A novel method based on signal sparsity to obtain fractional sample delay

In many applications, such as communication, speech coding, and audio technology, not only the sampling frequency but also the actual sampling instants are of crucial importance. Fractional sample delay has been widely used in the domain of signal processing. There are many methods to obtain higher delay resolution. However the common defect is that they can not provide a continuous variable accurate delay. In this paper we take into account the characteristic of the information carried by the signal, which is the essence of the signal. A novel method based on the signal sparsity is prosed. Compared to the traditional interpolation algorithm, this method has lower normalized mean square error (NMSE) and can obtain arbitrary sample delay.

[1]  Andrzej Tarczynski,et al.  Evaluation of several variable FIR fractional-sample delay filters , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[2]  Cagatay Candan.  An Efficient Filtering Structure for Lagrange Interpolation , 2007, IEEE Signal Processing Letters.

[3]  Che-Ho Wei,et al.  Programmable fractional sample delay filter with Lagrange interpolation , 1990 .

[4]  Unto K. Laine,et al.  Splitting the Unit Delay - Tools for fractional delay filter design , 1996 .

[5]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[6]  Vesa Välimäki,et al.  Principles of fractional delay filters , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[7]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[8]  Avideh Zakhor,et al.  Very low bit-rate video coding based on matching pursuits , 1997, IEEE Trans. Circuits Syst. Video Technol..

[9]  Peter J. Kootsookos,et al.  FIR approximation of fractional sample delay systems , 1996 .

[10]  S. C. Dutta Roy,et al.  A note on the fir approximation of a fractional sample delay , 1993, Int. J. Circuit Theory Appl..

[11]  Andrzej Tarczynski,et al.  An efficient fractional sample delayer for digital beam steering , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[13]  Unto K. Laine,et al.  Splitting the unit delay [FIR/all pass filters design] , 1996, IEEE Signal Process. Mag..

[14]  K. Rajamani,et al.  An efficient algorithm for sample rate conversion from CD to DAT , 2000, IEEE Signal Processing Letters.

[15]  Jean Armstrong,et al.  Symbol synchronization using signal samples and interpolation , 1993, IEEE Trans. Commun..

[16]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..