Structure Optimization And Performance Research Of Finite Word Length FIR Digital Filter

Digital filter,as an important part of digital signal processing system,is widely used in signal processing,communication,and control.The actual performance of the system on an infinite precision device is deviated from the ideal performance because of the finite word length(FWL)effects.The system performance is closely related to the implementation structure,so the system implementation structure and the finite word length effects become an important issue to be considered in the implementation of digital filters.The finite impulse response(FIR)filter is widely used in broadband wireless communication systems since its stability,implementation of linear phase easily and suitability for multi-sampling rate conversion.At present,most of the research on quantization errors caused by finite word length in filter structures focuses on infinite impulse response(IIR)filter.To improve the ability of FIR filter of resisting the finite word length effects,this thesis studies the roundoff noise performance and coefficient sensitivity of FIR digital filter based on the implementation structure of the filter.The contents are described as follows:1.Aiming at the problem of the signal quantization error introduced by the finite word length,the roundoff noise performance of FIR filter is discussed based on the filter implementation structure.Firstly,this thesis introduces a polynomial operator structure,which has feedback characteristics,into the direct structure of FIR filter,and an optimization structure of roundoff noise for FIR filter is proposed.Secondly,the state space realization of the optimization structure is given by using the polynomial parameterization method,and the roundoff noise gain expression of the FIR filter structure is analyzed and derived based on the statistically independent Gaussian white noise model.Simulation analysis and results show that the optimization structure has better roundoff noise performance than other structures of FIR filters.Its amplitude-frequency and phase-frequency response are close to the ideal frequency response characteristics,and are suitable for low-pass,high-pass and band-pass filters under the finite word length quantization.2.Aiming at the problem of the coefficient quantization error introduced by the finite word length,the sensitivity of FIR filter system function to the coefficient quantization is studied based on the state-space model.Firstly,this thesis gives the FIR filter system function based on the forward difference delta operator,and the bilinear transformation relationship between the analog domain and the digital domain is applied to derive a FIR filter sensitivity optimization structure.Secondly,the parameter sensitivity of the optimization structure is analyzed by the state space method,and the sensitivity expression is derived.Then,the roundoff noise of the optimization structure is analyzed,and its roundoff noise gain expression is formulated.Simulation analysis and results show that compared with other structures of FIR filters,the optimization structure in delta operator has lower sensitivity under high-speed sampling,and the amplitude-frequency and phase-frequency response of the proposed optimization structure are more stable under the finite word length constraint.