Sound Analysis and Synthesis Adaptive in Time and Two Frequency Bands

We present an algorithm for sound analysis and resynthesis with local automatic adaptation of time-frequency resolution. There exists several algorithms allowing to adapt the analysis window depending on its time or frequency location; in what follows we propose a method which select the optimal resolution depending on both time and frequency. We consider an approach that we denote as analysis-weighting, from the point of view of Gabor frame theory. We analyze in particular the case of different adaptive timevarying resolutions within two complementary frequency bands; this is a typical case where perfect signal reconstruction c annot in general be achieved with fast algorithms, causing a certain error to be minimized. We provide examples of adaptive analyses of a music sound, and outline several possibilities that this wo rk opens.

[1]  Jelena Kovacevic,et al.  An Introduction to Frames , 2008, Found. Trends Signal Process..

[2]  Karol Zyczkowski,et al.  Rényi Extrapolation of Shannon Entropy , 2003, Open Syst. Inf. Dyn..

[3]  Monika Dörfler,et al.  Quilted Gabor frames - A new concept for adaptive time-frequency representation , 2009, Adv. Appl. Math..

[4]  R. Balan,et al.  On signal reconstruction without phase , 2006 .

[5]  Axel Röbel,et al.  A Reduced Multiple Gabor Frame for Local Time Adaptation of the Spectrogram , 2011, ArXiv.

[6]  A. Rényi.  On Measures of Entropy and Information , 1961 .

[7]  C. Beck,et al.  Thermodynamics of chaotic systems: Spin systems , 1993 .

[8]  P. Balázs.  Basic definition and properties of Bessel multipliers , 2005, math/0510091.

[9]  Bruno Torrésani,et al.  The Linear Time Frequency Analysis Toolbox , 2012, Int. J. Wavelets Multiresolution Inf. Process..

[10]  Yonina C. Eldar,et al.  Sub-Nyquist Sampling of Short Pulses: Part I , 2010, ArXiv.

[11]  O. Christensen.  An introduction to frames and Riesz bases , 2002 .

[12]  J P Antoine,et al.  FRAMES AND SEMIFRAMES , 2011 .

[13]  Bruno Torrésani,et al.  Time-Frequency Jigsaw Puzzle: Adaptive Multiwindow and Multilayered Gabor Expansions , 2007, Int. J. Wavelets Multiresolution Inf. Process..

[14]  Peter Balazs,et al.  Weighted and Controlled Frames , 2006 .

[15]  I. Daubechies,et al.  PAINLESS NONORTHOGONAL EXPANSIONS , 1986 .

[16]  Olivier J. J. Michel,et al.  Measuring time-Frequency information content using the Rényi entropies , 2001, IEEE Trans. Inf. Theory.

[17]  Peter Balazs,et al.  Nonstationary Gabor Frames , 2009 .

[18]  Nicki Holighaus,et al.  Theory, implementation and applications of nonstationary Gabor frames , 2011, J. Comput. Appl. Math..

[19]  Jae Lim,et al.  Signal estimation from modified short-time Fourier transform , 1984 .

[20]  Peter Balazs,et al.  Frames and semi-frames , 2011, 1101.2859.