**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32794

##### Efficient Alias-free Level Crossing Sampling

**Authors:**
Negar Riazifar,
Nigel G. Stocks

**Abstract:**

This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding a jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm.

**Keywords:**
Alias-free,
level crossing sampling,
spectrum,
trigonometric polynomial.

**References:**

[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] 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.

[3] 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.

[4] D. Hand and M. S. W. Chen, “A non-uniform sampling ADC architecture with embedded alias-free asynchronous filter,” GLOBECOM - Signal Process. Commun. Symp., pp. 3707–3712, 2012.

[5] B. Schell and Y. Tsividis, “A continuous-time ADC/DSP/DAC system with no clock and with activity-dependent power dissipation,” IEEE J. Solid-State Circuits, vol. 43, pp. 2472–2481, 2008.

[6] T. F. Wu, S. Dey and M. S. W. Chen, “A nonuniform sampling ADC architecture with reconfigurable digital anti-aliasing filter,” IEEE Trans. Circuits Syst. I Regul. Pap., vol. 63, pp. 1639–1651, 2016.

[7] S. Patil, A. Ratiu, D. Morche and Y. Tsividis, “A 3–10 fJ/conv-step error-shaping alias-free continuous-time ADC,” IEEE Journal of Solid-State Circuits, vol. 51, pp. 908–918, 2016.

[8] M. Kurchuk, C. W. Wu, D. Morche and Y. Tsividis, “Event-driven GHz-range continuous-time digital signal processor with activity-dependent power dissipation,” IEEE Journal of Solid-State Circuits, vol. 47, pp. 2164-2173, 2012.

[9] C. Luo, “Non-uniform sampling: algorithms and architectures,” PhD Thesis, Georgia Institute of Technology, 2012.

[10] Y. Tsividis, “Digital signal processing in continuous time: A possibility for avoiding aliasing and reducing quantization error ,” IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 589-592, 2004.

[11] T. F. Wu, C. R. Ho and M. S. W. Chen, “A flash-based non-uniform sampling ADC with hybrid quantization enabling digital anti-aliasing filter,” IEEE J. Solid-State Circuits, vol. 52, pp. 2335–2349, 2017.

[12] 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.

[13] H. G. Feichtinger, K. Grochenig and T. Strohmer, “Efficent numerical methods in non-uniform sampling theory,” Numer. Math., vol. 69, pp. 423-440, 1995.

[14] K. Grochenig, “Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type,” Math. Comput., vol. 68, pp. 749-765, 2002.

[15] 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.

[16] 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.

[17] 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.

[18] N. Riazifar and N. G. Stocks, “Efficient high fidelity signal reconstruction based on level crossing sampling,” World Academy of Science, Engineering and Technology, vol. 5, pp. 487-496, 2021.

[19] I. Bilinskis, E. Boole and K. Sudars, “Combination of periodic and alias-free non-uniform signal sampling for wideband signal digitizing and compressed transmitting based on picosecond-resolution event timing,” Signal Processing Symposium, 2017.