The popular Discrete Fourier Transform (DFT) is known to be a sub‐optimal frequency estimation technique for a finite transform length. In order to approach the Cramer‐Rao Lower Bound (CRLB), many refinement techniques have been considered, but little considering both zero padding or tapering, also known as windowing or apodisation. In this paper, a frequency estimator with closed‐form combination of three DFT samples is generalized to zero padding and tapered data within the class of cosine windowing. Root Mean Squared Error (RMSE) is shown to approach the CRLB in the case of a single tone signal with additive white Gaussian noise. Compared to state‐of‐the‐art techniques, the proposed algorithm improves the frequency RMSE up to 1 dB when using significant zero‐padding lengths (K ≥ 2 N) and for small to moderate SNR, which is the most challenging case for practical radar applications.

Detection and delineation of P- and T-waves are important issues in the analysis and interpretation of electrocardiogram (ECG) signals. This paper addresses this problem by using Bayesian inference to represent a priori relationships among ECG wave components. Based on the recently introduced partially collapsed Gibbs sampler principle, the wave delineation and estimation are conducted simultaneously by using a Bayesian algorithm combined with a Markov chain Monte Carlo method. This method exploits the strong local dependency of ECG signals. The proposed strategy is evaluated on the annotated QT database and compared to other classical algorithms. An important feature of this paper is that it allows not only for the detection of P- and T-wave peaks and boundaries, but also for the accurate estimation of waveforms for each analysis window. This can be useful for some ECG analysis that require wave morphology information.

The delineation of P and T waves is important for the interpretation of ECG signals. We propose a Bayesian detection-estimation algorithm for simultaneous detection, delineation, and estimation of P and T waves. A block Gibbs sampler exploits the strong local dependencies in ECG signals by imposing block constraints on the P and T wave locations. The proposed algorithm is evaluated on the annotated QT database and compared with two classical algorithms.

The subject of this thesis is to study Bayesian estimation/detection algorithms suitable for P and T wave analysis in ECG signals. In this work, different statistical models and associated Bayesian methods are proposed to solve simultaneously the P and T wave delineation task (determination of the positions of the peaks and boundaries of the individual waves) and the waveform-estimation problem. These models take into account appropriate prior distributions for the unknown parameters (wave locations and amplitudes, and waveform coefficients). These prior distributions are combined with the likelihood of the observed data to provide the posterior distribution of the unknown parameters. Due to the complexity of the resulting posterior distributions, we propose to use Markov chain Monte Carlo algorithms for (sample-based) detection/estimation.

The subject of this thesis is to study Bayesian estimation/detection algorithms suitable for P and T wave analysis in ECG signals. In this work, different statistical models and associated Bayesian methods are proposed to solve simultaneously the P and T wave delineation task (determination of the positions of the peaks and boundaries of the individual waves) and the waveform-estimation problem. These models take into account appropriate prior distributions for the unknown parameters (wave locations and amplitudes, and waveform coefficients). These prior distributions are combined with the likelihood of the observed data to provide the posterior distribution of the unknown parameters. Due to the complexity of the resulting posterior distributions, we propose to use Markov chain Monte Carlo algorithms for (sample-based) detection/estimation.