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A theory to analyse linear time-varying (LTV) discrete-time systems from the point of digital signal processing of view is established here. The LTV discrete-time system is changing with time slowly in comparison with the sampling frequency of the input signal is supposed. Three models were set up to simulate and analyse the LTV system. Models 1 and 2 can be used to design and analyse the LTV system, while the filter bank representation relates the LTV system with the time-varying filter bank. Based on the established models, the input-output relationship of a time-varying system in the frequency-domain was analysed in detail.