Development of Time - Frequency Techniques for Sonar Applications

Sonar signal processing comprises of a large number of signal processing algorithms for implementing functions such as Target Detection, Localisation, Classification, Tracking and Parameter estimation. Current implementations of these functions rely on conventional techniques largely based on Fourier Techniques, primarily meant for stationary signals. Interestingly enough, the signals received by the sonar sensors are often non-stationary and hence processing methods capable of handling the non-stationarity will definitely fare better than Fourier transform based methods.Time-frequency methods(TFMs) are known as one of the best DSP tools for nonstationary signal processing, with which one can analyze signals in time and frequency domains simultaneously. But, other than STFT, TFMs have been largely limited to academic research because of the complexity of the algorithms and the limitations of computing power. With the availability of fast processors, many applications of TFMs have been reported in the fields of speech and image processing and biomedical applications, but not many in sonar processing. A structured effort, to fill these lacunae by exploring the potential of TFMs in sonar applications, is the net outcome of this thesis. To this end, four TFMs have been explored in detail viz. Wavelet Transform, Fractional Fourier Transfonn, Wigner Ville Distribution and Ambiguity Function and their potential in implementing five major sonar functions has been demonstrated with very promising results. What has been conclusively brought out in this thesis, is that there is no "one best TFM" for all applications, but there is "one best TFM" for each application. Accordingly, the TFM has to be adapted and tailored in many ways in order to develop specific algorithms for each of the applications.

Development of a New Transform:MRT

Fourier transform methods are employed heavily in digital signal processing. Discrete Fourier Transform (DFT) is among the most commonly used digital signal transforms. The exponential kernel of the DFT has the properties of symmetry and periodicity. Fast Fourier Transform (FFT) methods for fast DFT computation exploit these kernel properties in different ways. In this thesis, an approach of grouping data on the basis of the corresponding phase of the exponential kernel of the DFT is exploited to introduce a new digital signal transform, named the M-dimensional Real Transform (MRT), for l-D and 2-D signals. The new transform is developed using number theoretic principles as regards its specific features. A few properties of the transform are explored, and an inverse transform presented. A fundamental assumption is that the size of the input signal be even. The transform computation involves only real additions. The MRT is an integer-to-integer transform. There are two kinds of redundancy, complete redundancy & derived redundancy, in MRT. Redundancy is analyzed and removed to arrive at a more compact version called the Unique MRT (UMRT). l-D UMRT is a non-expansive transform for all signal sizes, while the 2-D UMRT is non-expansive for signal sizes that are powers of 2. The 2-D UMRT is applied in image processing applications like image compression and orientation analysis. The MRT & UMRT, being general transforms, will find potential applications in various fields of signal and image processing.