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Performing fractional delay via fractional singular spectrum analysis

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Abstract

This paper proposes a fractional singular spectrum analysis (SSA)-based method for performing the fractional delay. First, the input sequence is divided into two overlapping sequences with the first sequence being the input sequence without its last point and the second sequence being the input sequence without its first point. Then, the singular value decompositions (SVD) are performed on the trajectory matrices constructed based on these two sequences. Next, the designs of both the right unitary matrix and the left unitary matrix for generating the new trajectory matrix are formulated as the quadratically constrained quadratic programing problems. The analytical solutions of these quadratically constrained quadratic programing problems are derived via the SVD approach. Finally, the fractional SSA components are obtained by performing the diagonal averaging operation, and the fractional delay sequence is obtained by summing up all the fractional SSA components together. Since the fractional SSA operations are nonlinear and adaptive, our proposed method is a kind of nonlinear and adaptive approach for performing the fractional delay. Besides, by discarding some fractional SSA components, the joint fractional delay operation and the denoising operation can be performed simultaneously.

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References

  1. Tseng, C.-C., Lee, S.-L.: Designs of fixed-fractional delay filters using fractional-derivative constraints. IEEE Trans. Circuits Syst. II Express Briefs 59(10), 683–687 (2012)

    Article  Google Scholar 

  2. Bensouici, T., Charef, A., I, Assadi, : A new approach for the design of fractional delay by an FIR filter. ISA Trans. 82, 73–77 (2018)

    Article  Google Scholar 

  3. Dam, H.H.: Design of variable fractional delay filter with fractional delay constraints. IEEE Signal Process. Lett. 21(11), 1361–1364 (2014)

    Article  Google Scholar 

  4. Tseng, C., Lee, S.: Designs of fixed-fractional-delay filters using fractional-derivative constraints. IEEE Trans. Circuits Syst. II Express Briefs 59(10), 683–687 (2012)

    Article  Google Scholar 

  5. Deng, T.B.: Decoupling minimax design of low-complexity variable fractional-delay FIR digital filters. IEEE Trans. Circuits Syst. I Regul. Pap. 58(10), 2398–2408 (2011)

    Article  MathSciNet  Google Scholar 

  6. Johansson, H., Lowenborg, P.: On the design of adjustable fractional delay FIR filters. IEEE Trans. Circuits Syst. II, Analog Digital Signal Process. 50(4), 164–169 (2003)

    Article  Google Scholar 

  7. Bensouici, T., Charef, A., Assadi, I.: A simple design of fractional delay FIR filter based on binomial series expansion theory. Circuits, Syst. Signal Process. 38, 3356–3369 (2019)

    Article  Google Scholar 

  8. Deng, T.-B.: Minimax design of low-complexity allpass variable fractional-delay digital filters. IEEE Trans. Circuits Syst. I Regul. Pap. 57(8), 2075–2086 (2010)

    Article  MathSciNet  Google Scholar 

  9. Verma, A.K., Jarial, R.K., Mohan Rao, U.: Modified non-adaptive bandpass filter based phase locked loop. Electr. Lett. 56(18), 95–954 (2020)

    Article  Google Scholar 

  10. Chen, H., Zhengyuan, Xu.: A two-dimensional constellation design method for visible light communications with signal-dependent shot noise. IEEE Commun. Lett. 22(9), 1786–1789 (2018)

    Article  Google Scholar 

  11. Ho, C.Y.F., Ling, B.W.K., Tam, P.K.S.: Representation of linear dual-rate system via single SISO LTI filter, conventional sampler and block sampler. IEEE Trans. Circuits Syst. II Express Briefs 55(2), 168–172 (2008)

    Article  Google Scholar 

  12. Chen, T., Qiu, Li., Bai, E.-W.: General multirate building structures with application to nonuniform filter banks. IEEE Trans. Circuits Syst. II: Analog Digital Signal Process. 45(8), 948–958 (1998)

    Article  Google Scholar 

  13. Hohansson, H., Wanhammar, L.: Filter structures composed of all-pass and FIR filters for interpolation and decimation by a factor of two. IEEE Trans. Circuits Syst. II Express Briefs 46(7), 896–905 (1999)

    Article  Google Scholar 

  14. Kuang, W., Wang, S., Lai, Y., Ling, W.-K.: Efficient and adaptive signal denoising based on multistage singular spectrum analysis. IEEE Trans. Instrum. Meas. 70, 6500120 (2021)

    Article  Google Scholar 

  15. Huang, Z., Ling, B.W.-K.: De-Hankelization of singular spectrum analysis matrices via L1 norm criterion. Signal, Image Video Process. 13(5), 933–940 (2019)

    Article  Google Scholar 

  16. Lin, P., Kuang, W., Liu, Y., Ling, B.W.K.: Grouping and selecting singular spectrum analysis components for denoising via empirical mode decomposition approach. Circuits, Syst., Signal Process. 38(1), 356–370 (2019)

    Article  Google Scholar 

  17. Feng, P., Ling, B.W.K., Lei, R., Chen, J.: Singular spectral analysis-based denoising without computing singular values via augmented Lagrange multiplier algorithm. IET Signal Process. 13(2), 149–156 (2019)

    Article  Google Scholar 

  18. Gu, J., Lin, P., Ling, B.W.K., Yang, C., Feng, P.: Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming. IET Signal Process. 12(5), 599–604 (2018)

    Article  Google Scholar 

  19. Kuang, W., Ling, B.W.K., Yang, Z.: Reconstructing signal from quantized signal based on singular spectral analysis. Digital Signal Process. 82, 11–30 (2018)

    Article  Google Scholar 

  20. Lin, Y., Ling, B.W.K., Xu, N., Lam, R.W.K., Ho, C.Y.F.: Effectiveness analysis of bio-electronic stimulation therapy to Parkinson’s diseases via joint singular spectrum analysis and discrete Fourier transform approach. Biomed. Signal Process. Control 62, 102131 (2020)

    Article  Google Scholar 

  21. Mo, X., Ling, B.W.K., Ye, Q., Zhou, Y.: Linear phase properties of the singular spectrum analysis components for the estimations of the RR intervals of electrocardiograms. Signal, Image Video Process. 14(2), 325–332 (2020)

    Article  Google Scholar 

  22. Tian, Z., Ling, B.W.K., Zhou, X., Lam, R.W.K., Teo, K.L.: Suppressing the spikes in electroencephalogram via an iterative joint singular spectrum analysis and low-rank decomposition approach. Sensors 20(2), 341 (2020)

    Article  Google Scholar 

  23. Ho, C.Y.F., Ling, B.W.K., Benmesbah, L., Kok, T.C.W., Siu, W.C., Teo, K.L.: Two-channel linear phase FIR QMF bank minimax design via global nonconvex optimization programming. IEEE Trans. Signal Process. 58(8), 4436–4441 (2010)

    Article  MathSciNet  Google Scholar 

  24. Ling, B.W.K., Tian, N., Ho, C.Y.F., Siu, W.C., Teo, K.L., Dai, Q.: Maximally decimated paraunitary linear phase FIR filter bank design via iterative SVD approach. IEEE Trans. Signal Process. 63(2), 466–481 (2014)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This paper was supported partly by the National Nature Science Foundation of China (No. U1701266, No. 61671163 and No. 62071128), the Team Project of the Education Ministry of the Guangdong Province (No. 2017KCXTD011), the Guangdong Higher Education Engineering Technology Research Center for Big Data on Manufacturing Knowledge Patent (No. 501130144) and Hong Kong Innovation and Technology Commission, Enterprise Support Scheme (No. S/E/070/17).

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Authors and Affiliations

  1. School of Information Engineering, Guangdong University of Technology, Guangzhou, 510006, China

    Yang Zhou, Bingo Wing-Kuen Ling & Yuxin Lin

  2. Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, China

    Ziyin Huang & Yui-Lam Chan

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  1. Yang Zhou
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  2. Bingo Wing-Kuen Ling
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  3. Ziyin Huang
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  5. Yuxin Lin
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Correspondence to Bingo Wing-Kuen Ling.

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Zhou, Y., Ling, B.WK., Huang, Z. et al. Performing fractional delay via fractional singular spectrum analysis. SIViP 16, 39–46 (2022). https://doi.org/10.1007/s11760-021-01954-x

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