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Signal Adaptive Pipelined Hardware Design of Time-Varying Optimal Filter for Highly Nonstationary FM Signal Estimation

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Abstract

In this paper we develop a multiple-clock-cycle signal adaptive hardware design of an optimal nonstationary (time-varying) filtering system. The proposed design is based on the real-time results of time-frequency (TF) analysis and the estimation of instantaneous frequency (IF). It permits multiple detection of the local filter’s region of support (FRS) in the observed increment of time, resulting in the efficient filtering of multicomponent frequency modulated (FM) signals. The proposed design takes a variable number of clock (CLK) cycles–the only necessary ones regarding the highest quality of IF estimation–in different TF points within the execution. In this way it allows the implemented system to optimize the computational cost, as well as the time required for execution. Further, the proposed serial design optimizes critical design performances, related to the hardware complexity, making it a suitable system for real-time implementation on an integrated chip. Also, by applying the pipelining technique, it allows overlapping between different TF points within the execution, additionally improving the time required for time-varying filtering. The design has been verified by a field-programmable gate array (FPGA) circuit design, capable of performing filtering of nonstationary FM signals in real-time.

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Notes

  1. S2 is a predefined reference level, determined as a few percent of the SPEC’s maximal value and practically selected based on a simple analysis of the processed signal, [23, 29].

  2. Boundaries of each STFT auto-term’s domain coincide with the detection of \( {\left| {STF{T_x}\left( {n,k \pm i} \right)} \right|^2} < {S^2} \) around corresponding signal component. It means that \( {\left| {STF{T_x}\left( {n,k \pm i} \right)} \right|^2} \geqslant {S^2} \), for i = 0,1,…,L(n,k), in each point (n,k) from STFT auto-terms’ domains, whereas \( {\left| {STF{T_x}\left( {n,k \pm i} \right)} \right|^2} < {S^2} \) for ∀i should be satisfied otherwise. Therefore, L(n,k) takes variable values in different TF points: zero (L(n,k) = 0) outside STFT auto-terms’ domains and at their boundaries (in the case of non-noisy signal), the higher one inside these domains, and the maximum one (L m ) only in the central points of the widest domain(s). In the case of noisy signal, depending on the noise distribution and the S 2 selection, \( {\left| {STF{T_x}\left( {n,k \pm i} \right)} \right|^2} \geqslant {S^2} \) can be satisfied in the particular (n,k) points existing outside the STFT auto-terms’ domains. This implies the non-zero L(n,k) values in these points.

  3. Parallel and hybrid designs minimize the total number of used memory locations, since the parallel one does not include LUT memory (of L m +2 locations), whereas the hybrid one includes LUT memory of only three locations (controls the execution in three CLKs by frequency point). In addition, the proposed signal adaptive design includes two input memories (used for storing the real and imaginary parts of input STFT samples), capacity of maximum N locations. However, note that the total number of used memory locations remains quite small in all considered cases.

References

  1. Matz, G. & Hlawatsch, F. (2002). Linear time-frequency filters: Online algorithms and applications. In Papandreou-Suppappola, A. (Ed.), Applications in Time-Frequency Signal Processing (pp.205–271). CRC Press.

  2. Zadeh, L. A. (1950). Frequency analysis of variable networks. Proceedings of IRE, 76, 291–299.

    Article  Google Scholar 

  3. Kramer, M. L. & Jones, D.L. (1994). Improved time-frequency filtering using as STFT analysis-modification-synthesis method, Proc. IEEE-SP Int. Sym. Time-Frequency Time-Scale Analysis, Philadelphia, 264–267

  4. Xia, X.-G., & Qian, S. (1999). Convergence of an iterative time-variant filtering based on discrete Gabor transform. IEEE Transactions on Signal Processing, 47(10), 2894–2899.

    Article  MathSciNet  MATH  Google Scholar 

  5. Feichtinger, H. G., & Strohmer, T. (Eds.). (1998). Gabor analysis and algorithms: Theory and applications. Boston: Birkhäuser.

    MATH  Google Scholar 

  6. Kozek, W. (1992). Time-frequency signal processing based on the Wigner-Weyl framework. Signal Processing, 29(10), 77–92.

    Article  MATH  Google Scholar 

  7. Kozek, W. & Hlawatsch, F.(1992). A comparative study of linear and nonlinear time-frequency filters, In Proc. IEEE-SP Int. Sympos. Time-Frequency Time-Scale Analysis, Victoria, Canada, 163–166.

  8. Shenoy, R. G., & Parks, T. W. (1994). The Weyl correspodence and time-frequency analysis. IEEE Transactions on Signal Processing, 42(2), 318–331.

    Article  Google Scholar 

  9. Hlawatsch, F., Matz, G., Kirchauer, H., & Kozek, W. (2000). Time-frequency formulation, design and implementation of time-varying optimal filters for signal estimation. IEEE Transactions on Signal Processing, 48(5), 1417–1432.

    Article  MATH  Google Scholar 

  10. Matz, G. & Hlawatsch, F.(2002). Linear time-frequency filters. In Time-Frequency Signal Analysis and Processing, Boashash, B. (ed.), Pretice Hall.

  11. Gröchenig, K. (2001). Foundations of Time-frequency analysis. Birkhäuser.

  12. Cohen, L. (1995). Time-frequency analysis. Prentice-Hall.

  13. Zeevi, Y. Y., Zibulski, M., & Porat, M. (1998). Multi-window Gabor schemes in signal and image representations. In H. G. Feichtinger & T. Strohmer (Eds.), Gabor analysis and algorithms: Theory and applications (pp. 381–407). Boston: Birkhäuser.

    Google Scholar 

  14. Zibulski, M., & Zeevi, Y. Y. (1997). Discrete multiwindow Gabor-type transforms. IEEE Transactions on Signal Processing, 45(6), 1428–1442.

    Article  MATH  Google Scholar 

  15. Zibulski, M., & Zeevi, Y. Y. (1997). Analysis of multiwindow Gabor-type schemes by frame methods. In Applied and Computational Harmonic Analysis, 4(4), 188–221.

    Article  MathSciNet  MATH  Google Scholar 

  16. Hlawatsch, F., & Kozek, W. (1994). Time-frequency projection filters and time-frequency signal expansions. IEEE Transactions on Signal Processing, 42(12), 3321–3334.

    Article  Google Scholar 

  17. Claasen, T. A. C. M., & Mecklenbräuker, W. F. G. (1982). On stationary linear time-varying systems. IEEE Transactions on Circuits and Systems, 29(3), 169–184.

    Article  MATH  Google Scholar 

  18. Matz, G. & Hlawatsch, F. (2002). Time-frequency projection filters: Online implementation, subspace tracking, and application to interference suppression. In Proceedings of IEEE International Conference on Acoustic, SPEECH, AND Signal Processing (ICASSP ’02)Fla. USA, 2(5), 1213–1216.

  19. Golub, G. H., & Van Loan, C. F. (1996). Matrix computations (3rd ed.). Baltimore: Johns Hopkins University Press.

    MATH  Google Scholar 

  20. Boudreaux-Bartels, G. F. (1997). Time-varying signal processing using Wigner distribution synthesis techniques. In Mecklenbräuker, W. & Hlawatsch, F. (Eds.), The wigner distribution—theory and applications in signal processing, pp.269–317. Elsevier.

  21. Hlawatsch, F. & Krattenthaler, W. (1997). Signal synthesis algorithms for bilinear time-frequency signal representation. In Mecklenbräuker, W. & Hlawatsch, F. (Eds.), The Wigner Distribution—Theory and Applications in Signal Processing, pp.135–209. Elsevier.

  22. Stanković, L. J. (2000). On the time-frequency analysis based filtering. Annals of Telecommunications, 55(5/6), 216–225.

    Google Scholar 

  23. Stanković, S., Stanković, L. J., Ivanović, V. N., & Stojanović, R. (2002). An architecture for the VLSI design of systems for time-frequency analysis and time-varyin filtering. Annals of Telecommunications, 57(9/10), 974–995.

    Google Scholar 

  24. Papoulis, A. (1997). Signal analysis. New York: McGraw-Hill.

    Google Scholar 

  25. Ivanović, V. N., Daković, M., & Stanković, L. J. (2003). Performances of quadratic time-frequency distributions as instantaneous frequency estimators. IEEE Transactions on Signal Processing, 51(1), 77–89.

    Article  MathSciNet  Google Scholar 

  26. Daković, M., Ivanović, V. N., & Stanković, L. J. (2003). On the S-method based instantaneous frequency estimation. Proc. Int. Sym. on SP and its Applications, Paris, France.

  27. Ivanović, V. N., & Jovanovski, S. (2008). A signal adaptive system for time-frequency analysis. Electronics Letters, 44(21), 1279–1280.

    Article  Google Scholar 

  28. Stanković, L. J. (1996). Auto-terms representation by the reduced interference distributions; The procedure for a kernel design. IEEE Transactions on Signal Processing, 44(6), 1557–1564.

    Article  Google Scholar 

  29. Stanković, L. J., & Böhme, J. F. (1999). Time-frequency analysis of multiple resonances in combustion engine signals. IEEE Transactions on Signal Processing, 42(1), 225–229.

    Article  Google Scholar 

  30. Liu, K. J. R. (1993). Novel parallel architectures for short-time Fourier transform. IEEE Transactions on Circuits and Systems II, Express Briefs, 40(12), 786–789.

    Article  Google Scholar 

  31. Maharatna, K., Dhar, A. S., & Banerjee, S. (2001). A VLSI array architecture for realization of DFT, DHT, DCT and DST. Signal Processing, 41(3), 1357–1377.

    Google Scholar 

  32. Jovanovski, S., Ivanović, V. N., & Radović, N. (2009). An efficient real-time method for time-varying filter region of support estimation. Proc. IEEE SPS DSP & SPE Workshops, Marco Island, USA, 513–517.

  33. Ivanović, V.N., Stojanović, R., Stanković, LJ. (2006). Multiple clock cycle architecture for the VLSI design of a system for time-frequency analysis. EURASIP J Appl.SP, Spec. Issue Design Methods for DSP Syst., 1–18.

  34. Jovanovski, S., Ivanovic, V.N. (2009). An efficient hardware design of an optimal nonstationary filtering system. Proc. IEEE ICASSP, Taipei, Taiwan, in print.

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  1. Department of Electrical Engineering, University of Montenegro, Cetinjski put bb, 20000, Podgorica, MONTENEGRO

    Srdjan Jovanovski & Veselin (Niko) Ivanović

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  1. Srdjan Jovanovski
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  2. Veselin (Niko) Ivanović
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Correspondence to Veselin (Niko) Ivanović.

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Jovanovski, S., Ivanović, V.(. Signal Adaptive Pipelined Hardware Design of Time-Varying Optimal Filter for Highly Nonstationary FM Signal Estimation. J Sign Process Syst 62, 287–300 (2011). https://doi.org/10.1007/s11265-010-0462-0

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