A Survey on Methods for Time-frequency Analysis

$FNQRZOHGJHPHQWV 3 This Master's thesis is the result of my final project at the University of Karlskrona/Ronneby. There are many people whom I'd like to thank for their assistance during the project. First, I would like to thank Jens Augustsson and Erik Pavlica, working at SSPA Maritime Consulting, for their guidance and the possibility to gain knowledge in an exciting field of science. In this context I also would like to thank Martin Almgren. Thanks also goes to Mathias Winberg for the useful discussions and Benny Lövström, both working at the Department of Signal Processing at the University of Karlskrona/Ronneby, for the final comments on my thesis and for the possibility to work on my project at the department. Last but not least, I would like to thank Karl Thorén for reading my thesis thoroughly and Nedelko Grbic and Xiao-Jiao Tao for their inspiring suggestions. Finally I would like to thank everyone who helped me during my project, and Lisa Lorentz for putting up with me during my studies in Sweden. Time analysis and frequency analysis are both well-established ways in engineering to gain more knowledge about a physical phenomena. Time and frequency analysis can be combined in a joint time and frequency distribution. A simple method to gain a joint distribution is to window segments of the data at different time locations and calculate its Fourier transform. By doing this a set of´local´spectra are gained and joined to present a time-frequency distribution. This method is well known as the Short-Time Fourier Transform. The Short-Time Fourier Transform has the disadvantage that is does not localize time and frequency phenomena very well. Instead the time-frequency information is scattered which depends on the length of the window. This can be attended to by altering the length of the window but a certain balance between good time and good frequency localization is unavoidable. To cope with this disadvantage, the Wavelet Transform uses dilated and translated functions, which are local in time, and frequency, which results in good frequency resolution for low-frequency phenomena and good time resolution for high-frequency phenomena. The advantage of the Wavelet Transform is its efficient fast transform in discrete time. But still, there is no complete solution to the localization problem. Adaptive Time-Frequency Analysis can be advantageous for solving the localization problem. The functionality of methods is hereby adapted to the time-frequency content of the signal. The Adaptive Wavelet Packets …