Perceptual audio coding schemes based on adaptive signal processing tools

Transcription

1 Biomedical Acoustics: Paper ICA Perceptual audio coding schemes based on adaptive signal processing tools Fernando A. Marengo Rodriguez (a), Sergio A. Castells (b), Gonzalo D. Sad (c) (a) National University of Rosario, Argentina, (b) National University of Rosario, Argentina, (c) National University of Rosario, Argentina, Abstract In this paper, new perceptual audio coding schemes based on adaptive processing tools are proposed. They rely on both the empirical mode decomposition (EMD) and the ensemble empirical mode decomposition (EEMD). In comparison with other perceptual coding schemes, the one presented here is simpler since physically meaningful components of the input signal are detected, then their extrema are extracted and Golomb-Rice encoding of the extracted samples is performed. The proposed scheme is assessed in terms of compression ratio and perceptual quality for various tracks from the EBU SQAM CD. The obtained results are compared with those corresponding to other perceptual audio coding methodologies. Keywords: Perceptual audio coding schemes, empirical mode decomposition, ensemble empirical mode decomposition, data compression.

2 Perceptual audio coding schemes based on adaptive signal processing tools 1 Introduction In order to optimize the use of data transmission channels as well as the storage capacity, different lossless and perceptual (lossy) audio coding schemes were developed. The former [1, 2, 4] allow to reduce the input audio file without introducing distortion. CD audio files can be reduced 2 to 6 times, depending on certain characteristics of the input data, such as the dynamic range and spectral content [3]. Perceptual audio encoders [5, 6, 7, 8] allow to obtain higher compression gains at a cost of higher complexity of the encoder. In both types of encoders, it is crucial that the decoder be of low complexity, so as to allow low-cost portable devices play in real time the audio file previously encoded. In this paper, new encoding schemes based on adaptive analysis techniques are proposed, and their performances are quantitatively analyzed and compared with previous techniques using musical tracks from the European Broad-casting Union Sound Quality Assessment Material (EBU-SQAM) CD [17]. This document is organized as follows. Section 2 briefly describes the adaptive tools used for the perceptual audio encoding methods outlined in Section 3. Audio files selection criterion and encoding results are summarized in Section 4 and 5 respectively, and final remarks are presented in Section 6. 2 ADAPTIVE TOOLS FOR THE ENCODER Unlike other encoding schemes, our method relies on adaptive signal decomposition. They are: 1) the empirical mode decomposition (EMD) [18, 19, 20] method and 2) the ensemble empirical mode decomposition (EEMD) [21] algorithm. These tools allow to decompose any 1D sequence into a reduced set of zero-mean amplitude and frequency modulated (AM-FM) signals, each usually related with a physical phenomenon underlying the system of study [20]. In the following, these tools will be briefly described. 2.1 Empirical mode decomposition method In the EMD method, details are extracted from the input data progressively, from the finest temporal resolution up to the coarsest one, by means of a sifting process. Intuitively, the input data x(t) is seen as an addition of zero-mean oscillatory details d k (t), each of which is added to slower temporal variations. Each detail is extracted as follows. 1) Local maxima (minima) are computed in the input signal and then interpolated, resulting the upper (lower) envelope e max (e min ). 2) The local mean m(t)=(e max + e min )/2 is computed, and the first order detail d 1 (t)=x(t) m(t) is determined. 2

3 3) The first residue r 1 (t) = x(t) d 1 (t) is computed and used as input for performing step 1). The output signal is the second order detail d 2 (t), as well as the second residue r 2 (t)=r 1 (t) d 2 (t). 4) This sifting process continues iteratively from steps 1) through 3) until the residue r K (t)= r K 1 (t) d K (t) has no more local extrema and hence no more details to extract. At this point, the input signal is decomposed as x(t)= K k=1 d k (t)+r K (t). (1) d k (t) is known as intrinsic mode function or IMF, and r K (t) is the final residue, also denoted as r(t) for simplicity. It has to be stressed that each detail function at the end of step 2) may have nonzero mean, in which case it has to be iterated from step 1) for subtracting such mean. This is performed until the mean is sufficiently small [18, 19]. Since each IMF depends solely on the input signal, the EMD algorithm is characterized for being fully data-driven, adaptive and always gives a small amount of IMFs which may be described as AM-FM signals, i.e., d k (t)=a k (t)cos[θ k (t)], where a k (t) is the instantaneous amplitude and 1/(2π) dθ k (t)/dt is the instantaneous frequency of the k-th IMF d k (t) [20]. The EMD method has been used extensively for robust data analysis [20], and also for data compression in 2D [9] and 1D [10] including audio signals [11, 12, 13]. The present paper introduces further improvements on the method introduced in [11]. 2.2 Ensemble empirical mode decomposition method This technique, also known by its acronym, EEMD [21], consists of multiple applications of the EMD algorithm to the input signal contaminated by different realizations of finite-power white Gaussian noise (WGN). Its purpose is to add spectral content to the input sequence, so as to allow the EMD work like a dyadic filter bank [14, 16] and obtain a set of IMFs more concentrated in some spectral bands. (Strictly speaking, EMD is fully data-driven and works as such filter bank only for a small class of wideband signals, since the resulting IMFs are not usually concentrated in one octave as expected. However, the EEMD method allows to obtain, after each realization, a set of IMFs spectrally better concentrated than those obtained via EMD.) Finally, the homologous IMFs are ensemble averaged over all the L realizations, resulting a set of average IMFs d k (t) (k=1,2,...k) given by d k (t)= 1 L L l=1 d k,l (t). (2) 3

4 One drawback of this method is that it does not fulfill completeness since (1) is not satisfied. However, this problem is minimized by reducing the power of the WGN added in the method [15], especially for signals with spectral power more concentrated at low frequencies [21]. An important advantage of EEMD over EMD is that each resulting IMF does not contain information regarding two or more different physical phenomena, also known in the literature as mode mixing. This is a consequence of the addition of WGN, which completes spectral information. This advantage is useful for the proposed encoder herein. Finally, it is important to mention that the EEMD algorithm may be optimized by adding less noise power. This option is recommended in [21] for signals more concentrated at low frequencies, which is true for many types of audio signals. An additional benefit for this is the need of less number of realizations, which increases the speed of the EEMD algorithm. 3 PROPOSED ENCODER/DECODER The proposed encoder and decoder are explained in the following subsections. 3.1 Encoder The encoder processes the input audio file (WAVE in this case) on a frame by frame basis, and its block diagram is illustrated in Figure 1. Figure 1: Block diagram for the proposed encoder. The encoder determines the sampling rate of the input file, the number of channels and the number of bits per sample. Then, the input data is segmented in frames of fixed length (4096 samples for the present case). For each frame, data are processed via either EMD or EEMD, resulting a set of IMFs. Irrelevant IMFs are deleted, according to their correlation with the input signal [22] and to a psychoacoustic model for spectral masking [23], see Figure 2. Figure 2: Diagram for detection of relevant IMFs. The most relevant IMFs resulting from the previous step are represented via the corresponding local extrema, which is equivalent to its critical sampling rate. Their interpolation (via e.g. splines) allow to reconstruct each IMF with low error [9, 10, 11]. The abscissas n i and ordinates P i of the local extrema are encoded separately. The former are differentiated, resulting a set of smaller numbers δ i = n i n i 1. Since IMFs extrema are shifting their sign, their ordinates are represented via their absolute values. Just one additional bit is added for indicating which 4

5 is the sign of the first ordinate in the corresponding IMF. The set of absolute ordinates is subtracted from their median, so as to obtain a dataset more concentrated around zero. Both the abscissas and ordinates are Golomb-Rice encoded [24] and finally multiplexed. 3.2 Decoder The decoder is shown in Figure 3 and works as follows. The encoded audio file is demultiplexed and Golomb-Rice decoded for both the differentiated abscissas δ i and processed ordinates P i. The abscissas are recovered by cumulative sum, and the ordinates are determined after addition of the corresponding median and sign shifting, according to the sign of the first ordinate. The resulting local extrema are then interpolated via piecewise 3rd order cubic Hermite interpolating polynomial (PCHIP), in order to reconstruct the relevant IMFs, which are added altogether, giving the decoded signal. Figure 3: Block diagram for the decoder. It has to be stressed that the encoder and above all the decoder are quite simple. The simplicity of the decoder is crucial for low-cost portable devices that allow to play the encoded audio file in real time. 4 PERFORMANCE ANALYSIS The EMD/EEMD based audio coding scheme was tested with WAVE audio files extracted from the EBU-SQAM CD [17]. The aim is to test a variety of audio signals according to the following parameters recommended in [25]: - Transients (pre-echo sensitive, smearing of noise in temporal domain), - Tonal structure (noise sensitive, roughness), - Natural speech (distortion sensitive, smearing of attacks), - Complex sound (stresses the device under test), - High bandwidth (stresses the device under test, loss of high frequencies, programmemodulated high frequency noise). Therefore, the selected files in the EBU-SQAM CD were: - Castanets (file 27.wav), - Clarinet (file 16.wav), 5

6 - Female speech (file 49.wav), - Soprano (file 44.wav), - Glockenspiel (file 35.wav). Each encoded audio file was evaluated in terms of the compression ratio, which is the ratio between the input and the output file sizes. The quality of the encoded data was measured via the objective difference grade (ODG) [25]. The results were compared with those obtained using these perceptual audio coding schemes: 1) OGG Vorbis [8] and 2) the audio coding standard ISO/IEC MPEG Layer 3 or MP3 [7]. 5 RESULTS The numerical values for both the compression ratio and the ODG associated with the audio files are shown in Table 1. For the EEMD algorithm, 100 realizations were performed, and different values for the percentual WGN power σ were used. For better compression, the value of σ depends on the audio file under analysis, and is indicated in Table 1. For each audio file, the best compression is achieved by the EMD-based encoder (see values in bold in Table 1). Besides, the EEMD-based approach gives almost as much compression as the EMD algorithm, but with higher fidelity (the ODG is less negative). Such fidelity improvement illustrates the advantage of the EEMD method for providing IMFs with better spectral concentration, i.e., less mode mixing. Finally, it is observed that the fidelity of the encoded audio files with the method is outperformed by previous techniques. This issue is currently under study for further improvements. 6 CONCLUDING REMARKS The EMD/EEMD audio encoding scheme was presented and tested with well-known audio files and compared with other existing encoding algorithms. This encoder is simple and provides higher compression. Further improvements regarding fidelity and speed are under development. An important advantage is that one single low-cost decoder is needed regardless of the use of the EMD or the EEMD method for encoding. This is crucial for low-cost portable devices that perform audio decoding and playing. References [1] xiph.org Foundation. FLAC - Free lossless audio codec, [2] Ashland, M. Monkey s Audio, [3] Marengo Rodriguez, F. A.; Roveri, E. A., Rodríguez Guerrero, J. M.; Treffiló, M. Análisis comparativo de codificadores de audio sin pérdidas y una herramienta gráfica para su se- 6

7 Table 1: Compression ratio and ODG for different audio files processed by different encoding algorithms. EMD EEMD MP3 OGG MP3 VBR VBR 64k Castanets (Note 1) FC ODG Clarinet (Note 1) FC ODG Female FC speech (Note 2) ODG Soprano (Note 2) FC ODG Glockenspiel (Note 1) FC ODG Note 1: σ = 0.01 in EEMD. Note 2: σ = 0.05 in EEMD. lección y predicción de su desempeño. Mecánica Computacional, Vol 30 (41), 2011, pp , Acoustics and Mechanical Vibrations (B). [4] Hans, M.; Schafer, R. W. Lossless compression of digital audio. IEEE Signal Processing Magazine, Vol 18 (4), 2001, pp [5] Bonello, O. Tecnología de radiodifusión para la década del 90. Revista telegráfica electrónica, 1990, pp 293. [6] Bonello, O. AUDICOM - Un invento argentino. Coordenadas, Vol 85, 2010, pp 4-8. [7] ISO/IEC, ISO/IEC : Information technology Coding of moving pictures and associated audio for digital storage media at up to about 1.5 Mbit/s Part 3: Audio, [8] xiph.org Foundation. Vorbis audio compression, [9] Linderhed, A. 2-D empirical mode decompositions - in the spirit of image compression. Proceeding of SPIE, Wavelet and Independent Component Analysis Applications IXI, Orlando, USA, 2002, Vol 4738, pp 1-8. [10] Ho, C. C. Empirical Mode Decomposition Based Novel Data Compression Algorithm for Wireless Data Transmission in Machine Health Monitoring. Master s Thesis. City University of Hong Kong, [11] Marengo Rodriguez, F. A.; Miyara, F. Representación de Señales de Audio con Descomposición Empírica de Modos y Submuestreo Adaptativo. Primeras Jornadas Regionales de Acústica, Rosario, Argentina, 2009, number A056R. In CD-ROM. 7

8 [12] Khaldi, K.; Boudraa, A. O.; Turki, M.; Samaali, I.; Chonavel, T. Audio encoding based on the empirical mode decomposition, EUSIPCO 09, Glasgow, United Kingdom, [13] Khaldi, K.; Boudraa, A. O.; Torresani, B.; Chonavel, T. HHT - based audio coding. Signal, image and video processing, Vol 7 (2), 2013, pp 1-9. [14] Wu, Z.; Huang, N. E. A study of the characteristics of white noise using the empirical mode decomposition method. Proc. of the Royal Society of London(A), Vol 460 (2046), 2004, pp [15] Torres, M. E.; Colominas, M. A.; Schlotthauer, G.; Flandrin, P. A complete ensemble empirical mode decomposition with adaptive noise. ICASSP, Prague, Czech Republic, 2011, pp [16] Flandrin, P.; Rilling, G.; Gonçalves, P. Empirical mode decomposition as a filter bank. IEEE, Signal Processing Letters, Vol 11 (2), 2004, pp [17] European Broadcasting Union, Sound Quality Assessment Material, Recordings for subjective tests Users Handbook for the EBU-SQAM Compact Disc [18] Huang, N. E.; Shen, Z.; Long, S. R.; Wu, M. C.; Shih, H. H.; Zheng, Q.; Yen, N.; Tung, C. C.; Liu, H. H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. of the Royal Soc. of London (A), Vol 454 (1971), 1998, pp [19] Rilling, G; Flandrin, P; Gonçalves, P. On empirical mode decomposition and its algorithms. Proc. of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03. Grado, Italy, [20] Huang, N. E.; Shen, S. S. P. The Hilbert-Huang Transform and Its Applications (Interdisciplinary Mathematical Sciences). World Scientific Publishing Company [21] Wu, Z.; Huang, N. E. Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method. Advances in Adaptive Data Analysis, Vol 1 (1), 2009, pp [22] Peng, Z. K.; Tse, P. W.; Chu, F. L. A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing. Mechanical Systems and Signal Processing, Vol 19 (5), 2005, pp [23] Zwicker, E; Fastl, H. Psychoacoustics: Facts and Models. Springer-Verlag, Berlin (Germany), 3rd edition, [24] Salomon, D. Data Compression.: The Complete Reference. Springer-Verlag, New York (USA), 3rd edition, [25] ITU, Method for objective measurements of perceived audio quality, Recommendation ITU- R BS ,