Abstract
The relationship between difference equations with constant coefficients, obtained by establishing forward and backward differences in the filter design concepts of digital signal processing is explored in this paper. Moreover, thecorrelation is established between the input-output difference equations along with definite time invariant linear systemand the state spacedifference equationsrelated to filter design andthisleads to identify the efficient adaptive filterdesign and validate its function. Finally, the state space illustration of a system is provided, that is acceptable to construct and validate a new developed system between the difference equation and the digital signal processor.
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