A High-Quality, Energy Optimized, Real-Time Sampling Rate Conversion Library for the StrongARM Microprocessor

Transcription

1 A Hgh-Qualty, Energy Optmzed, Real-Tme Samplng Rate Converson Lbrary for the StrongARM Mcroprocessor Chung-Tse Mar 1, Mat C. Hans, Mark T. Smth, Tajana Smunc, Ronald W. Schafer 1 Moble& Meda Systems Laboratory HP Laboratores Palo Alto HPL June 3 rd, 2002* dgtal sgnal processng, sample rate converson, audo, StrongARM, Ths paper presents a dgtal audo samplng rate converson lbrary that converts between arbtrary samplng frequences. The lbrary s mplemented as a tme-varyng fractonal delay flter wth coeffcents stored n a lookup table. It s desgned for use by realtme applcatons and optmzed for executon on Intel's StrongARM mcroprocessor. * Internal Accesson Date Only Approved for External Publcaton 1 Center for Sgnal & Image Processng, Georga Insttute of Technology, Atlanta, GA Copyrght Hewlett-Packard Company 2002

2 A Hgh-Qualty, Energy Optmzed, Real-Tme Samplng Rate Converson Lbrary for the StrongARM Mcroprocessor Chung-Tse Mar, Mat C. Hans, Mark T. Smth, Tajana Smunc, Ronald W. Schafer * Abstract Ths paper presents a dgtal audo samplng rate converson lbrary that converts between arbtrary samplng frequences. The lbrary s mplemented as a tme-varyng fractonal delay flter wth coeffcents stored n a lookup table. It s desgned for use by real-tme applcatons and optmzed for executon on Intel s StrongARM mcroprocessor. 1. Introducton Many dfferent samplng rates are used n today s dgtal sgnal processng applcatons. Telephone systems sample speech at 8 khz, khz s used for AM-rado qualty audo, and 44.1 khz s the standard for CD qualty dgtal musc. The problem of convertng between dfferent samplng rates has been dscussed n numerous papers and books, and dfferent methods have been proposed n [1]-[5]. The proposed samplng rate converson lbrary s targeted for processng blocks of audo data n real-tme applcatons. It s mplemented wth a tme-varyng fractonal delay flter that s controlled usng a lookup table to convert between arbtrary rates. The lbrary optmzaton has been performed wth the energy proflng tools presented n [6] for Intel s StrongARM SA-110 mcroprocessor. The motvaton for ths project s dscussed n Secton 2; the theory descrpton s gven n Secton 3; the desgn and mplementaton of the lbrary s descrbed n Secton 4; test results are n Secton 5; optmzaton s dscussed n Secton 6. The lbrary API s gven n the Appendx. 2. Motvaton The motvaton for mplementng a samplng rate converson lbrary came from workng wth the audo on the SmartBadge IV [7]. The SmartBadge IV s the next-generaton contextaware devce from Hewlett-Packard Laboratores. It s controlled by Intel s StrongARM SA processor and a StrongARM SA-1111 companon chp. In addton to the processors, the Badge has on chp memory (FLASH and RAM), Phlps UDA-1341 audo codec and varous onboard sensors. * Chung-Tse Mar and Ronald W. Schafer are wth the Center for Sgnal & Image Processng, Georga Insttute of Technology, Atlanta, Georga. Mat C. Hans, Mark T. Smth, and Tajana Smunc are wth the Applance Platforms Department, Hewlett-Packard Laboratores, Palo Alto, CA. 1

3 One challenge wth dgtal audo on ths research platform prototype s the rate at whch the UDA-1341 codec samples the audo at both playback and recordng. The codec on the SmartBadge IV does not have a dedcated clock; nstead t uses the clock sgnal from the StrongARM. Ths wll produce slght devatons from the standard samplng rates llustrated n Table 1. Table 1 Dfferences n Samplng Rates on the SmartBadge IV Ideal Samplng Frequency Actual Samplng Frequency 8.0 khz khz khz khz 32.0 khz 44.1 khz 8.0 khz khz khz khz 31.2 khz 43.2 khz Real-tme samplng rate converson must be done on both the audo nput and put to record and play hgh qualty audo, avodng dstorton and possble over or under-flow n real-tme communcaton applcaton. Dfferent methods for samplng rate converson are dscussed n Secton 3. Energy consumpton and power dsspaton are crtcal to portable systems lke the SmartBadge IV. System s energy consumpton dctates ts battery lfe. Whle mcroprocessors have become smaller and more powerful, the same advances have not been made by batteres. As a result, engneers need to explctly desgn both hardware and software of portable systems for low energy consumpton. The samplng rate converson lbrary proposed n ths paper s optmzed for executon on the StrongARM processor used by the SmartBadge IV. The optmzaton s summarzed n Secton Theory of Operaton Samplng rate converson s a problem of nterpolatng a sgnal at non-nteger multples of the orgnal samplng perod. Ths may also be vewed as delayng the sgnal by a tmevaryng fractonal amount as demonstrated n Fgure 1, for a rate converson of a sgnal wth samplng perod, T n, to a new perod, T. Fgure 1 Delayng the sgnal by a tme-varyng fractonal amount x[n] T n y[n] T Tme d d 1 d 2 3 2

4 To calculate each samples of the put, y [n], the nput, x [n], must be delayed by fractonal amounts, d, of the orgnal samplng perod. Delayng a sgnal by d corresponds to j d a multplcaton by the complex exponental, e ω, n the frequency doman. Ths may be acheved by a system wth the frequency response: H jω jωd ( e ) = e, for all ω (1) whch corresponds to an all-pass flter. For use n samplng rate converson, a bandlmtng factor must be added to prevent alasng f the nput rate, F n, s hgher than the put rate, F. Specfcally, the converson requres a set of flters, known as fractonal delay flters: H jω jωd ( e ) = e, for 0 ω mn( π, ) πf (2) F n The correspondng mpulse response of these flters, h [n], may be calculated to be: where γ s a bandlmtng factor computed as: sn[ γπ( n d)] h[ n] =, for all n, (3) π( n d ) F γ = mn( 1, ) (4) F The mpulse response s a delayed snc functon of nfnte length. Dfferent methods exst for approxmatng ths unrealzable system wth a causal flter of fnte length. A detaled analyss may be found n [8]. Several dfferent rate converson methods were consdered for use n ths lbrary. They dffer n the method used to desgn the fractonal delay flters. The method proposed n [3] uses B-splne functons. [5] uses the Farrow polynomal approxmaton proposed n [9]. In both cases, the flter coeffcents are low-order polynomal functons of the delay: n N h n 1 ] = cn k= 0 k [ [ k] d (5) where N s the order of the polynomal used to approxmate each flter coeffcent. The coeffcents may be easly updated for an arbtrary delay at run-tme as the nput s beng fltered. Ths s effcent only f the flter length s kept very short. For processng of hgh qualty audo, the nput sgnal must frst be upsampled by some factor n order for the short varable-delay flter to generate accurate puts. Ths method s feasble for a fxed converson factor, F F, but n 3

5 t may get complex f the converson factor s to be made flexble because the coeffcents, c n [k], n (5) must be recomputed to approxmate a flter response wth a dfferent cutoff frequency. The method proposed n [4] does not requred upsamplng of the nput. It uses the wndow method for flter desgn [10], where the flter coeffcents are computed as: h n] = w( n d )snc[ γ ( n d )] for n = 1... N, (6) [ where w (n) s the wndow functon, γ s the bandlmtng factor computed n (4), and N s the length of the flter. Commonly used wndow functons nclude the Kaser wndow and the Dolph-Chebyshev wndow. Snce calculatng snc and wndow functons for arbtrary delays at run-tme s too computatonally expensve, a lookup table may be used. Interestngly, for a gven factor of converson, F Fn, the total number of dfferent delays, d, s fnte. The delays also vary perodcally durng the converson. Suppose that ths factor may be reduced to the an ntegral fracton, R Rn. The delays, d, may be computed as: where = 0,1, ( R 1) R n Rn d = (7) R R, and x denotes the largest nteger less than or equal to x. Observe that 0 d < 1. A table of flters correspondng to the set of R delays for a partcular factor of converson may be pre-computed. The number of elements n the flter table s equal to R N, where N s the flter length. For example, when convertng 44.1 khz to 48 khz, we may use R n = 147 and R = 160, there are 160 put samples for 147 nput samples, and a total of 160 dfferent delays to be calculated. If a flter length of 65 s used wth 16-bt resoluton for each coeffcent, the lookup table would requre 20 Kbytes of memory. An mportant pont to note s that the flter must be operated at the put samplng rate. Ths can be acheved by shftng the nput samples by a tme-varyng number of samples, s, nto the flter s delay lne: The put s calculated usng: R n Rn s = ( 1) (8) R R N 1 k = 0 y [ n] = h ( k) x( n + s k) (9) where the varable ndexes the partcular flter coeffcents and shft values to use. It s perodc and s equal to n mod R. The lookup table method s hghly effcent snce the coeffcents are only computed once. On the other hand, dfferent tables are needed for dfferent rates, and for some factors of 4

6 converson, n whch R s a large number, the table may take up more than 100 Kbytes of memory. A more flexble method s proposed n [2]. A low-pass flter wth an arbtrary delay may be computed by lnearly nterpolatng an over-sampled and wndowed snc functon. To llustrate how ths may be done, suppose the wndowed snc functon wth zero delay s represented as h [n], ths s oversampled by a factor, L, to produce: h oversampled n [ n] = h[ ] (10) L Ths oversampled functon can be computed beforehand and stored nto a header fle to be compled wth the lbrary code. To calculate h [n] for the delay d : oversampled h [ n] = h[ n d ] = h [ nl d L] (11) As n (7), 0 d < 1, and d L usually wll not be an nteger. But f L s large enough, lnear nterpolatng between the oversampled coeffcents wll produce accurate estmates for h[ n d]. Detals on how ths s done wth fxed pont numbers and an analyss on the sze requrement of L may be found n [2]. Ths s the method employed n ths lbrary. The flter coeffcents may ether be computed at run-tme wth mnmum overhead (one multplcaton and one addton for each coeffcent), or they may be computed and stored n a lookup table. Ths lbrary offers the user both optons, but the lookup table should be used f possble because of the sgnfcant reducton n computatonal complexty (see Secton 5). 4. Lbrary Desgn and Implementaton The samplng rate converson s mplemented as a tme-varyng FIR flter n our lbrary. The flter coeffcents may be ether pre-computed and stored n a lookup table, or computed at run-tme by lnearly nterpolatng an oversampled flter response. The desgn of the lbrary s smlar to the block FIR flterng functons n Intel s Integrated Performance Prmtves Lbrary [11]. The lbrary can be used both to process large chunks of data as a whole and small blocks of data wth repeated lbrary calls; such s the case when streamng audo over the Internet n real-tme. To avod transent flter response between contguous blocks of data, the nternal state of the system should be mantaned. Ths ncludes the ndex of the partcular flter coeffcents to use and some nput samples at the end of a block. If the system s ntalzed at the start of each new block to the state that was reached at the end of the prevous block, then a steady-state flter response s mantaned. A dagram of the samplng rate converson system as mplemented n the lbrary s shown n Fgure 2. 5

7 Fgure 2 Block dagram of samplng rate converson system. Interleaved Stereo Audo Input Channel 1 buffer Shft Delay Control Shft Channel 2 buffer Index Tme -Varyng FIR Flter Coeffcents Lookup Table Coeffcents Tme -Varyng FIR Flter Interleaved Stereo Audo Output A block of nterleaved stereo data s frst separated nto two buffers nternal to the lbrary. The delay control element s mplemented as a table contanng the possble shft values as calculated n (8). It controls how many nput samples should be shfted nto the flter and whch set of coeffcents s to be used. The put s calculated followng (9). The resultng effect s a tme-varyng flter operatng at the put samplng frequency. To avod transent response at the end of a block, some nput samples are saved n the nternal buffers untl the next lbrary call. A flush rne s provded n the lbrary for transent response calculaton. 5. Tests Results The lbrary was tested usng both natural audo sgnals and computer generated sne waves. The converson from 44.1 khz to 48 khz and khz wll be llustrated here as examples. The test nput sgnal used s a sum of two snusods wth the frequences 4 khz and 16 khz; t was generated usng 16-bts of resoluton. Its spectrum s plotted n Fgure 3. Fgure 3. Spectrum of nput sgnal sampled at 44.1 khz. 6

8 The nput was resampled to 48 khz usng the samplng rate converson lbrary, and the put spectrum s shown n Fgure 4. Fgure 4. Spectrum of put sgnal resampled to 48 khz. Most dstortons generated by the converson are 80 db below the sgnal level. The converson was repeated for an put rate of khz, and the result s shown n Fgure 5. Fgure 5. Spectrum of put sgnal resampled to khz. As expected, the frequency component above 11 khz has been elmnated by the bandlmtng factor n the nterpolaton flters. The dstortons are stll mostly 80 db below the sgnal level. 7

9 6. Optmzaton The fxed-pont samplng rate converson mplementaton code [12] for the method proposed n [2] was used as a startng pont for the lbrary mplementaton. It was modfed to ft the lbrary specfcatons and optmzed for executon on the Hewlett-Packard Laboratores SmartBadge portable devce. Optmzaton was done manually n the ARM Software Development Toolkt (SDT) [13] wth the gudance of the cycle-accurate energy profler proposed n [6] and the applcaton notes publshed by ARM [14]. At the mplementaton level, many trcks from [14] were used to optmze the code. They ncluded, among others, condtonal executon, functon nlnng, and effcent regster allocaton. Two other major modfcatons are dscussed below. Stereo audo s usually stored as nterleaved 16-bt ntegers, but for samplng rate converson, each channel must be processed separately. In the orgnal code, the separaton was done by the user applcaton, and two lbrary calls must be made, one for each channel. Ths ntroduces redundances. To process stereo data more effcently, the channel separaton was moved nsde of the lbrary, such that a sngle lbrary call s used for converson. Addtonally, a lookup table for the flter coeffcents was added to the orgnal code to elmnate the calculaton of the coeffcent at run-tme. On the other hand, t requres an ntalzaton functon to comple the flter table. The result of the optmzaton s summarzed n Table 2. Table 2 Performance and Energy for Samplng Rate Converson Implementatons, 44.1 khz to 48 khz Performance Energy (mwhr) Code Revson Total Cycles (%Reducton) Processor Memory Total Battery (%Reducton) Orgnal [12] (0%) 1.10E E E-02 (0%) Optmzed (39%) 1.02E E E-02 (10%) Optmzed wth Lookup Table (64%) 6.89E E E-02 (37%) The above data were collected from the energy profler, whch was confgured for the StrongARM-110 processor usng 1 MB of Flash memory and 2 MB of SRAM. The StrongARM SA-1110 processor on the SmartBadge IV s not yet supported by the ARM SDT, so the SA-110 s used nstead for the smulaton. To generate the data, the lbrary was used to convert fve seconds of stereo audo recorded at 44.1 khz to 48 khz n blocks of 1024 samples usng a 13-tap flter. Smlar reductons may be found n the down-samplng converson from 44.1 khz to 8 khz shown n Table 3. Table 3 Performance and Energy for Samplng Rate Converson Implementatons, 44.1 khz to 8 khz Performance Energy (mwhr) Code Revson Total Cycles (%Reducton) Processor Memory Total Battery (%Reducton) Orgnal [12] (0%) 8.00E E E-02 (0%) Optmzed (38%) 6.31E E E-02 (23%) Optmzed wth Lookup Table (61%) 5.94E E E-02 (25%) 8

10 These results are overall lower than those n Table 2 because the down-samplng put data length s much shorter. The reductons may be even more dramatc f the flter length was ncreased to 65 as n Table 4. Table 4 Performance and Energy for Samplng Rate Converson Implementatons, 44.1 khz to 8 khz Performance Energy (mwhr) Code Revson Total Cycles (%Reducton) Processor Memory Total Battery (%Reducton) Orgnal [12] (0%) 7.39E E E+00 (0%) Optmzed (44%) 3.82E E E+00 (48%) Optmzed wth Lookup Table (90%) 5.06E E E-01 (93%) The ncreased savngs are manly due to the large overhead n calculatng 65 coeffcents at runtme that s avoded by usng a lookup table. References [1] R. E. Crochere and L. R. Rabner, Multrate Dgtal Sgnal Processng. Englewood Clffs, NJ: Prentce-Hall, [2] J. O. Smth and P. Gosset, A flexble samplng-rate converson method, n Proc. IEEE Int. Conf. Acoustc Speech Sgnal Processng, vol.2, pp , [3] S. Cucch, F. Desnan, G. Parlador, and G. Scuranza, DSP Implementaton of Arbtrary Samplng Frequency Converson for Hgh Qualty Sound Applcaton, Int. Conf. Acoustc Speech Sgnal Processng, vol. 5, pp , [4] S. Park, G. Hllman, and R. Robles, A Novel Structure for Real-Tme Dgtal Sample-Rate Converters wth Fnte Precson Error Analyss, Int. Conf. Acoustc Speech Sgnal Processng, vol. 5, pp , [5] K. Rajaman, Y. La, and C. W. Farrow, An Effcent Algorthm for Sample Rate Converson from CD to DAT, IEEE Sgnal Processng Letters, vol. 7, no. 10, October, pp , [6] T. Smunc, L. Benn, and G. De Mchel, Energy-Effcent Desgn of Battery-Powered Embedded Systems, IEEE Transactons on VLSI Systems, vol. 9, February, pp , More nformaton: [7] M. T. Smth and G. Q. Magure Jr., SmartBadge/BadgePad verson 4, HP Labs and Royal Insttute of Technology (KTH), date of access [8] T. I. Laakso, V. Valmak, M. Karjalanen, and U. K. Lane, Splttng the Unt Delay, IEEE Sgnal Processng Magazne, vol. 13, January, pp , [9] C. W. Farrow, A contnuously varable dgtal delay element, n Proc. IEEE Int. Symp. Crcuts Syst., vol. 3, pp , [10] A. V. Oppenhem, R. W. Schafer, and J. R. Buck, Flter Desgn Technques, Chap. 7 n Dscrete-Tme Sgnal Processng. Upper Saddle Rver, NJ: Prentce-Hall, [11] Intel Corporaton, Intel Integrated Performance Prmtves for the Intel StrongARM SA Mcroprocessor Reference Manual, verson 1.01,

11 [12] Julus Smth, Samplng Rate Converson Program Verson 1.6, Avalable: [13] Advanced RISC Machnes Ltd (ARM), ARM Software Development Toolkt Verson 2.11, [14] Advanced RISC Machne Ltd (ARM), Applcaton Note 34: Wrtng Effcent C for ARM, [Onlne document], Avalable: [15] J. F. Kaser, Nonrecursve Dgtal Flter Desgn Usng the Io-Snh Wndow Functon, n Proc. IEEE Int. Symp. Crcuts Syst., pp , Appendx 1. Lbrary API Ths lbrary supports sample rate converson of contguous data blocks usng repeated calls wth loss of nternal flter state. Transent flter responses are avoded at block boundares by provdng a state ntalzaton mechansm for the functon. If the flter s ntalzed at the start of each new block to the state that was reached at the end of the prevous block, then a steady-state flter response s mantaned when flterng a long data record on a block-by-block bass. Applcaton code makng use of the resample functon should adhere to the followng usage model: a. Intalzaton Pror to callng resample for the frst tme, nvoke resampleinit() wth the approprate parameters to ntalze the nternal varables used by the lbrary. b. Resamplng If samples from a long sequence are processed n blocks usng repeated calls to the lbrary, the applcaton should not modfy the RESAMPLE_STATE varable n between successve calls. Ths mplementaton wll produce around (TAP*factor) samples of start-up transent put when t s called for the frst tme. c. Extng When there are no more nputs, the applcaton should frst call resampleblock() wth nlength set to zero. Ths should resample what's left n the nternal buffer. If transent response s desred at the end, resampleflush() should then be called. Once converson has been completed, call resampleexit() to free up the memory used by the nternal varables (lookup tables and nternal buffer). Block sze management: Block processng n sample rate converson presents a unque problem because the nput block sze s dfferent from the put. In ths lbrary, the user should request (nt)(nlength*factor) samples of put per nlength nput samples. Requestng too many or too few puts may result n resampleblock returnng an abnormal ext condton. Processng nterleaved stereo audo: Two channel (stereo) audo data s often stored wth the channels nterleaved. Ths lbrary provdes functons for resamplng nterleaved data so the applcaton won't have to separate the channels. 10

12 2. Example code Ths s a smple example code that uses the lbrary to convert a two-channel, raw PCM audo fle recorded at 44.1 khz to 32 khz. Converson s done n blocks of 100 ms. #nclude <stdo.h> #nclude <stdlb.h> #nclude "resample_smth_gossett.h" vod example(vod) { RESAMPLE_STATE state; nt qualty, stereo, use_table; nt Fn, F; nt Nn; /* number of nput samples per block */ nt N; /* number of put samples per block */ nt nbytes; /* bytes per nput block */ nt Bytes; /* bytes per put block*/ nt *nbuffer, *Buffer; double factor; FILE *nfp, *Fp; Fn = 44100; F = 32000; factor = (double)f/(double)fn; /* the audo s processed n blocks of 0.1 second */ Nn = 4410; N = (nt)( (double)nn*factor ); /* Allocate memory for n/ blocks */ nbytes = Nn*szeof(nt); Bytes = N*szeof(nt); nbuffer = (nt *)malloc(nbytes); Buffer = (nt *)malloc(bytes); /* Open up the fles we need */ nfp = fopen("n.pcm", "rb"); Fp = fopen(".pcm", "wb"); qualty = 0; /* normal qualty */ stereo = 1; /* stereo audo */ use_table = 1; /* use lookup table */ resampleinit(&state, factor, qualty, stereo, use_table); /* ntalze nternal varables */ /* resample Nn nput samples at a tme untl the end of the nput fle */ whle (fread(nbuffer, szeof(nt), Nn, nfp)==nn) { resampleblock_stereo(nbuffer, Buffer, Nn, &N, &state); fwrte(buffer, szeof(nt), N, Fp); } /* flush what's left n the nternal buffer */ resampleblock_stereo(n Buffer, Buffer, 0, &N, &state); fwrte(buffer, szeof(nt), N, Fp); N = resampleflush_stereo(buffer, &state); fwrte(buffer, szeof(nt), N, Fp); resampleexit(&state); /* free up memory used by nternal varables */ } fclose(nfp); fclose(fp); free(buffer); free(nbuffer); 11