5.2 System Representation with signal flow-graph o Basic signal flow-graph Only basic branch in signal flow-graph Must have unit delay branch have finite nodes and branchs
5.2 System Representation with signal flow-graph ⚫ Basic signal flow-graph ◆ Only basic branch in signal flow-graph; ◆ Must have unit delay branch; ◆ have finite nodes and branchs
5.2 System Representation with signal flow-graph o Basic signal flow-graph a digital filter structure is said to be canonic if the number of delays in the block diagram representation is equal to the order of the difference equation. otherwise it is nocanonic structure
5.2 System Representation with signal flow-graph ⚫ Basic signal flow-graph A digital filter structure is said to be canonic if the number of delays in the block diagram representation is equal to the order of the difference equation. Otherwise, it is nocanonic structure
5.2 System Representation with signal flow-graph O Equivalent structures o Two digital filter structures are defined to be equivalent if they have the same transfer function o We can obtain equivalent structures with a number of methoas. However, a fairly simple way to generate an equivalent structure from a given realization is via the transpose operation
5.2 System Representation with signal flow-graph Two digital filter structures are defined to be equivalent if they have the same transfer function. We can obtain equivalent structures with a number of methods. However, a fairly simple way to generate an equivalent structure from a given realization is via the transpose operation. ⚫ Equivalent Structures
5.2 System Representation with signal flow-graph o Transpose Operation (1) Reverse all paths (2) Replace pick-off nodes by adders, and vice versa ()Interchange the input and output nodes o All other methods for developing equivalent structures are based on a specific algorithm for each structure
5.2 System Representation with signal flow-graph Transpose Operation (1) Reverse all paths (2) Replace pick-off nodes by adders, and vice versa. (3) Interchange the input and output nodes All other methods for developing equivalent structures are based on a specific algorithm for each structure
5.2 System Representation with signal flow-graph o It should be noted that under infinite-precision arithmetic, any given realization of a digital filter behaves identically to any other equivalent structure o However, in practice, due to the finite wordlength limitations, a specific realization behaves differently from its other equivalent realizations
5.2 System Representation with signal flow-graph It should be noted that 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 differently from its other equivalent realizations