The aim of this thesis is to determine the horse’s gait types using the acceleration values measured from the horse. A measurement was taken in Gävletravet, a total of five Nanotrak sensors were used, four on the different parts of the horse, and one on the hand of the horse’s driver, a car was driven parallel to the horse and the motions of the horse was recorded by a camera in order to synchronize with the data measured by the sensors, a total of four videos were recorded. The software to process the data was Matlab R2010b, and the methods to analyze them were Fast Fourier Transform (FFT), Short Time Fourier Transform (STFT), and Least Squares (LS). Different window functions were tried when applying the STFT, and the Hanning window was the best to smooth the curves, different window sizes (or data length) were also tried, the data length of 512 was found to be the most proper value. The methods for classification of horse’s gaits included amplitude, ratio, and LS. The method of amplitude worked well for the first three videos except for the last one, and performed better than the other two. The method of ratio was more reliable, but the results were not satisfactory. The method of LS gave bad results, so it was not trustworthy. More measurements and more analysis needed to be done in the future to find a proper way to automatic determine the horse’s gaits, and the use of modern technology will be very popular in other fields like animal science.

In this thesis,red noise analysis techniques are presented. The necessity of the use of the window functions and the Deeter polynomial method in order to determine red noise is discussed. The method was applied to the source SAX J2103.5+4545 which showed a white torque noise with a relatively low noise strength due to its being a transient system.

This thesis is interested in describing stationary random discrete signals, especially) in music discrete signals. Here is described when is signal stationary and when is not stationary. It contains tip for preprocessing of signal for accurate recognition of local stationarity. Thesis contain mathematical definition of parameters of random digital signals, which are used for stationarity recognition. It is followed by description of basic windows, their categories, describing of their parameters and comparing of each. In next part of thesis are described mothods of segmentations with constant window constant overlap save, constant window constant ovelap add, variable window constant overlap save, variable window constant ovelap add and variable window variable overlap add. It is followed by analyzing of windows used in segmentations with variable lengths of segments. As next point of thesis are transients made by step changes of coefficients of filter in filtering of segments with variable lengths. At the end is investigated the best accurate method of signal stationarity detection. Segments made by accurate method of detection are analyzed. thesis contains exapmle of music signal segmentation.

The traditional Computed Tomography (CT) is based on the Radon Transform and its inversion. The Radon transform uses parallel beam geometry and its inversion is based on the Fourier slice theorem. In practice, it is very efficient to employ a back-projection algorithm in connection with the Fast Fourier Transform, and which can be interpreted as a 1-D filtering across the radial dimension of the 2-D Fourier plane of the transformed image. This approach can easily be adapted to windowing techniques in the frequency domain, giving the capability to reduce image noise. In this work we are investigating the capabilities of the so called Kaiser window (giving an optimal trade-off between the main lobe energy and the sidelobe suppression) to achieve a near optimal trade-off between the noise reduction and the image sharpness in the context of Radon inversion. Finally, we simulate our image reconstruction using MATLAB software and compare and estimate our results based on the normalized Least Square Error (LSE). We conclude that the Kaiser window can be used to achieve an optimal trade-off between noise reduction and sharpness in the image, and hence outperforms all the other classical window function in this regard.