Time-frequency and time-scale analysis of non-stationary biomedical signals

Fourier transform (FT), which assumes that the analyzed signal is stationary, is not entirely appropriate to analyze biomedical signals since they are in non-stationary nature. To overcome this drawback, FT can be applied over short-windows of time within which the signal can be considered to be stationary. However, this short-time Fourier transform is hampered with a serious time-frequency (TF) trade-off dilemma. Recently, a number of different TF analysis techniques has been developed that provide improved TF resolution. In this dissertation, we consider two strongly non-stationary biomedical signals, lung sound and blood-flow signals, and propose novel and effective systems for the detection of crackles from the former and emboli from the latter. The crackle detection system uses the dual tree complex wavelet transform (DTCWT) for denoising and time-frequency/scale analysis with various windows/wavelets for feature extraction. The emboli detection system processes forward and reverse flow signals using FT, discrete wavelet transform (DWT), and DTCWT. Dimensionality of the extracted coefficients is reduced using Principal Component Analysis, and the new features are used for predicting whether a signal is emboli, speckle or artifact. Since the dyadic TF tiling of classical DWT is not appropriate for processing embolic signals, and since the discrete wavelet packet transform (DWPT) can adaptively decompose the TF axis, we also propose a directional complex DWPT for mapping directional information while processing quadrature signals (QSs). This method has significantly less computational complexity than the existing methods. To overcome the poor frequency resolution, severe frequency aliasing and lack of shift-invariance drawbacks of the DWT, we also propose a novel directional complex DWT. It consists of filter-banks with rational sampling factors and can be applied directly to QSs.