6.2 Equivalent Structures There are literally an infinite number of equivalent structures realizing the same transfer function It is thus impossible to develop all equivalent realizations In this course we restrict our attention to a discussion of some commonly used structures
§6.2 Equivalent Structures • There are literally an infinite number of equivalent structures realizing the same transfer function • It is thus impossible to develop all equivalent realizations • In this course we restrict our attention to a discussion of some commonly used structures
6.2 Equivalent Structures Under infinite precision arithmetic any given realization of a digital filter behaves identically to any other equivalent structure However,in practice,due to the finite wordlength limitations,a specific realization behaves totally differently from its other equivalent realizations
§6.2 Equivalent Structures • Under infinite precision arithmetic any given realization of a digital filter behaves identically to any other equivalent structure • However, in practice, due to the finite wordlength limitations, a specific realization behaves totally differently from its other equivalent realizations
6.2 Equivalent Structures Hence,it is important to choose a structure that has the least quantization effects when implemented using finite precision arithmetic One way to arrive at such a structure is to determine a large number of equivalent structures,analyze the finite wordlength effects in each case,and select the one showing the least effects
§6.2 Equivalent Structures • Hence, it is important to choose a structure that has the least quantization effects when implemented using finite precision arithmetic • One way to arrive at such a structure is to determine a large number of equivalent structures, analyze the finite wordlength effects in each case, and select the one showing the least effects