Patent Document ID: 8185568
Application ID: 12054339
Patent Status: 1

Claim One:
1. A method of obtaining a Hilbert index from a linear-based index, the method comprising the step of: performing a bit-wise transformation on the linear-based index to obtain the Hilbert index; wherein the step of performing includes the steps of: selecting an input index length that corresponds to the linear-based index, where the input index length is an even integer greater than or equal to 2; constructing a Hilbert transform matrix for each linear-based index digit, wherein each Hilbert transform matrix is filled using digit sums of the associated linear-based index digit, partial sums of the associated linear-based index digit, zeros and ones; and multiplying each linear-based index digit with the associated Hilbert transform matrix to obtain the Hilbert index that contains the associated Hilbert index digits; wherein the step of constructing each Hilbert transform matrix includes the steps of: setting the input index I to 0; computing digit sums of the set input index using equation S n = i 2 ⁢ ( n + 1 ) + i 2 ⁢ ( n + 1 ) + 1 , ⁢ for ⁢ ⁢ n = 0 , … ⁢ ⁢ K , ⁢ where ⁢ ⁢ K = N 2 - 2 ; computing partial sums of the set input index using σ l = ∑ n = l K ⁢ ⁢ S n , ⁢ for ⁢ ⁢ l = 0 , … ⁢ ⁢ K ; constructing the Hilbert transform matrix for that set input index; and incrementing the set input index by 1 to obtain a new set input index until the new set input index is equal to the input index length minus 1, such that for each new set input index the steps of computing the digit sums, computing the partial sums, and constructing the Hilbert transform matrix are repeated to obtain digit sums, partial sums and the Hilbert transform matrix for each set input index; wherein at least said steps of selecting, constructing and multiplying are automatically performed using a computer processor.