Extended Fourier analysis of signals

This summary of the doctoral thesis is created to emphasize the close connection of the proposed spectral analysis method with the Discrete Fourier Transform (DFT), the most extensively studied and frequently used approach in the history of signal processing. It is shown that in a typical application case, where uniform data readings are transformed to the same number of uniformly spaced frequencies, the results of the classical DFT and proposed approach coincide. The difference in performance appears when the length of the DFT is selected to be greater than the length of the data. The DFT solves the unknown data problem by padding readings with zeros up to the length of the DFT, while the proposed Extended DFT (EDFT) deals with this situation in a different way, it uses the Fourier integral transform as a target and optimizes the transform basis in the extended frequency range without putting such restrictions on the time domain. Consequently, the Inverse DFT (IDFT) applied to the result of EDFT returns not only known readings, but also the extrapolated data, where classical DFT is able to give back just zeros, and higher resolution are achieved at frequencies where the data has been successfully extended. It has been demonstrated that EDFT able to process data with missing readings or gaps inside or even nonuniformly distributed data. Thus, EDFT significantly extends the usability of the DFT-based methods, where previously these approaches have been considered as not applicable. The EDFT founds the solution in an iterative way and requires repeated calculations to get the adaptive basis, and this makes it numerical complexity much higher compared to DFT. This disadvantage was a serious problem in the 1990s, when the method has been proposed. Fortunately, since then the power of computers has increased so much that nowadays EDFT application could be considered as a real alternative.Comment: 29 pages, 8 figure

Augstas izskirsanas spejas spektrala analize, pielietojot bazes funkciju adaptacijas pieeju

Spectral analysis is a common part of the signal theory dealing with possibilities of representation of signals in the frequency domain. The subject of the investigations is very wide, therefore in the present work attention is fixed on band-limited signals registered during the finite time interval. Selection of this particular signal class is not accidental because a lot of practical tasks in the field of signal processing faced with or can be reduced onto band-limited signal analysis, for instance, speech, radio and communications signals. Moreover main part of spectral analysis methods are developed without taking into account information could be extracted from frequency domain and based on frequency range unlimited signal models. In the current work a band-limited signal features are studied and hypothesis in order to estimate spectrum of different signal components are proved. A method for continuous time signal spectral analysis is developed. The proposed method is distinguished by the possibility of its application both for uniformly and nonuniformly sampled signals. Development of new high frequency resolution algorithms for spectral analysis satisfying the present-day requirements and its implementation by using advanced signal processing tools represents a topical problem of signal processing. The original basis functions adaptation approach is proposed to distinguish this goal and practically realizable algorithms for discrete signal processing are developed. The computer simulations results confirn effectively of new algorithms. Comparison with well-known classical, parametrical and modern spectral analysis algorithms for uniformly and nonuniformly sampled signals with corresponding classification of signal models and analysis methods is done. Nowadays nonuniformly digitized signal analysis is one of increasing interests directions for theoretical investigations and the research work has been done in this field allows more deeply understand problems connected with the subject of these thesisSeparate summaries in English, RussianAvailable from Latvian Academic Library / LAL - Latvian Academic LibrarySIGLELVLatvi

Stereokimiski homogenu diribonukleotidu fosfotioatu un tos saturosu oligonukleotidu ka ribozimu aktiva centra sastavdalu sinteze

Available from Latvian Academic Library / LAL - Latvian Academic LibrarySIGLELVLatvi