The characterization, analysis and filtering of a slowly time-varying (STV) deterministic signal are considered. A STV signal is characterized as a sophisticated signal whose windowed sections are elementary signals. Mixed time-frequency representations (MTFRs) such as the Wigner distribution (WD), the Pseudo-Wigner distribution (PWD), the Short-time Fourier transform (STFT) and the optimally smoothed Wigner distribution (OSWD) used in analyzing STV signals are analyzed and compared. The OSWD is shown to perform satisfactorily even if the signals are amplitude modulated. The OSWD is shown to yield the exact instantaneous frequency for STV signals having quadratic phase: and to have a minimal and meaningful Bandwidth (BW) that does not depend on the slope of the instantaneous frequency curve in the time-frequency plane, unlike the BW of the spectrogram. We also present some contributions to the ongoing debate addressing the issue of choosing the MTFR that is best suited to the analysis of STV signals. Using analytical and experimental results, the performances of the different MTFRs are compared, and the conditions under which a given MTFR performs better are considered. The filtering of a signal from a noise-corrupted measurement, and the decomposition of a STV signal into its components in the presence of noise, are considered. These two related problems have been solved through masking the MTFRs of the measured signal. This approach has been successfully used in the case of the WD, PWD and the STFT. We propose extending the use of this approach to the OSWD. An equivalent time-domain implementation based on linear shift-variant (LSV) filters is derived and fully analyzed. It is based on the concept of local nonstationarity cancellation. The proposed filter is shown to have a superior performance when compared to the filter based on masking the STFT. The sensitivity of the filter is studied. The filter ability to suppress white noise and to decompose a STV signal into its components is analyzed and illustrated. / Master of Science