Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30827
Improved Estimation of Evolutionary Spectrum based on Short Time Fourier Transforms and Modified Magnitude Group Delay by Signal Decomposition

Authors: H K Lakshminarayana, J S Bhat, H M Mahesh


A new estimator for evolutionary spectrum (ES) based on short time Fourier transform (STFT) and modified group delay function (MGDF) by signal decomposition (SD) is proposed. The STFT due to its built-in averaging, suppresses the cross terms and the MGDF preserves the frequency resolution of the rectangular window with the reduction in the Gibbs ripple. The present work overcomes the magnitude distortion observed in multi-component non-stationary signals with STFT and MGDF estimation of ES using SD. The SD is achieved either through discrete cosine transform based harmonic wavelet transform (DCTHWT) or perfect reconstruction filter banks (PRFB). The MGDF also improves the signal to noise ratio by removing associated noise. The performance of the present method is illustrated for cross chirp and frequency shift keying (FSK) signals, which indicates that its performance is better than STFT-MGDF (STFT-GD) alone. Further its noise immunity is better than STFT. The SD based methods, however cannot bring out the frequency transition path from band to band clearly, as there will be gap in the contour plot at the transition. The PRFB based STFT-SD shows good performance than DCTHWT decomposition method for STFT-GD.

Keywords: discrete cosine transform, Short Time Fourier Transform, Evolutionary Spectrum, Modified Group Delay, Harmonic Wavelet Transform, Perfect Reconstruction Filter Banks

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1330


[1] B. Boshash, "Time frequency signal analysis," in Advances In Spectrum Analysis And Array Processing, vol. 1, S. Haykin, Ed. NJ: Englewood Cliffs Prentice-Hall, 1991.
[2] L. Cohen, "Time-frequency distribution - a review," in July 1989 Proc. IEEE , vol.77-7, pp. 941-981.
[3] S. V. Narasimhan, S. Pavanalatha, "Estimation of evolutionary spectrum based on short time Fourier transform and modified group delay," Signal Processing, vol.84, pp. 2139-2152. 2004.
[4] S. V. Narasimhan, A. R. Haripriya, B. K. Shreyamsha Kumar, "Improved Wigner-Ville distribution performance based on DCT/DFT harmonic wavelet transform and modified magnitude group delay ," Signal Processing, vol. 88, pp. 1-18, 2008.
[5] G. Matz and F. Hlawatsch, "Linear Tme-Frequency Filters: Online Algorithms and Applications", in Applications in time frequency signal processing, A. Papandreou - Suppappola, Ed., Boca Raton FL: CRC press, 2002.
[6] A. S. Kayhan, A. El-Jaroudi, L. F. Chaparro, "Evolutionary periodogram for nonstationary signals," IEEE Trans. Signal Process. Vol. 42 pp. 1527-1536, June 1994.
[7] C. S. Detka, A. El-Jaroudi, L. F. Chaparro, "Relating the bilinear distributions and the evolutionary spectrum," in 1993, Proc.ICASSP-93 IV pp. 496-499.
[8] S. V. Narasimhan, "Improved instantaneous power spectrum performance: a group delay approach," Signal Processing, vol. 80, pp. 75-88. 2000.
[9] S. V. Narasimhan, E. I. Plotkin, M. N. S. Swamy, "Power Spectrum Estimation of Complex Signals and its Application to Wigner-Ville Distribution: A Group Delay Approach," Sadhana, Part-1, Indian Academy of Sciences, Bangalore, India, vol. 23, pp. 57-71. February 1998.
[10] A. Hema Murthy, B. Yegnanarayana, "Speech processing using group delay functions," Signal Processing, pp.259-267. 1991
[11] S. V. Narasimhan, E. I. Plotkin, M. N. S. Swamy, "Power spectrum estimation of complex signals: a group delay approach," Electron. Lett, vol. 35, pp. 2182-2184. December 1999.
[12] B. Yegananarayana, A. Hema Murthy, "Significance of group delay functions in spectrum estimation", IEEE Trans Signal Processing, vol. 40, pp. 2281-2289, Sept. 1992.
[13] M. B. Nayak, S. V. Narasimhan, "Autoregressive modeling of the Wigner-Ville distribution based on signal decomposition and modified group delay," Signal Processing, vol. 84, pp. 407-420, 2004.
[14] S. V. Narasimhan, M. B. Nayak, "Improved Wigner-Ville distribution performance by signal decomposition and modified group delay," Signal Processing, vol.83, pp. 2253-2538, 2003.
[15] S. V. Narasimhan, S. Pavanalatha, "Estimation of evolutionary spectrum based on STFT and modified group delay," IEEE TENCOMÔÇö2003, Bangalore, India, pp.1198-1203.
[16] M. B. Priestly, "Power spectral analysis of nonstationary random processes," J. Sound Vib. vol. 6 -I, pp. 86-97, 1967.
[17] M. Sansal, A. S. Kayhan, "IF and GD estimation from evolutionary spectrum," Signal Processing, vol. 81, pp. 197-202, 2001.
[18] P. P. Vaidyanathan, Multirate systems and filter banks. Pearson, 2006, ISBN 81-7758-942-3, ch. 6.
[19] L. Zhang, Y. Lian, and C. C. Ko, "A new approach for design sharp FIR filters using frequency masking technique," in DSP Workshop, Oct. 2000.
[20] D.E. Newland, "Wavelet analysis of vibration, Part-1: theory," J. Vib. Acoust. Trans. ASME 116, pp. 409-416, 1994.