This paper presents an approach for the development of a number theoretic discrete Hilbert transform. The forward transformation has been applied by taking the odd reciprocals that occur in the DHT matrix with respect to a power of 2. Specifically, the expression for a 16-point transform is provided and results of a few representative signals are provided.… (More)
Dean of the Graduate College iii ACKNOWLEDGMENTS Firstly, I would like to thank my adviser Dr. Johnson P Thomas for his support, advice, time and patience. He showed me different ways to approach a research problem and taught me that persistence is essential to accomplish any goal. I, furthermore, would like to thank my committee members Dr. Subhash Kak and… (More)
This paper presents a new discrete Hilbert transform (DHT) based measure of randomness for discrete sequences. The measure has been used to test three different classes of sequences with satisfactory results.
This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be quite small and, for example, it is of the order of 10-17 for the chirp signal. The use of the discrete Hilbert transform… (More)