Improved Approximation to the Derivative of a Digital Signal Using Wavelet Transforms for Crosstalk Analysis
The information revealed by derivatives can help to
better characterize digital near-end crosstalk signatures with the
ultimate goal of identifying the specific aggressor signal.
Unfortunately, derivatives tend to be very sensitive to even low
levels of noise. In this work we approximated the derivatives of both
quiet and noisy digital signals using a wavelet-based technique. The
results are presented for Gaussian digital edges, IBIS Model digital
edges, and digital edges in oscilloscope data captured from an actual
printed circuit board. Tradeoffs between accuracy and noise
immunity are presented. The results show that the wavelet technique
can produce first derivative approximations that are accurate to
within 5% or better, even under noisy conditions. The wavelet
technique can be used to calculate the derivative of a digital signal
edge when conventional methods fail.
[1] J. Song, K. Hoover and E. Wheeler, "Effectiveness of PCB Simulation in
Teaching High-Speed Digital Design," in Conf. Rec. 2007 IEEE
International Symposium on Electromagnetic Compatibility, pp. 1-6.
[2] M. Basu, "Gaussian-based edge-detection methods - A survey," IEEE
Trans. on Systems, Man and Cybernetics Part C: Applications and
Reviews, vol. 32, no. 3, pp. 252-260, 2002.
[3] F. Faghih, and M. Smith, "Combining spatial and scale-space techniques
for edge detection to provide a spatially adaptive wavelet-based noise
filtering algorithm," IEEE Trans. on Image Processing, vol. 11, no. 9,
pp, 1062-1071, 2002.
[4] A. Leung , F.-T. Chau, and J.-B. Gao, "Wavelet Transform: A Method
for Derivative Calculation in Analytical Chemistry," Analytical
Chemistry, vol. 70, no. 24, pp. 5222-5229, Dec. 1998.
[5] Y. Lee, and S. P. Kozaitis, "Multiresolution gradient-based edge
detection in noisy images using wavelet domain filters," Optical
Engineering, vol. 39, no. 9, pp, 2405-2412, 2000.
[6] A. Kacha, F. Grenez, P. De Doncker, and K. Benmahammed, "A
wavelet-based approach for disturbance line identification in printed
circuit boards," J. of Electromagn. Waves and Appl., vol. 18, no. 5, pp.
675-690, 2004.
[7] G. Antonini and A. Orlandi, "Wavelet packet-based EMI signal
processing and source identification," IEEE Trans. Electromagn.
Compat., vol. 43, no. 2, pp. 140-148, May 2001.
[1] J. Song, K. Hoover and E. Wheeler, "Effectiveness of PCB Simulation in
Teaching High-Speed Digital Design," in Conf. Rec. 2007 IEEE
International Symposium on Electromagnetic Compatibility, pp. 1-6.
[2] M. Basu, "Gaussian-based edge-detection methods - A survey," IEEE
Trans. on Systems, Man and Cybernetics Part C: Applications and
Reviews, vol. 32, no. 3, pp. 252-260, 2002.
[3] F. Faghih, and M. Smith, "Combining spatial and scale-space techniques
for edge detection to provide a spatially adaptive wavelet-based noise
filtering algorithm," IEEE Trans. on Image Processing, vol. 11, no. 9,
pp, 1062-1071, 2002.
[4] A. Leung , F.-T. Chau, and J.-B. Gao, "Wavelet Transform: A Method
for Derivative Calculation in Analytical Chemistry," Analytical
Chemistry, vol. 70, no. 24, pp. 5222-5229, Dec. 1998.
[5] Y. Lee, and S. P. Kozaitis, "Multiresolution gradient-based edge
detection in noisy images using wavelet domain filters," Optical
Engineering, vol. 39, no. 9, pp, 2405-2412, 2000.
[6] A. Kacha, F. Grenez, P. De Doncker, and K. Benmahammed, "A
wavelet-based approach for disturbance line identification in printed
circuit boards," J. of Electromagn. Waves and Appl., vol. 18, no. 5, pp.
675-690, 2004.
[7] G. Antonini and A. Orlandi, "Wavelet packet-based EMI signal
processing and source identification," IEEE Trans. Electromagn.
Compat., vol. 43, no. 2, pp. 140-148, May 2001.
@article{"International Journal of Electrical, Electronic and Communication Sciences:57021", author = "S. P. Kozaitis and R. L. Kriner", title = "Improved Approximation to the Derivative of a Digital Signal Using Wavelet Transforms for Crosstalk Analysis", abstract = "The information revealed by derivatives can help to
better characterize digital near-end crosstalk signatures with the
ultimate goal of identifying the specific aggressor signal.
Unfortunately, derivatives tend to be very sensitive to even low
levels of noise. In this work we approximated the derivatives of both
quiet and noisy digital signals using a wavelet-based technique. The
results are presented for Gaussian digital edges, IBIS Model digital
edges, and digital edges in oscilloscope data captured from an actual
printed circuit board. Tradeoffs between accuracy and noise
immunity are presented. The results show that the wavelet technique
can produce first derivative approximations that are accurate to
within 5% or better, even under noisy conditions. The wavelet
technique can be used to calculate the derivative of a digital signal
edge when conventional methods fail.", keywords = "digital signals, electronics, IBIS model, printedcircuit board, wavelets", volume = "3", number = "4", pages = "770-6", }