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**Extra info for A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing**

**Example text**

32 2. FundamentalOperations on T w o Dimensional Signals The distributive laws given in R2) could be reduced to only one law because of R3). The system 81zxz using the above identities along with the group structure is a commutative ring with unity. However, even further structure is present. The SCALAR operation commutes with digital signal processing multiplication as the following property Al) shows. Al) Commutative Law: a( fg) = af g = f ag Thus, RzXz is a commutative, associative algebra with unity.

This operation exists, and therefore can be applied digital signal since every integer has a successor. The operator S is unary, that is S : R Z X Z ”+ R Z X Z It is defined by ( S ( f ) ) ( n , m )= f ( n - 1 9 4 The shift operation, when applied to a digital signal “moves” it one unit to the right. Accordingly, for any digital signal f , given as the bound matrix \ e f 9 d m h c b a ... a.. I 36 2. Fundamental Operations on Two Dimensional Signals we have ... = a.. a.. l(b), respectively. 5.

2) = T(f; n,m ) t T ( 9 ;n, M > P10)T(f g;n,m ) = T(f; n,m ) . Accordingly, a representative block diagram shall be chosen from each of these . Property P2) holds true since the following two block diagrams have the same output. f-i I M U L T 4-1 NINETY -1 52 2. FundamentalOperationson Two DimensionalSignals Property P8) holds true since the following two block diagrams always have identical outputs. f c MIN f c 8 REFLECT REFLECT r 8 MIN 9 8 d REFLECT 4 8 Property P11)holds true since the following two block diagrams have the same output.