# 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 machine architectures and the production of parallel electronic sign processing (DSP) algorithms. This paintings bargains an method of electronic sign processing using the unified sign algebra setting to enhance certainly happening parallel DSP algorithms. collage or collage booklet outlets may possibly order 5 or extra copies at a distinct pupil cost. expense is offered on request.

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

**Example text**

First we let 0 0,0 then and fvg=( 4 0 0 2 1 0 0,l U180 so 2. Fundamental Operations on Two Dimensional Signals 34 which illustrates property M l ) . ) 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.

Property G1) willallow us to use the block diagram for addition as if it is a ternary or higher arty operator. That is, to add three digital signals we will use +- + + + Equivalently, in mathematical terms,we could write f + g + h instead (f t g) t h. ,fN,we will write of f t (g t h) or N instead of f’ t be f2 Cfi or A D D ( f i ) i=l t .... t f N . The equivalent block fl c f2 c ADD fN diagram would i c Moreover, the order of summation does not matter due to G4). 4. Equational Identities InvolvingRangeInducedOperations 31 Observe also, that the SCALAR operation whose arguments are a real number along with a digital signal satisfies the following: V1) Associative Law: (ab)f = a ( b f ) V2) Unity Preservation: If = f VS) Distributive Law: a(f g ) = af ag V4) Distributive Law: ( a b ) f = af bf The first distributive law shows that scalar multiplication by reals is distributivewith respect to digital signal processing addition.

S ... W.. ... 0 0 0 0 0 a . 0 0 0 0 0 1 0 0 0 . 0 0 0 0 0 . a.. ... ... . . . m Various other reflection type operations exist besides the transpose type reflection D . Specifically, there is a horizontal, a vertical, and 2. Fundamental Operations on Two Dimensional Signale 48 a 4 5 O diagonal reflection. These are respectively denoted by HOR, V E R T , and DIFLIP. They are defined by: )(W = f (4 - j > V E R T U) ( i , j >= f (-4j) and DIFLIP( f)(i,j) = f(j,i) Thefollowingblockdiagramsillustratetheseoperationsandalso show that they are terms.