Efficient High Fidelity Signal Reconstruction Based on Level Crossing Sampling
This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide high fidelity signal reconstruction for speech signals; these strategies circumvent the problem of exponentially increasing number of samples as the bit-depth is increased and hence are highly efficient. Specifically, the results indicate that the distribution of the intervals between samples is one of the key factors in the quality of signal reconstruction; including samples with short intervals does not improve the accuracy of the signal reconstruction, whilst samples with large intervals lead to numerical instability. The proposed sampling method, termed reduced conventional level crossing (RCLC) sampling, exploits redundancy between samples to improve the efficiency of the sampling without compromising performance. A reconstruction technique is also proposed that enhances the numerical stability through linear interpolation of samples separated by large intervals. Interpolation is demonstrated to improve the accuracy of the signal reconstruction in addition to the numerical stability. We further demonstrate that the RCLC and interpolation methods can give useful levels of signal recovery even if the average sampling rate is less than the Nyquist rate.
[1] E. Allier, G. Sicard, L. Fesquet and M. Renaudin, “Asynchronous level
crossing analog to digital converters,” Meas. J. Int. Meas. Confed., vol.
37, pp. 296–309, 2005.
[2] D. Kinniment, A. Yakovlev and B. Gao, “Synchronous and asynchronous
A-D conversion,” IEEE Trans. Very Large Scale Integr. Syst., vol. 8, pp.
217-220, 2000.
[3] Y. Tsividis, “Event-driven data acquisition and digital signal processing-A
tutorial,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 57, pp.
577-581, 2010.
[4] N. Sayiner, H. V. Sorensen and T. R. Viswanathan, “A level-crossing
sampling scheme for A/D conversion,” IEEE Transaction on Circuits and
Systems-11: Analog and Digital Signal Processing, vol. 43, pp. 335-339,
1996.
[5] B. Schell and Y. Tsividis, “A continuous-time ADC/DSP/DAC system
with no clock and with activity-dependent power dissipation,” Jssc., vol.
43, pp. 2472–2481, 2008.
[6] R. W. Stewart, E. Pine and D. Sweeney, “A digital signal processing
audiometric workstation,” IEE., 1993.
[7] C. Wijenayake, J. Scutts and A. Ignjatovi´c, “Signal recovery algorithm
for 2-level amplitude sampling using chromatic signal approximations,”
Signal Processing, vol. 153, pp. 143–152, 2018.
[8] K. Kozmin, J. Johansson and J. Delsing, “Level-crossing ADC
performance evaluation toward ultrasound application,” IEEE Trans.
Circuits Syst. I Regul. Pap., vol. 56, pp. 1708–1719, 2009.
[9] T. Wang, D. Wang, P. J. Hurst, B. C. Levy and S. H. Lewis, “A
level-crossing analog-to-digital converter with triangular dither,” IEEE
Trans. Circuits Syst. I Regul. Pap., vol. 56, pp. 2089–2099, 2009.
[10] M. Ben-Romdhane, A. Maalej, M. Tlili, C. Rebai, F. Rivet and
D. Dallet, “Event-driven ECG sensor in healthcare devices for data
transfer optimization,” Arabian Journal for Science and Engineering, vol.
45, pp. 6361–6387, 2020.
[11] K. Grochenig, “Irregular sampling, Toeplitz matrices, and the
approximation of entire functions of exponential type,” Math. Comput.,
vol. 68, pp. 749-765, 2002.
[12] K. Grochenig, “Reconstruction algorithm in irregular sampling,” Math.
Comput., vol. 59, pp. 181-194, 1992. [13] J. L. Yen, “On nonuniform sampling of bandlimited signals,” IRE Trans.
Circuit Theory, vol. 3, pp. 251–257, 1956.
[14] F. J. Beutler, “Error-free recovery of signals from irregularly spaced
samples,” SIAM., vol. 8, pp. 328–335, 1966.
[15] C. Vezyrtzis and Y. Tsividis, “Processing of signals using level-crossing
sampling,” Proc. - IEEE Int. Symp. Circuits Syst., vol. 37, pp. 2293–2296,
2009.
[16] F. A. Marvasti, Nonuniform Sampling: Theory and Practice, Springer,
2001.
[17] E. I. Plotkin, M. N. S. Swamy and Y. Yoganandam, “A novel iterative
method for the reconstruction of signal from nonuniformly spaced
samples,” Signal Processing, vol. 37, pp. 203–213, 1994.
[18] H. Lai, P. Mart and A. V. Oppenheim, “An iterative reconstruction
algorithm for amplitude sampling,” ICASSP., pp. 4576–4580, 2017.
[19] R. Kumaresan and N. Panchal, “Encoding bandpass signals using
zero/level crossings: A model-based approach,” IEEE Transactions Audio,
Speech Lang. Process., vol. 18, pp. 17–33, 2010.
[20] N. K. Sharma and T. V. Sreenivas, “Event-triggered sampling and
reconstruction of sparse real-valued trigonometric polynomials,” Int. Conf.
Signal Process. Commun., 2014.
[21] U. Grunde, “Non-stationary signal reconstruction from level-crossing
samples using akima spline,” Elektronika Ir Elektrotechnika, vol. 117,
pp. 9–12, 2012.
[22] T. I. Laakso, A. Tarczynski, N. P. Murphy and V. V¨alim¨aki, “Polynomial
filtering approach to reconstruction and noise reduction of nonuniformly
sampled signals,” Signal Processing, vol. 80, pp. 567–575, 2000.
[23] J. Y. Rheem, B. H. Kim and S. G. Ann, “A nonuniform sampling method
of speech signal and its application to speech coding,” Signal Processing,
vol. 41, pp. 43-48, 1995.
[24] A. Antony, S. R. Paulson and D. J. Moni, “Asynchronous level crossing
ADC design for wearable devices: A review,” Int. J. Appl. Eng. Res., vol.
13, pp. 1858–1865, 2018.
[25] H. G. Feichtinger, K. Grochenig and T. Strohmer, “Efficent numerical
methods in non-uniform sampling theory,” Numer. Math., vol. 69, pp.
423-440, 1995.
[26] E. Allier, G. Sicard, L. Fesquet and M. Renaudin, “A new class of
asynchronous A/D converters based on time quantization,” Ninth Int.
Symp. Asynchronous Circuits Syst. Proceedings, pp. 196–205, 2003.
[27] D. Rzepka, M. Mi´skowicz, D. Koscielnik and N. T. Thao,
“Reconstruction of signals from level-crossing samples using implicit
information,” IEEE Access, vol. 6, pp. 35001–35011, 2018.
[28] Y. Hou, J. Qu, Z. Tian, M. Atef, K. Yousef, Y. Lian and G. Wang,
“A 61-nW level-Crossing ADC with adaptive sampling for biomedical
applications,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 66, pp.
56–60, 2019.
[29] T. Wu and M. S. Chen, “A subranging-based nonuniform sampling ADC
with sampling event filtering,” IEEE Solid-State Circuits Lett., vol. 1, pp.
78–81, 2018.
[30] H. Teimoori, N. Ravanshad and H. Rezaee-Dehsorkh, “Ultra-low-power
fully-synchronous level-crossing analog-to-digital converter for
bioemdical signal acquisition,” Int. Conf. Microelectron, vol. 9, pp.
7–10, 2017.
[31] M. Trakimas and S. Sonkusale, “A 0.8 v asynchronous ADC for energy
constrained sensing applications,” Proc. Cust. Integr. Circuits Conf., pp.
173–176, 2008.
[32] T. Strohmer, “Numerical analysis of the non-uniform sampling problem,”
J. Comput. Appl. Math., vol. 122, pp. 297-316, 2000.
[33] M. B. Mashhadi, N. Salarieh, E. S. Farahani and F. Marvasti, “Level
crossing speech sampling and its sparsity promoting reconstruction using
an iterative method with adaptive thresholding,” IET Signal Process., vol.
11, pp. 721–726, 2017.
[34] J. S. Garofolo, L. F. Lamel, W. M. Fisher, J. G. Fiscus, D. S. Pallett,
N. L. Dahlgren and V. Zue, “TIMIT acoustic-phonetic continuous speech
corpus,” 1993. URL: https://catalog.ldc.upenn.edu/LDC93S1.
[35] J. A. Fernandez and B. V. K. V. Kumar, “Multidimensional overlap-add
and overlap-save for correlation and convolution,” ICIP., pp. 509–513,
2013.
[36] M. W. Hauser, “Principles of oversampling A/D conversion,” J. Audio
Eng. Soc., vol. 39, pp. 3-26, 1991.
[37] F. James, “On the Runge example,” Taylor Fr., Ltd . behalf Math. Assoc.
Am., vol. 94, pp. 329–341, 1987.
[1] E. Allier, G. Sicard, L. Fesquet and M. Renaudin, “Asynchronous level
crossing analog to digital converters,” Meas. J. Int. Meas. Confed., vol.
37, pp. 296–309, 2005.
[2] D. Kinniment, A. Yakovlev and B. Gao, “Synchronous and asynchronous
A-D conversion,” IEEE Trans. Very Large Scale Integr. Syst., vol. 8, pp.
217-220, 2000.
[3] Y. Tsividis, “Event-driven data acquisition and digital signal processing-A
tutorial,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 57, pp.
577-581, 2010.
[4] N. Sayiner, H. V. Sorensen and T. R. Viswanathan, “A level-crossing
sampling scheme for A/D conversion,” IEEE Transaction on Circuits and
Systems-11: Analog and Digital Signal Processing, vol. 43, pp. 335-339,
1996.
[5] B. Schell and Y. Tsividis, “A continuous-time ADC/DSP/DAC system
with no clock and with activity-dependent power dissipation,” Jssc., vol.
43, pp. 2472–2481, 2008.
[6] R. W. Stewart, E. Pine and D. Sweeney, “A digital signal processing
audiometric workstation,” IEE., 1993.
[7] C. Wijenayake, J. Scutts and A. Ignjatovi´c, “Signal recovery algorithm
for 2-level amplitude sampling using chromatic signal approximations,”
Signal Processing, vol. 153, pp. 143–152, 2018.
[8] K. Kozmin, J. Johansson and J. Delsing, “Level-crossing ADC
performance evaluation toward ultrasound application,” IEEE Trans.
Circuits Syst. I Regul. Pap., vol. 56, pp. 1708–1719, 2009.
[9] T. Wang, D. Wang, P. J. Hurst, B. C. Levy and S. H. Lewis, “A
level-crossing analog-to-digital converter with triangular dither,” IEEE
Trans. Circuits Syst. I Regul. Pap., vol. 56, pp. 2089–2099, 2009.
[10] M. Ben-Romdhane, A. Maalej, M. Tlili, C. Rebai, F. Rivet and
D. Dallet, “Event-driven ECG sensor in healthcare devices for data
transfer optimization,” Arabian Journal for Science and Engineering, vol.
45, pp. 6361–6387, 2020.
[11] K. Grochenig, “Irregular sampling, Toeplitz matrices, and the
approximation of entire functions of exponential type,” Math. Comput.,
vol. 68, pp. 749-765, 2002.
[12] K. Grochenig, “Reconstruction algorithm in irregular sampling,” Math.
Comput., vol. 59, pp. 181-194, 1992. [13] J. L. Yen, “On nonuniform sampling of bandlimited signals,” IRE Trans.
Circuit Theory, vol. 3, pp. 251–257, 1956.
[14] F. J. Beutler, “Error-free recovery of signals from irregularly spaced
samples,” SIAM., vol. 8, pp. 328–335, 1966.
[15] C. Vezyrtzis and Y. Tsividis, “Processing of signals using level-crossing
sampling,” Proc. - IEEE Int. Symp. Circuits Syst., vol. 37, pp. 2293–2296,
2009.
[16] F. A. Marvasti, Nonuniform Sampling: Theory and Practice, Springer,
2001.
[17] E. I. Plotkin, M. N. S. Swamy and Y. Yoganandam, “A novel iterative
method for the reconstruction of signal from nonuniformly spaced
samples,” Signal Processing, vol. 37, pp. 203–213, 1994.
[18] H. Lai, P. Mart and A. V. Oppenheim, “An iterative reconstruction
algorithm for amplitude sampling,” ICASSP., pp. 4576–4580, 2017.
[19] R. Kumaresan and N. Panchal, “Encoding bandpass signals using
zero/level crossings: A model-based approach,” IEEE Transactions Audio,
Speech Lang. Process., vol. 18, pp. 17–33, 2010.
[20] N. K. Sharma and T. V. Sreenivas, “Event-triggered sampling and
reconstruction of sparse real-valued trigonometric polynomials,” Int. Conf.
Signal Process. Commun., 2014.
[21] U. Grunde, “Non-stationary signal reconstruction from level-crossing
samples using akima spline,” Elektronika Ir Elektrotechnika, vol. 117,
pp. 9–12, 2012.
[22] T. I. Laakso, A. Tarczynski, N. P. Murphy and V. V¨alim¨aki, “Polynomial
filtering approach to reconstruction and noise reduction of nonuniformly
sampled signals,” Signal Processing, vol. 80, pp. 567–575, 2000.
[23] J. Y. Rheem, B. H. Kim and S. G. Ann, “A nonuniform sampling method
of speech signal and its application to speech coding,” Signal Processing,
vol. 41, pp. 43-48, 1995.
[24] A. Antony, S. R. Paulson and D. J. Moni, “Asynchronous level crossing
ADC design for wearable devices: A review,” Int. J. Appl. Eng. Res., vol.
13, pp. 1858–1865, 2018.
[25] H. G. Feichtinger, K. Grochenig and T. Strohmer, “Efficent numerical
methods in non-uniform sampling theory,” Numer. Math., vol. 69, pp.
423-440, 1995.
[26] E. Allier, G. Sicard, L. Fesquet and M. Renaudin, “A new class of
asynchronous A/D converters based on time quantization,” Ninth Int.
Symp. Asynchronous Circuits Syst. Proceedings, pp. 196–205, 2003.
[27] D. Rzepka, M. Mi´skowicz, D. Koscielnik and N. T. Thao,
“Reconstruction of signals from level-crossing samples using implicit
information,” IEEE Access, vol. 6, pp. 35001–35011, 2018.
[28] Y. Hou, J. Qu, Z. Tian, M. Atef, K. Yousef, Y. Lian and G. Wang,
“A 61-nW level-Crossing ADC with adaptive sampling for biomedical
applications,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 66, pp.
56–60, 2019.
[29] T. Wu and M. S. Chen, “A subranging-based nonuniform sampling ADC
with sampling event filtering,” IEEE Solid-State Circuits Lett., vol. 1, pp.
78–81, 2018.
[30] H. Teimoori, N. Ravanshad and H. Rezaee-Dehsorkh, “Ultra-low-power
fully-synchronous level-crossing analog-to-digital converter for
bioemdical signal acquisition,” Int. Conf. Microelectron, vol. 9, pp.
7–10, 2017.
[31] M. Trakimas and S. Sonkusale, “A 0.8 v asynchronous ADC for energy
constrained sensing applications,” Proc. Cust. Integr. Circuits Conf., pp.
173–176, 2008.
[32] T. Strohmer, “Numerical analysis of the non-uniform sampling problem,”
J. Comput. Appl. Math., vol. 122, pp. 297-316, 2000.
[33] M. B. Mashhadi, N. Salarieh, E. S. Farahani and F. Marvasti, “Level
crossing speech sampling and its sparsity promoting reconstruction using
an iterative method with adaptive thresholding,” IET Signal Process., vol.
11, pp. 721–726, 2017.
[34] J. S. Garofolo, L. F. Lamel, W. M. Fisher, J. G. Fiscus, D. S. Pallett,
N. L. Dahlgren and V. Zue, “TIMIT acoustic-phonetic continuous speech
corpus,” 1993. URL: https://catalog.ldc.upenn.edu/LDC93S1.
[35] J. A. Fernandez and B. V. K. V. Kumar, “Multidimensional overlap-add
and overlap-save for correlation and convolution,” ICIP., pp. 509–513,
2013.
[36] M. W. Hauser, “Principles of oversampling A/D conversion,” J. Audio
Eng. Soc., vol. 39, pp. 3-26, 1991.
[37] F. James, “On the Runge example,” Taylor Fr., Ltd . behalf Math. Assoc.
Am., vol. 94, pp. 329–341, 1987.
@article{"International Journal of Information, Control and Computer Sciences:80811", author = "Negar Riazifar and Nigel G. Stocks", title = "Efficient High Fidelity Signal Reconstruction Based on Level Crossing Sampling", abstract = "This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide high fidelity signal reconstruction for speech signals; these strategies circumvent the problem of exponentially increasing number of samples as the bit-depth is increased and hence are highly efficient. Specifically, the results indicate that the distribution of the intervals between samples is one of the key factors in the quality of signal reconstruction; including samples with short intervals does not improve the accuracy of the signal reconstruction, whilst samples with large intervals lead to numerical instability. The proposed sampling method, termed reduced conventional level crossing (RCLC) sampling, exploits redundancy between samples to improve the efficiency of the sampling without compromising performance. A reconstruction technique is also proposed that enhances the numerical stability through linear interpolation of samples separated by large intervals. Interpolation is demonstrated to improve the accuracy of the signal reconstruction in addition to the numerical stability. We further demonstrate that the RCLC and interpolation methods can give useful levels of signal recovery even if the average sampling rate is less than the Nyquist rate.", keywords = "Level crossing sampling, numerical stability, speech processing, trigonometric polynomial.", volume = "16", number = "5", pages = "148-10", }
