Parametric modelling of decomposed subbands: resolution improvement and applications for narrow-band signals

• Authors: Abdulnasir Hossen;Ulrich Heute
• Venue: Signal Processing - Signal processing in communications
• Year: 2004

In (Proceedings of ECMCS 2001, Budapest, Hungary, Proceedings of EUSIPCO 2002, Toulouse, France) the subband-decomposition idea applied to both FFT (Signal Processing 41(3) (February 1995) 261, Signal Processing 41(3) (February 1995) 279) and DCT (IEEE Trans. Circuits Syst. Video Technol. 6(3) (June 1996), Proceedings of ECSAP-97, Prague, Czech Republic, June 1997) to reduce the complexity of those algorithms, was used in combination with linear prediction to implement a new zoom technique for narrow-band signal applications. In this work the combination of the two advantages, the smaller complexity of the classical spectrum methods (with the SB-FFT as an example) and the high resolution of the parametric algorithms (Digital Spectral Analysis with Applications, Prentice-Hall, Englewood Cliffs, NJ, 1987, The Mathworks, Natick, MA, 1996) (with linear prediction as an example), yields a new spectral analysis zoom technique with higher spectral resolution efficiency than other techniques. The algorithm uses less points for the linear prediction, but the resolution obtained is improved due to the zoom ability of the subband-decomposition.In this paper the new algorithm's computational complexity is studied. The zoom capability of this subband decomposition technique is also explained by considering many factors such as the gain of the linear prediction modelling and the power spectral density of the linear prediction coefficients and the autocorrelation between them (The Mathworks, Natick, MA, 1996). The accuracy of the technique in terms of the prediction error and minimum allowable signal-to-noise ratio is also included. Also, the adaptation capabilty of the subband-FFT (Proceedings of the IEEE International Symposium on Circuits and Systems, Chicago, IL, 1993) is included into the zoom algorithm to select the band of most energy (the band to be zoomed). Three different parametric modelling algorithms are implemented with the new zoom technique: The linear prediction method also called maximum entropy method (MEM) (Digital Filters and Signal Processing, second ed., Kluwer Academic Publishers, Dordrecht, 1995, Modern Spectral Estimation-Theory and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1988), Prony's method (Digital Filter Designs, Wiley, New York, 1987), and Steiglitz' and McBride's method (System Identification: Theory for the User, second ed., PTR Prentice-Hall, Englewood Cliffs, NJ, 1999). Comparison between these three algorithms in terms of their complexity and prediction accuracy are included. A real-time scanning zoom is implemented with applications in spectral analysis and in radar signal processing.