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 construction of parallel electronic sign processing (DSP) algorithms. This paintings bargains an method of electronic sign processing using the unified sign algebra atmosphere to strengthen clearly taking place parallel DSP algorithms. university or college ebook outlets may possibly order 5 or extra copies at a different scholar cost. cost is offered on request.

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M a.. then we obtain . . . * . m S(u)= 0 0 pJ . 1 1 1 1 1 1 0 1 ... *. 11 The shift operation performed on the impulse function 6 = (l)&J results in V ) = (Q,O The shift operation is denoted by the block diagram The second domain induced operation, N I N E T Y , arises due to the structure of the integral lattice. When the integral lattice is rotated a full 90°, the new lattice which occurs has exactly the same geometric configuration as the original lattice. 5. 12 Say we want to find N(f) where f = ( g i) 0 -1 ,l then we can find N ( f ) “point by point”.

To begin,notice that a doubleapplication of D to any digital signal always results in the original signal. That is, property 11) Involution of D : D D ( f )= f m, holds true. Accordingly, D is said to be involutory. The same is true for N 2 ,thus we have 12) Involution of N2: N 2 N 2 ( f) = N4(f ) = f The translation operation also satisfies the obvious property C l ) Commutative Law: T ( T ( f ;n , m), i,j) = T(T(f; & j ) ,n , m ) = T ( f ;n t i, m t j ) Of most importance is the theorem that domain induced and range induced operations commute.

Accordingly, it is useful at this time to define two binary macro operations called SCALAR and OFFSET. Both of these operations are terms including constant signals as one of their arguments. However, unlike previous terms, both of these operations involve inputs of different types. 3. Additional Important Digital Signals andMacro Operators 27 Specifically, they both have arguments consisting of a real number and a digital signal. Hence SCALAR : RzXz X R -+ Rzxz and O F F S E T : Rzxz X R -+ RzXz These terms are defined by SCALAR( f, a ) ( n , m ) = U f(n,m) and + O F F S E T (f , a ) ( n ,m ) = f ( n , m) a Thus, the SCALAR operation is just like scalar multiplication in a vector space.

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