Abstract
This paper introduces a method for optimizing non-recursive filtering algorithms. A mathematical model of a non-recursive digital filter is proposed and a performance estimation is given. A method for optimizing the structural implementation of the modular digital filter is described. The essence of the optimization is that by using the property of the residue ring and the properties of the symmetric impulse response of the filter, it is possible to obtain a filter having almost a half the length of the impulse response compared to the traditional modular filter. A difference equation is given by calculating the output sample of modules p1 … pn in the modified modular digital filter. The performance of the modular filters was compared with the performance of positional non-recursive filters implemented on a digital signal processor. An example of the estimation of the hardware costs is shown to be required for implementing a modular digital filter with a modified structure. This paper substantiates the expediency of applying the natural redundancy of finite field algebra codes on the example of the possibility to reduce hardware costs by a factor of two. It is demonstrated that the accuracy of data processing in the modular digital filter is higher than the accuracy achieved with the implementation of filters on digital processors. The accuracy advantage of the proposed approach is shown experimentally by the construction of the frequency response of the non-recursive low-pass filters.
Highlights
The implementation of digital signal processing (DSP) methods is effective in many practical applications, e.g., noise-resistive data processing system with high precision and resolution, easy subsystems connection, the stabilization of data processing channel etc. [1,2,3].The development of DSP applications triggered many studies in a field of creating specializedDSP devices with maximal efficiency
This paper shows the efficiency of executing DSP methods and algorithms based on ring and field algebraic structures, e.g., Residue Number System (RNS)
We described the structure of the RNS FIR filter and provided several practical tests, aimed both at a frequency characteristics study and error estimation
Summary
The implementation of digital signal processing (DSP) methods is effective in many practical applications, e.g., noise-resistive data processing system with high precision and resolution, easy subsystems connection, the stabilization of data processing channel etc. [1,2,3].The development of DSP applications triggered many studies in a field of creating specializedDSP devices with maximal efficiency. The implementation of digital signal processing (DSP) methods is effective in many practical applications, e.g., noise-resistive data processing system with high precision and resolution, easy subsystems connection, the stabilization of data processing channel etc. The development of DSP applications triggered many studies in a field of creating specialized. To solve this problem, the parallel pipeline computing was introduced. This approach allowed the performing of real-time DSP tasks. Most of the DSP tasks consider large amount of computations over the big data arrays. The increased speed of DSP calculations can be achieved through the introduction of new mathematics, based on non-positional modular codes. This paper shows the efficiency of executing DSP methods and algorithms based on ring and field algebraic structures, e.g., Residue Number System (RNS)
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