Tracking Theory of Adaptive Filters with Input-Output Sampling Rate Offset

Adaptive filter theory for supervised identification of linear time-invariant (LTI) systems is an established and fruitful discipline in digital signal processing. In certain applications, however, the input and output signals of an LTI system may be asynchronously sampled at slightly different sampling frequencies resulting in a small input-output sampling rate offset (IO-SRO). In this contribution, we argue that an LTI system with IO-SRO is seen as a linear time-variant system by the adaptive filter. By conducting a convergence-in-the-mean analysis, we propose a model to capture the influence of IO-SRO on the tracking properties of the adaptive filter. Eventually, we validate our model by reconstruction of the IO-SRO based on the proposed model and the observable adaptive filter behavior. The model-based IO-SRO reconstruction turns out to be highly precise and robust against noise and excitation bandwidth limitations when compared to a state-of-the-art method.

[1]  W. Grassman.  Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory (Harold J. Kushner) , 1986 .

[2]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[3]  David I. Havelock,et al.  Drift-Compensated Adaptive Filtering for Improving Speech Intelligibility in Cases with Asynchronous Inputs , 2010, EURASIP J. Adv. Signal Process..

[4]  Ted S. Wada,et al.  On Dealing with Sampling Rate Mismatches in Blind Source Separation and Acoustic Echo Cancellation , 2007, 2007 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics.

[5]  Mototsugu Abe,et al.  Frequency domain acoustic echo canceller that handles asynchronous A/D and D/A clocks , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[6]  E. Hänsler,et al.  Acoustic Echo and Noise Control: A Practical Approach , 2004 .

[7]  Marc Moonen,et al.  Fifty Years of Acoustic Feedback Control: State of the Art and Future Challenges , 2011, Proceedings of the IEEE.

[8]  Henrique S. Malvar,et al.  Acoustic echo cancellation with arbitrary playback sampling rate , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  Johan Schoukens,et al.  Survey of excitation signals for FFT based signal analyzers , 1988 .

[10]  Karin Ackermann,et al.  Advances In Network And Acoustic Echo Cancellation , 2016 .

[11]  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.

[12]  Gerald Enzner,et al.  Low-Rate Farrow Structure with Discrete-Lowpass and Polynomial Support for Audio Resampling , 2018, 2018 26th European Signal Processing Conference (EUSIPCO).

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

[14]  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.

[15]  Peter Vary,et al.  Adaptive Sampling Rate Correction for Acoustic Echo Control in Voice-Over-IP , 2010, IEEE Transactions on Signal Processing.

[16]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

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

[18]  Peter Vary,et al.  Digital Speech Transmission: Enhancement, Coding and Error Concealment , 2006 .

[19]  Ali H. Sayed,et al.  Adaptive Filters , 2008 .

[20]  Lawrence R. Rabiner,et al.  Multirate Digital Signal Processing , 2019 .

[21]  Minerva M. Yeung,et al.  On the importance of exact synchronization for distributed audio signal processing , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..