Multiple-Clock-Cycle Architecture for the VLSI Design of a System for Time-Frequency Analysis

  • Veselin N. IvanovićEmail author
  • Radovan Stojanović
  • L Jubivša Stanković
Open Access
Research Article
Part of the following topical collections:
  1. Design Methods for DSP Systems


Multiple-clock-cycle implementation (MCI) of a flexible system for time-frequency (TF) signal analysis is presented. Some very important and frequently used time-frequency distributions (TFDs) can be realized by using the proposed architecture: (i) the spectrogram (SPEC) and the pseudo-Wigner distribution (WD), as the oldest and the most important tools used in TF signal analysis; (ii) the S-method (SM) with various convolution window widths, as intensively used reduced interference TFD. This architecture is based on the short-time Fourier transformation (STFT) realization in the first clock cycle. It allows the mentioned TFDs to take different numbers of clock cycles and to share functional units within their execution. These abilities represent the major advantages of multicycle design and they help reduce both hardware complexity and cost. The designed hardware is suitable for a wide range of applications, because it allows sharing in simultaneous realizations of the higher-order TFDs. Also, it can be accommodated for the implementation of the SM with signal-dependent convolution window width. In order to verify the results on real devices, proposed architecture has been implemented with a field programmable gate array (FPGA) chips. Also, at the implementation (silicon) level, it has been compared with the single-cycle implementation (SCI) architecture.


Silicon Fourier Fourier Transformation Information Technology Convolution 


  1. 1.
    Cohen L: Time-frequency distributions—a review. Proceedings of the IEEE 1989, 77(7):941–981. 10.1109/5.30749CrossRefGoogle Scholar
  2. 2.
    Hlawatsch F, Boudreaux-Bartels GF: Linear and quadratic time-frequency signal representations. IEEE Signal Processing Magazine 1992, 9(2):21–67. 10.1109/79.127284CrossRefGoogle Scholar
  3. 3.
    Cohen L: Preface to the special issue on time-frequency analysis. Proceedings of the IEEE 1996, 84(9):1197–1197. 10.1109/JPROC.1996.535240CrossRefGoogle Scholar
  4. 4.
    Stanković LJ: A method for time-frequency analysis. IEEE Transactions on Signal Processing 1994, 42(1):225–229. 10.1109/78.258146MathSciNetCrossRefGoogle Scholar
  5. 5.
    Boashash B, Ristic B: Polynomial time-frequency distributions and time-varying higher order spectra: application to the analysis of multicomponent FM signals and to the treatment of multiplicative noise. Signal Processing 1998, 67(1):1–23. 10.1016/S0165-1684(98)00018-8CrossRefGoogle Scholar
  6. 6.
    Goncalves P, Baraniuk RG: Pseudo affine Wigner distributions: definition and kernel formulation. IEEE Transactions on Signal Processing 1998, 46(6):1505–1516. 10.1109/78.678464MathSciNetCrossRefGoogle Scholar
  7. 7.
    Richard C: Time-frequency-based detection using discrete-time discrete-frequency Wigner distributions. IEEE Transactions on Signal Processing 2002, 50(9):2170–2176. 10.1109/TSP.2002.801927MathSciNetCrossRefGoogle Scholar
  8. 8.
    Scharf LL, Friedlander B: Toeplitz and Hankel kernels for estimating time-varying spectra of discrete-time random processes. IEEE Transactions on Signal Processing 2001, 49(1):179–189. 10.1109/78.890359MathSciNetCrossRefGoogle Scholar
  9. 9.
    Stanković LJ, Ivanović VN, Petrović Z: Unified approach to the noise analysis in the spectrogram and Wigner distribution. Annales des Telecommunications 1996, 51(11–12):585–594.Google Scholar
  10. 10.
    Stanković S, Stanković LJ: An architecture for the realization of a system for time-frequency signal analysis. IEEE Transactions on Circuits And Systems—Part II: Analog and Digital Signal Processing 1997, 44(7):600–604.CrossRefGoogle Scholar
  11. 11.
    Stanković LJ, Böhme JF: Time-frequency analysis of multiple resonances in combustion engine signals. Signal Processing 1999, 79(1):15–28. 10.1016/S0165-1684(99)00077-8CrossRefGoogle Scholar
  12. 12.
    Stanković LJ: A method for improved distribution concentration in the time-frequency analysis of multicomponent signals using the L-Wigner distribution. IEEE Signal Processing Magazine 1995, 43(5):1262–1268.CrossRefGoogle Scholar
  13. 13.
    Liu KJR: Novel parallel architectures for short-time Fourier transform. IEEE Transactions on Circuits And Systems—Part II: Analog and Digital Signal Processing 1993, 40(12):786–790.CrossRefGoogle Scholar
  14. 14.
    Amin MG, Feng KD: Short-time Fourier transforms using cascade filter structures. IEEE Transactions on Circuits And Systems—Part II: Analog and Digital Signal Processing 1995, 42(10):631–641.CrossRefGoogle Scholar
  15. 15.
    Boashash B, Black P: An efficient real-time implementation of the Wigner-Ville distribution. IEEE Transactions on Acoustics, Speech, and Signal Processing 1987, 35(11):1611–1618. 10.1109/TASSP.1987.1165070CrossRefGoogle Scholar
  16. 16.
    Petranović D, Stanković S, Stanković LJ: Special purpose hardware for time-frequency analysis. Electronics Letters 1997, 33(6):464–466. 10.1049/el:19970361CrossRefGoogle Scholar
  17. 17.
    Stanković S, Stanković LJ, Ivanović VN, Stojanović R: An architecture for the VLSI design of systems for time-frequency analysis and time-varying filtering. Annales des Telecommunications 2002, 57(9–10):974–995.Google Scholar
  18. 18.
    Maharatna K, Dhar AS, Banerjee S: A VLSI array architecture for realization of DFT, DHT, DCT and DST. Signal Processing 2001, 81(9):1813–1822. 10.1016/S0165-1684(01)00061-5CrossRefGoogle Scholar
  19. 19.
    Liu KJR, Chiu C-T: Unified parallel lattice structures for time-recursive discrete cosine/sine/Hartley transforms. IEEE Transactions on Signal Processing 1993, 41(3):1357–1377. 10.1109/78.205735CrossRefGoogle Scholar
  20. 20.
    Papoulis A: Signal Analysis. McGraw-Hill, New York, NY, USA; 1977.zbMATHGoogle Scholar
  21. 21.
    Oppenheim AV, Schafer RW: Digital Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, USA; 1975.zbMATHGoogle Scholar
  22. 22.
    Amin MG: A new approach to recursive Fourier transform. Proceedings of the IEEE 1987, 75(11):1537–1538.CrossRefGoogle Scholar
  23. 23.
    Unser M: Recursion in short-time signal analysis. Signal Processing 1983, 5(3):229–240. 10.1016/0165-1684(83)90071-3CrossRefGoogle Scholar
  24. 24.
    Amin MG: Spectral smoothing and recursion based on the nonstationarity of the autocorrelation function. IEEE Transactions on Signal Processing 1991, 39(1):183–185. 10.1109/78.80776CrossRefGoogle Scholar
  25. 25.
    Ivanović VN, Stanković LJ: Multiple clock cycle real-time implementation of a system for time-frequency analysis. Proceedings of 12th European Signal Processing Conference (EUSIPCO '04), September 2004, Vienna, Austria 1633–1636.Google Scholar
  26. 26.
    Ivanović VN, Stanković LJ, Petranović D: Finite word-length effects in implementation of distributions for time-frequency signal analysis. IEEE Transactions on Signal Processing 1998, 46(7):2035–2040. 10.1109/78.700977CrossRefGoogle Scholar

Copyright information

© Ivanović et al. 2006

Authors and Affiliations

  • Veselin N. Ivanović
    • 1
    Email author
  • Radovan Stojanović
    • 1
  • L Jubivša Stanković
    • 1
  1. 1.Department of Electrical EngineeringUniversity of MontenegroPodgoricaSerbia and Montenegro

Personalised recommendations