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 improve evidently taking place parallel DSP algorithms. collage or college publication outlets may perhaps order 5 or extra copies at a unique scholar rate. expense is on the market on request.
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Extra resources for A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing
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. The output of thefollowingtwoblock diagrams is H O R ( f ) .
5. Fundamental Domain Induced Operations 41 D applied to any digital signal f makes rows of f become columns in D ( f ) and columns in f become rows in D(f). More precisely, D is defined pointwise using R E F L E C T ( f ) ( i , j )= f(-j,-i) Thus D ( f ) can also be obtained by flipping f around a 1 3 5 O line in the z,y-plane. 14 Let f= (: 4 1q o -1,l Then using the pointwise definition since f(-j,4)= f(0, -1) = 1 we have D(f)(190) = 1 Similarly, f(-j, 4)= f(-l, 1) = 2 80 D(f)(-L 1) = 2 Observe that D( f) can also befound by placing a mirror dong the 1 3 5 O line and observing f ; the resulting digital signal is D ( f ) .
Both of these operations are binary, thereby taking two signals as input arguments and yielding a signal as output. Thus, MULT : Rzxz X Rzxz -+ Rzxz and M A X : Rzxz X szxz+ Rzxz They axe defined using the pointwise definition. Indeed, M U J w f , d ( n ,4 = f ( n ,4 s ( n ,m) and 4 f ( n ,4 , d n , 4 Again, we will abuse notation by letting M A X ( f ,g ) ( % 4=m ) M U L T ( f , g )= f ' g Additionally, we will often write f V g instead of M A X ( f , g ) . 1. Since 0 2 3 0 f = ( 1 4 0) -1 '1 0 3,* 20 2.
A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing by Louis A. D'Alotto, Charles R. Giardina, Hua Luo