cosne Transform (IMDCT and flter bank use. These blocks transform the MP from the frequency doman nto the tme doman. A more n-depth descrpton of the decodng process as well as MP encodng can be found n [-2]. The task of the Huffman decoder s to transform ncomng compressed data nto scalefactors and symbols representng the 576 orgnal frequency lnes. The scalefactors are then used n the net block (the descalng block to rescale the symbols nto non-scaled frequency lnes. Btstream Huffman Decodng Alas Reducton Descalng IMDCT 2. Huffman Decoder Reorderng Flter Bank Synthess Fg.. The MP decodng process. Pulse Code Modulaton Channel The decoder compares the nput sequence wth nformaton n the Huffman table and produces a symbol when a match s found. Informaton on what table to use for any gven frame s found n the frames sde nformaton. Output from the Huffman decoder s 576 scaled frequency lnes (symbols whch are dvded nto three parttons: Bg-values contan the lowest frequency lnes and are coded wth the hghest precson. Normally the scaled value s between -5 and 5, but hgher precson can be obtaned by usng an escape sequence. When the decoder fnds the value 5 t assumes that hgher precson s needed and reads addtonal bts from the nput stream. Ths value s then added to the orgnal value of 5. The number of bts s specfed n the Huffman table. Countl represents the hgher frequency lnes and does not need the hgh precson, they are smply coded wth the values, and l. Rzero represents the hghest frequency lnes. They have smply been removed by the encoder. These values are flled wth zeros by the decoder. 2.2 Descalng The descalng block rescales Huffman decoded scaled and quantzed frequency lnes. The result from the Descalzer s the orgnal frequency lnes. What equatons to use

2 RADIOENGINEERING, VOL., NO. 4, DECEMBER 24 2 depend on the wndowng functon used n the encodng procces? The descalng step must be performed once for each frequency lne n the btstream. 2. Reorderng The reorder block has one task; t reorders the frequency lnes wthn a granule. The way that the frequency lnes are reordered depends on flags n the sde nformaton header. The block works n three dfferent ways dependng on the sde nformaton header: All frequency lnes are reordered. Only frequency lnes after the lne number 6 are reordered. No frequency lnes are reordered. 2.4 Antalas The antalas block attempts to reduce the nevtable alas effects ntroduced by the use of a non-deal bandpass flter. Ths reducton s done by mergng frequences usng butterfly calculatons. 2.5 IMDCT IMDCT reproduces, n cooperaton wth the synthess polyphase flter bank, tme samples from frequency lnes. Gven the frequency lnes X k, tme samples can be obtaned by usng the followng equaton: = n / 2 k = X k π n cos ( 2k +, n. ( 2n 2 In our case, n = 6, whch means that the IMDCT takes 8 frequency lnes as an nput and generates 6 polyphase flter sub-band samples. These samples are multpled wth a 6-pont wndow before they can be passed on to the net step n the decodng process. Wndowng contans four dfferent types of wndows; the types are normal, short, start and stop. Informaton on what type to use s found n the sde nformaton part of each frame. Dependng on wndow type two dfferent mplementatons are used. Producng 6 samples from 8 frequency lnes means that only 8 of the samples are unque. Therefore IMDCT s sad to use a 5 % overlap. The 6 values from the wndowng operaton are dvded nto two groups, a low group and a hgh group, contanng 8 values each. Overlappng s carred out by nterleavng (addng values from the lower group wth correspondng values from the hgher group from the prevous frame. The general vew of the "operaton flow" s shown n Fg. 2. The entre cosne term for each output can be treated as a known constant factor based on the combnaton of and k n (. Some nvestgaton of these terms shows the symmetry between the dfferent. Only half of the values are unquely determned. The rest can be obtaned as a functon of the prevously calculated terms. The followng symmetry holds: and n =... 4, = n 2 n n = , = n 2 (2a. (2b Therefore, calculatng the frst quarter and the thrd quarter of all values wll be enough to determne the entre set. block type 8 nput values IMDCT 6 output values Wndowng 8 lower values 8 hgher values + 8 output values last 8 values Fg. 2. IMDCT wth wndowng and overlap add. 2.6 Flter Bank The synthess of a polyphase flter bank s the fnal step n the decodng process [5]. It eplots alasng and wndowng to move the subbands back nto ther frequency doman orgns. The process s naturally dvded n two parts, an MDCT part for translatng the alased subband sgnals, and a wndowng part to flter out the undesred alasng n the translated sgnal. Modfed dscrete cosne transform: The sub-samples from the transpose block are ordered s such a way that the 2 frst values are the frst sub-sample from each subband, the net 2 are the second sub-sample and so forth. The MDCT processes 2 values at a tme usng the followng equatons: Y = N S (a and N k k= k k π = cos ( 6 + ( 2k + 64, (b where S k are nput PCM samples. The output values Y are stored n a barrel shfter.

3 24 M. GALABOV, IMPLEMENTATION OF IMDCT BLOCK OF AN MP DECODER THROUGH OPTIMIZATION... Wndowng: Multplyng the values from the barrel shfter wth the wndow functon, specfed n the ISO standard. 2 Pulse Code Modulaton (PCM samples are computed each teraton. The MDCT and wndowng are performed 8 tmes for each granule, resultng n 576 PCM samples,.e. 27 ms at 44. khz.. Software Implementaton of the IMDCT Decoder Block The IMDCT used n MP s an 8-pont DCT that produces 6 output values from 8 nput values. The IMDCT can be mplemented many ways [2]. The optmzaton on the DCT matr s the technque currently used by the decoder.. Optmzatons on the DCT Matr A program was developed wth the purpose of eamnng the DCT matr and generatng the source code drectly. The program tres to mnmze the number of multplcatons needed by keepng track of prevous calculatons. If t fnds two dentcal multplcatons, the result from the frst calculaton wll be fetched and used. It can also fnd summatons of two dentcal multplcatons, where t can remove both multplcatons and use the prevously calculated summaton nstead. Ths sgnfcantly ncreases the computaton speed and the requred number of multplcatons wll drop from 648 to 256. Thanks to the archtecture of the sgnal processors, the summatons can be done n parallel usng the multply and accumulate (MLA nstructon, reducng the number of addtons from 62 down to zero. The synthess polyphase flter bank uses the output from the IMDCT calculaton. Accordng to the ISO/IEC 72- standard [], the synthess polyphase flter bank must transpose the nput before t s beng used. To avod ths, the output from the DCT s rearranged so t can be fed drectly to the synthess polyphase flter bank nstead. 24 old values 2 nput values MDCT 2 output values Wndowng (52 ponts The mplementaton of the synthess polyphase flter bank can be dvded nto two parts. The frst part s a 2- pont modfed DCT calculaton and the second part s the wndowng and summaton of 52 values to produce 2 output samples. A flowchart of the operatons can be found n Fg Fg. 4. Modfed DCT matr redundancy. A 2-pont modfed DCT requres 2 2 multplcatons usng a non-optmzed calculaton method. Algorthms performng fast DCT computatons are avalable, and based on the symmetry of the DCT matr. The problem s that the modfed DCT used by the subband synthess has to be translated nto a normal DCT before optmzatons can be appled. The dfference between normal DCT and the modfed DCT s the transform matr beng used. For a normal DCT, the transform matr N k for a DCT wth sze M can be calculated from the followng equaton: π N = cos ( 2 + k, 2 k. (4 k M The matr used n the orgnal subband synthess has the followng propertes: π N = cos ( 6 + ( 2k +, 6 2 k. (5 k M It can easly be converted to a 2 2 matr by the observaton that t s unform, leadng to 5 % redundancy. The frst and last 6 tnes n the matr are dentcal wth the 2 center-most lnes, as shown n Fg. 4. The reason for usng a 64 2 matr s that the modfed DCT produces 64 output values, also wth 5 % redundancy, whch wll be fed to the wndowng block. When the sze of the DCT matr s reduces the 2 output values stll need to be doubled n a way shown by Fg output values Fg.. The subband synthess flter bank dvded nto two parts. The frequency nverson has been ntegrated n the IMDCT calculaton. Ths mproves performance, but t s not crucal to the mplementaton. 6 Fg. 5. Convertng 2 output values from the DCT nto 64 values. Before any optmzaton technques can be used, the modfed DCT mast s mapped nto a standard DCT. By

4 RADIOENGINEERING, VOL., NO. 4, DECEMBER plottng N k for both transforms, dentcal lnes and columns can be found. The nformaton n the modfed DCT can also be found n the normal DCT. Row, 2, etc n the modfed matr can be mapped to row,, 29 etc n the normal DCT matr f they are negated. Row n the normal DCT matr s all zeros and can therefore be neglected. ( Net, we have to fnd a sutable optmzaton method. One of these methods was proposed by B.G Lee n 984 [], decreasng the requred number of multplcaton needed from 24 down to 8 for a 2-pont IDCT calculaton. Ths leads to a speed gan appromately tmes. Lee's algorthm s based on the dvde-an-concur pattern, splttng large DCT nto a seres of smaller DCTs (Fg. 6. ( (4 (2 (6 ( (5 ( ( A program was developed to auto-generate the source code usng Lee's algorthm for any matr of sze 2 M. The program can generate DCT transforms as well as nverse DCT transforms. Bult-n memory optmzaton keeps the temporary varables needed to a mnmum. 4. Epermental Results In order to test the decoder, MPEG supples a number of test sequences. Most test sequences are sne sweeps wth varous ampltudes. Durng the eperment, we use the developed assembler program of decoder for DSP ТМS 2C5, Teas Instruments DSP Starter Kt and test sequences accordng to the ISO/IEC72- standard []. Fg. 6. Eght pont DCT usng Lee's algorthm. A suppled sgnal s sne sweep from 2 Hz to khz wth the ampltude of 2dB (full scale s normalzed to the range between and +. Two tests only verfy computatonal accuracy of mplementaton, and not functonalty. The frst crteron states that the mamum allowed dfference between two 6-bt waveforms s ± []. The dfference between the sgnals does not eceed ±2 accordng to the plot. The second crteron states that the root mean square value may not eceed.88 []. In our case, we are 892 samplng ponts on the waveforms contanng 5 errors, whch gve Both crterons passed the test. The decoder producng output above s vald ISO/IEC 72- MP decoder. ( ( (2 (7 (6 (4 (5 C k = cosπ k Fg. 7. Two waveforms produced wth the reference source code and our decoder and the dfference between.

5 26 M. GALABOV, IMPLEMENTATION OF IMDCT BLOCK OF AN MP DECODER THROUGH OPTIMIZATION Conclusons Already at the begnnng of the artcle, crtcal decsons concernng what algorthms of IMDCT to use had been made. Many fast algorthms were found, but choce was done to use the most straghtforward one, due ts low complety compared to another more sophstcated algorthms. Loss of effcency could be accepted to as quckly as possble acheve workng archtecture n the frst hand; especally that loss of effcency was not crtcal for the entre desgn. The result s an effcent audo decoder, capable of streamng and decodng MP n real tme. The software decoder comples wth the qualty requrements n the ISO/IEC 72- standard. References [] ISO/IEC 72-:99 Informaton technology - Codng of movng pctures and assocated audo for dgtal storage meda at up to about,5 Mbt/s 99. [2] GADD, S., LENART, T. A hardware accelerated mp decoder wth Bluetooth streamng capabltes. Master's thess, Lund Insttute of Technology, Sweden, 2. [] LEE, B.G. A new algorthm to compute the dscrete cosne transforms. IEEE Transactons on Acoustcs, Speech and Sgnal Processng. 984, vol. 2, no. 6, p [4] BRITANAK, V., RAO, K. R. A new fast algorthm for the unfed forward and nverse mdct/mdst computaton. Sgnal Processng. 22, vol. 82,no., p [5] PAIK, W., HWANG, S. Desgn of a novel synthess flter for realtme MPEG-2 audo decoder mplementaton on a DSP chp. IEEE Transacton on CE. 999, vol. 45, no. 4, p Acknowledgements Research descrbed n the paper was fnancally supported by the Unversty of Velko Turnovo. About Authors... Mroslav Galabov was born n Velko Turnovo. He receved hs M.S.E degree n rado televson engneerng from the Hgher Naval School N. Vapcarov,Varna, Bulgara, n 989. After that he worked as desgn engneer for Insttute of Rado Electroncs, Velko Turnovo. From 992 to 2 he was assstant professor at Hgher Mltary Unversty, Velko Turnovo. He receved hs Ph.D. degree n automaton systems for processng of nformaton and control from the Hgher Mltary Unversty, n 999. Snce 22 he has been assstant professor n Computer Systems and technologes department at St. Cyrl and St.Methodus Unversty of Velko Turnovo. He s the author of three tetbooks, and over 2 papers. Hs current nterests are n sgnal processng, DSP and multmeda. RADIOENGINEERING REVIEWERS December 24, Volume, Number 4 AHMED., B. T., Unversdad Poltécnca de Madrd BERNAS, M., Czech Techncal Unversty, Prague FRÝZA, T., Brno Unversty of Technology, Brno FUČÍK, O., Brno Unversty of Technology, Brno HALÁMEK, J., Czech Academy of Scences, Brno HANUS, S., Brno Unversty of Technology, Brno KLÍMA, M., Czech Techncal Unversty, Prague KOCUR, D., Techncal Unversty of Košce KOLOUCH, J., Brno Unversty of Technology, Brno KOTULIAKOVÁ, J., Slovak Unv. Tech., Bratslava KRATOCHVÍL, T., Brno Unv. of Technology, Brno KVIČERA, V., TESTCOM, Praha LEVICKÝ, D., Techncal Unversty of Košce LUKÁČ, R., Unversty of Toronto, Toronto MARCHEVSKÝ, S., Techncal Unversty of Košce MAZÁNEK, M., Czech Techncal Unversty, Prague MOHR, F., Unv. of Appled Scences, Pforzhem NOVOTNÝ, K., Czech Techncal Unversty, Prague PÁTA, P., Czech Techncal Unversty, Prague PECHAČ, P., Czech Techncal Unversty, Prague POLEC, J., Slovak Unv. of Technology, Bratslava PROKEŠ, A., Brno Unversty of Technology, Brno PROVAZNÍK, I., Brno Unv. of Technology, Brno ŘÍČNÝ, V., Brno Unversty of Technology, Brno SCHIMMEL, J., Brno Unv. of Technology, Brno SMÉKAL, Z., Brno Unversty of Technology, Brno SZOKE, I., Brno Unversty of Technology, Brno ŠEBESTA, J., Brno Unversty of Technology, Brno VARGICA, R., Slovak Unv. of Technol., Bratslava WIESER, V., Unversty of Žlna, Žlna WILFERT, O., Brno Unversty of Technology, Brno ZAVACKÝ, J., Techncal Unversty of Košce