Fir Digital Filter Design And Application

As an important part of digital signal processing,FIR digital filter has a wide range of applications in wireless communication,radar,sonar,biomedical and other fields with its precise linear phase and stability.At the same time,different application areas and standards also impose different requirements on the design of FIR digital filters.When implemented in a digital computer or dedicated digital hardware,the filter coefficients must be represented by a finite word length,so the truncation or rounding effect makes the designed filter characteristics significantly different from what is desired.When the hardware applied to the compressed sensing implements the random demodulation system,the filter acts as a substitute for the integrator,and changes in the index of the filter order and the cutoff frequency have a significant effect on the recovered signal quality.In response to these problems,this paper mainly studies the filter design method and its application that are not sensitive to quantization,and the optimal design of the filter in the compressed sensing.This paper first introduces the mathematical model of the digital filter and the difference between the four linear phase FIR filters,as well as the common FIR digital filter design method.The principle of equilibrium and classical algorithms are studied,and the basic principles of compressed sensing are analyzed.Then,a FRM filter design method with minimum coefficient sensitivity is studied.For the problem that the finite word length quantization of filter coefficients will lead to performance degradation,a direct discrete coefficient filter design based on coefficient quantization error minimization is proposed.The method is to reduce the effect of the filter due to coefficient quantization.This method outperforms the continuous design on multiple indicators and then directly quantizes the results of the coefficients.Moreover,for thecase where the equalizer coefficients in digital communication also face direct quantization and have a significant impact on the equalization performance,the new discrete coefficient filter design method is applied to the equalizer design.The simulation experiment results show that the equalization effect is obviously improved under the new design idea.Finally,this paper studies a hardware implementation model of compressed sensing-a random demodulation system for sparse frequency signals,and comprehensively analyzes the impact of the filter application part on the quality of the recovered signal in the random demodulation system,and proposes compression.The optimal design method of the filter index in perception is to search for the optimal index strategy through multiple simulation results.The simulation results show that under the same conditions,the filter under the optimization index has higher reconstruction signal-to-noise ratio than the traditional Butterworth filter,and it can be applied to more frequency input signals,and can also be based on specific requirements.The advantages of trade-off between performance and complexity provide a guiding reference for practical applications.