A Unified Signal Algebra Approach to Two-Dimensional by Louis A. D'Alotto, Charles R. Giardina, Hua Luo

By Louis A. D'Alotto, Charles R. Giardina, Hua Luo

Goals to bridge the distance among parallel desktop architectures and the construction of parallel electronic sign processing (DSP) algorithms. This paintings deals an method of electronic sign processing using the unified sign algebra surroundings to improve obviously taking place parallel DSP algorithms. collage or college booklet outlets may possibly order 5 or extra copies at a distinct pupil fee. cost is obtainable on request.

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4 3 4 (f+h)V(g+h)= ( 4 1 0 0,l which illustrates property M2). 5. Accordingly, the structure is a subdistributive lattice commutative associative algebra. The zero function Ozxzin Rzxz is also in F , but the unity functionlzxzin Rzxz is not in F. 5 Fundamental Domain Induced Operations Digital signals have as their domain the set of lattice points that are pairs of integers. Similar to the way that the algebraic structure of the reals induced operations in Rzxz,group operations in the integers induce operations in Rzxz, Precisely three domain induced operations are defined herein.

We have The negation of a signal f is denoted by M I N U S ( f). It will also be denoted by -f . In any case, it is a unary operation which is defined by M I N U S : SzXz+ Rzxz where M I N U S ( f ) ( n ,m ) = -f (n,m ) Using the fact that the following two block diagrams always provide the same output shows that M I N U S is a term. 22 " 2. FundamentalOperationson , Two DimensionalSignals -f f -1zxz The lastblock diagram involved the multiplication of the twoinput signals, f , and the constant function-lzxz of value -1 everywhere in the integral lattice.

L . 2. Fundamental Operations on Two Dimensional Signals 44 Successive applicationsof the ninety degree rotation produces various other rotations. The 180° rotation of f is given by N 2 ( f ) ;the 270° rotation of f is given by N 3 ( f ) . 6. TermsInvolvingFundamentalDomainInduced Operations 45 or and f -NINETY - NINETY c NINETY - N3(f) or What is of additional consequenceis that a general translationoperation can be formed using theSHIFT and NINETY operations. O n < 0,m 2 0 N3S-mNSn(f) nlO,m

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