In this thesis, a new technique for signal subband decomposition using time-variant and non-linear filter banks is proposed. Construction of the proposed perfect reconstruction filter banks is based on ladder structure, derived from a method of biorthogonal wavelet filter bank design. Filter’s parameters are being changed by predefined criteria, in purpose to adapt filters to the signal properties. In spite of their time-variance, described filter banks posses good convergence and regularity properties. It makes possible to form wavelet trees or wavelet packets, which leads to efficient realizations. Resulting time-variant and non-linear filter banks still retain good properties of wavelets: good localization in time and frequency domain. On the other hand, proposed filter banks have the ability to adapt to the properties of the analyzed signal, resulting in a good approximation of the optimal filter banks. Since decomposition functions are changed at each step, this technique represents a new class of wavelet-like transforms or second-generation wavelets. It is shown that time-variant filter banks are more suitable for analysis of non-stationary signals, compared to the fixed filter banks. Employed ladder structure enables mapping of integer signals to the integer transformation coefficients. Also, it enables different non-linear operations on signal, such us statistical signal processing (e.g. median filter), and many others. Despite of non-linearity, the proposed filter banks retain the perfect reconstruction property. Proposed filter banks are designed by the interpolation of samples in the time domain. Instead of fixed filter bank design, described algorithms determine the filter parameters at each step of the analysis. Filters in the bank consist of a fixed and a variant part. The role of the fixed part is to ensure the satisfactory convergence and regularity properties, corresponding to the number of zero moments of wavelet and scale functions. Furthermore, the fixed part provides limits on filters’ frequency responses and defines the adaptation space. The variable part of the filter bank enables changes of the filters’ parameters within the allowed adaptation space, in order to adapt the filters’ properties to the analyzed signal. A new factorization of biorthogonal filters into lifting steps is proposed to enable filter separation into a fixed and a variable part. There is a significant level of independence between lifting step and dual lifting step in the proposed factorization, which results in a certain degree of independence between low-pass and high-pass filters in the bank. Furthermore, proposed factorization is suitable for determination of necessary filter order at each level of decomposition. That fact is used for the construction of new wavelet filter banks with variable number of zero moments. Such filter banks show significant benefits when compared to the fixed banks: residual signal after interpolation is smaller, with no amplified transients on signal singularities, which is typical for the high order fixed filters. In this thesis, the algorithms of filter adaptation were compared based on criterion and adaptation interval, as well as the convergence properties. Criteria of the minimum absolute error and the minimum square error were used, due to their efficient implementation. The adaptation interval determines the speed of adaptation, as well as the degree of optimum filter bank approximation. Position of the adaptation area with reference to the observed moment also influences the degree of approximation. It is shown that only causal and asymmetric adaptation intervals can enable the perfect reconstruction without the need for filter parameter transfer to the reconstruction side. Fixed part of the filter bank causes the additional requirement for spectral compensation of the adaptation criterion. All necessary algorithms for spectral compensation of the error were developed in the thesis. Consequently, proposed time-variant and non-linear filter banks represent a new approach to signal decomposition. In the analytical sense, described filter banks offer new information about the decomposed signal, useful for the extraction of its basic components. They combine subband decomposition, parametric modeling and multiresolution analysis of the signal. The proposed new filter banks enable a number of applications, like compression and noise suppression resulting with lower signal degradation then for the case of fixed filter banks.