ABSTRACT
Shannon’s theorem tells us that reliable communication in a communication channel depends on the bandwidth (BW) and the signal-to-noise ratio (SNR). Applying the same concept to radar implies that a reflected signal with a large signal BW and a high SNR radar return will contain information about the target. The problem lies in finding ways to analyze the return signal to access relevant information about a target in whatever form it might be and determine its characteristics in a usable format so that a description
CONTENTS
4.1 Introduction and Objectives ........................................................................................... 105 4.1.1 Overview ............................................................................................................. 105 4.1.2 Modern UWB Radar Time-Frequency Signal-Processing Requirements ....106 4.1.3 Time and Frequency Domain Signal-Processing Methods and Objectives .....106
4.2 The Wigner-Ville Distribution ...................................................................................... 108 4.3 The Ambiguity Function ................................................................................................ 110 4.4 The Weber-Hermite Transform and Weber-Hermite Wave Functions .................. 112 4.5 The Fractional Fourier Transform ................................................................................. 125 4.6 Multiple Window Spectral Analysis ............................................................................. 133 4.7 The Hilbert-Huang Transform ...................................................................................... 136 4.8 Carrier Frequency-Envelope Frequency Spectra ......................................................... 142 4.9 The Radon Transform ..................................................................................................... 149 4.10 Target Linear Frequency Response Functions ............................................................ 153 4.11 Singular Value Decomposition and Independent Component Analysis ................ 153
4.12 Blind Source Separation, Matching Pursuit, and Complexity Pursuit ................... 158 4.13 Conclusions ....................................................................................................................... 163 4.14 Signal Processing and Future UWB Radar Systems ................................................... 166 Appendix 4.A Derivations of Weber-Hermite Wave Functions (WHWFs) ...................... 174 Appendix 4.B Relationship of WHWFs to Fractional Calculus........................................... 186 References ..................................................................................................................................... 189
of the target is obtained upon which relevant decisions can be made. As explained in Chapter 1, the significance of these new signal analysis methods requires understanding the difference between ultrawideband (UWB) and conventional narrowband radar systems. Briefly stated, conventional narrowband radar uses frequency domain (energy) collection methods, while advanced UWB radar for target identification uses time-and-frequency (time-frequency) collection and analysis approaches.
