Non-uniform sampling comes natural in many applications, due to for example imperfect sensors, mismatched clocks or event-triggered phenomena. Examples can be found in automotive industry and data communication as well as medicine and astronomy. Yet, the literature on statistical signal processing to a large extent focuses on algorithms and analysis for uniformly, or regularly, sampled data. This work focuses on Fourier analysis, system identification and decimation of non-uniformly sampled data. In non-uniform sampling (NUS), signal amplitude and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this thesis, the sampling times are assumed to be generated by a stochastic process, and the main idea is to use information about the stochastic sampling process to calculate a priori properties of approximate frequency transforms. These results are also used to give insight in frequency domain system identification and help with analysis of down-sampling algorithms. The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Based on this, decimation of non-uniformly sampled signals, using continuous-time anti-alias filters, is analyzed. The decimation is based on interpolation in different domains, and interpolation in the convolution integral proves particularly useful. The same idea is also used to investigate how stochastic unmeasurable sampling jitter noise affects the result of system identification. The result is a modification of known approaches to mitigate the bias and variance increase caused by the sampling jitter noise. The bottom line is that, when non-uniform sampling is present, the approximate frequency transform, identified transfer function and anti-alias filter are all biased to what is expected from classical theory on uniform sampling. This work gives tools to analyze and correct for this bias.

Inverse Synthetic Aperture Radar coherently processes the return signal from the target in order to construct the image of the target. The conventional methodology used for obtaining the image is the Fourier transform which is not capable of suppressing the Doppler change in the return signal. As a result, Range-Doppler image is degraded. A proper time-frequency transform suppresses the degradation due to time varying Doppler shift. In this thesis, high resolution joint-time frequency transformations that can be used in place of the conventional method are evaluated. Wigner-Ville Distribution, Adaptive Gabor Representation with Coarse-to-Fine search algorithm, and Time-Frequency Distribution Series are examined for the target imaging system. The techniques applied to sample signals compared with each other. The computational and memorial complexity of the methods are evaluated and compared to each other and possible improvements are discussed. The application of these techniques in the target imaging system is also performed and resulting images compared to each other.

A proper time-frequency transform technique suppresses the blurring and smearing effect of the time-varying Doppler shift on the target image. The conventional target imaging method uses the Fourier transform for extracting the Doppler shift from the received radar pulse. Since the Doppler shift is timevarying for rotating targets, the constructed images will be degraded. In this thesis, the Doppler shift information required for the Range-Doppler image of the target is extracted by using high resolution time-frequency transform techniques. The Wigner-Ville Distribution and the Adaptive Gabor Representation with the Coarse-to-Fine and the Matching Pursuit Search Algorithms are examined techniques for the target imaging system. The modified Matching Pursuit Algorithm, the Matching Pursuit with Reduced Dictionary is proposed which decreases the signal processing time required by the Adaptive Gabor Representation. The Hybrid Matching Pursuit Search Algorithm is also introduced in this thesis work and the Coarse-to-Fine Algorithm and the Matching Pursuit Algorithm are combined for obtaining better representation quality of a signal in the time-frequency domain. The stated techniques are applied on to the sample signals and compared with each other. The application of these techniques in the target imaging system is also performed for the simulated aircrafts.

This thesis deals with the detection of QRS complexes from electrocardiograms using time-frequency analysis. Detection procedures are based on wavelet and Stockwell transform. The theoretical part describes the basics of electrocardiography, then introduces common approaches to time-frequency analysis, such as short-time Fourier transform (STFT), wavelet transform and Stockwell transform. These algorithms were tested on a set of electrograms from the MIT-BIH and CSE-MO1 arrhythmia database. For the CSE database worked best the method based on the wavelet transform with the filter bank Symlet4, with the resulting value of sensitivity 100 % and positive predictivity 99.86%. For the MIT database had the best performance the detector using the Stockwell transform with values of sensitivity 99.54% and positive predictivity 99.68%. The results were compared with the values of other authors mentioned in the text.