By Salvatore D. Morgera
ISBN-10: 0125069952
ISBN-13: 9780125069953
ISBN-10: 0323158935
ISBN-13: 9780323158930
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Additional resources for Digital Signal Processing. Applications to Communications and Algebraic Coding Theories
Sample text
The trilinear form T is given by k-l d-l k+d-2 T = z r Xy = Σ > Σ Xt+jVj = Σ t=0 j=0 t χ *Σ t=0 z iVt-i> (2· 20 ) j=0 where it is understood that zt = 0 for t > k — 1 and y3; = 0 for j > d— 1. Using the method described earlier for extracting Φ from the trilinear form, we find that ί = 0 , 1 , . . 21) where N = k + d — 1. The bilinear forms associated with the yl-dual are, therefore, computable as the elements of the aperiodic convolution φ= z Θ y of the length k sequence z and the length d sequence y.
M5 defined in the degree-2 polynomial multiplication algorithm. 1. CYCLIC CONVOLUTION 43 Step 2: Prom Pi(u), we obtain the difference equation ti,· = U{-
This leads us to the first step. Steps 1-5 are carried out for all Θ = (pn - 1)/(ρσθ - l)eS. Step 1: Using a bilinear small degree polynomial multiplication algo rithm for polynomials of degree σ$ — 1, directly obtain the first σ$ elements of any row of AQ. Step 2: Extend the remaining portion of each row of A$ by the MLRS generated by Pe{u). The σ# elements obtained in Step 1 provide the necessary initial conditions. Step 3: Use the same procedure of Steps 1 and 2 to obtain BeStep 4: Evaluate 2σ 0 -2 ifiet = (l/N) Σ r m trie-**-"*)), t = 0,1, · · · ,σβ - 1, ra=0 and then use a bilinear small degree polynomial multiplication algorithm to obtain the first σ# rows of C$.
Digital Signal Processing. Applications to Communications and Algebraic Coding Theories by Salvatore D. Morgera
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