Low-Rate Farrow Structure with Discrete-Lowpass and Polynomial Support for Audio Resampling

Arbitrary sampling rate conversion (ASRC) of audio signals currently receives a lot of new attention due to its potential for aligning autonomous recording clients in ad-hoc acoustic sensor networks. State-of-the-art for digital-to-digital ASRC has been outlined in terms of a two-stage architecture comprising a) synchronous lowpass interpolation by an integer factor and b) subsequent asynchronous polynomial interpolation. While this composite ASRC achieves high resampling accuracy, its mere disadvantage is the intermediate oversampling to high rate. In our paper we thus fuse the high-rate discrete-time lowpass interpolation with a polynomial Farrow filter into a monolithic FIR filter form. We then show that decimation of the output rate effectively yields a polyphase set of Farrow filters with quasi-fixed coefficients. Simulations with broadband multitone signals confirm that the proposed low-rate monolithic ASRC achieves the same performance as the conventional composite resampling in terms of signal-to-interpolation-noise ratio. The main practical benefit of quasi-fixed coefficients of the system stands out when resampling by a small factor is desired, i.e., when the input rate almost matches the output rate - a scenario to be encountered in acoustic sensor networks.

[1]  Gennaro Evangelista,et al.  Design of digital systems for arbitrary sampling rate conversion , 2003, Signal Process..

[2]  Sharon Gannot,et al.  Blind Synchronization in Wireless Acoustic Sensor Networks , 2017, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[3]  L. Rabiner,et al.  A digital signal processing approach to interpolation , 1973 .

[4]  John G. Proakis,et al.  Digital Signal Processing: Principles, Algorithms, and Applications , 1992 .

[5]  E. Meijering A chronology of interpolation: from ancient astronomy to modern signal and image processing , 2002, Proc. IEEE.

[6]  Reinhold Häb-Umbach,et al.  Efficient Sampling Rate Offset Compensation - an Overlap-Save Based Approach , 2018, 2018 26th European Signal Processing Conference (EUSIPCO).

[7]  G. Oetken A new approach for the design of digital interpolating filters , 1979 .

[8]  E. Meijering,et al.  A chronology of interpolation: from ancient astronomy to modern signal and image processing , 2002, Proc. IEEE.

[9]  Marek Blok,et al.  Fractional delay filter design for sample rate conversion , 2012, 2012 Federated Conference on Computer Science and Information Systems (FedCSIS).

[10]  T. Saramaki,et al.  Interpolation filters with arbitrary frequency response for all-digital receivers , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[11]  Tim Hentschel Sample rate conversion in software configurable radios , 2002 .

[12]  Lin Wang,et al.  Correlation Maximization-Based Sampling Rate Offset Estimation for Distributed Microphone Arrays , 2016, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[13]  T. Ramstad Digital methods for conversion between arbitrary sampling frequencies , 1984 .

[14]  Shoji Makino,et al.  Blind compensation of interchannel sampling frequency mismatch for ad hoc microphone array based on maximum likelihood estimation , 2015, Signal Process..

[15]  T. Saramaki,et al.  An efficient approach for conversion between arbitrary sampling frequencies , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[16]  Wasfy B. Mikhael,et al.  A novel Farrow Structure with reduced complexity , 2009, 2009 52nd IEEE International Midwest Symposium on Circuits and Systems.

[17]  Vesa Välimäki A New Filter Implementation Strategy for Lagrange Interpolation , 1995, ISCAS.

[18]  Reinhold Häb-Umbach,et al.  A combined hardware-software approach for acoustic sensor network synchronization , 2015, Signal Process..

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

[20]  Paul E. Beckmann,et al.  Efficient arbitrary sampling rate conversion with recursive calculation of coefficients , 2002, IEEE Trans. Signal Process..

[21]  Richard G. Lyons Sampling Rate Conversion in the Frequency Domain , 2012 .

[22]  K. Yıldırım CLOCK SYNCHRONIZATION IN WIRELESS SENSOR NETWORKS , 2012 .

[23]  Tor A. Ramstad Fractional rate decimator and interpolator design , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[24]  Fred Harris,et al.  Performance and design of Farrow filter used for arbitrary resampling , 1997, Proceedings of 13th International Conference on Digital Signal Processing.

[25]  Markku Renfors,et al.  Structures for Interpolation, Decimation, and Nonuniform Sampling Based on Newton's Interpolation Formula , 2016 .

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

[27]  Reinhold Häb-Umbach,et al.  Multi-stage coherence drift based sampling rate synchronization for acoustic beamforming , 2017, 2017 IEEE 19th International Workshop on Multimedia Signal Processing (MMSP).

[28]  Andreas Dr.-Ing. Franck,et al.  Efficient algorithms for arbitrary sample rate conversion with application to wave field synthesis , 2012 .

[29]  Tim Hentschel,et al.  Continuous-Time Digital Filters for Sample-Rate Conversion in Reconfigurable Radio Terminals , 2001 .

[30]  Marc Moonen,et al.  Blind Sampling Rate Offset Estimation for Wireless Acoustic Sensor Networks Through Weighted Least-Squares Coherence Drift Estimation , 2017, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[31]  Tapio Saramäki,et al.  Prolonged transposed polynomial-based filters for decimation , 2003, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..

[32]  Gerald D. Cain,et al.  Offset windowing for FIR fractional-sample delay , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[33]  H. Göckler,et al.  Conversion between Arbitrary Sampling Rates: an Implementation Cost Trade-off Study for the Family of Farrow Structures , 2008 .

[34]  Tapio Saramäki,et al.  Implementation of the transposed Farrow structure , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[35]  C. W. Farrow,et al.  A continuously variable digital delay element , 1988, 1988., IEEE International Symposium on Circuits and Systems.