Hadamard transformation method and apparatus
AssigneeCanon Kabushiki Kaisha
InventorTadayoshi Nakayama
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Abstract
The present invention provides a method and apparatus that transforms input signals X0, X1, X2, X3 using a 4-point Hadamard transform matrix, and of the resulting transformation data, rounds up the LSB of the first transformed data and rounds down the LSB of the remaining odd-numbered data. When restoring the data to its original state the rounding is executed after a Hadamard inverse transformation is performed, thereby restoring the data to its original state X0, X1, X2, X3.
Claims18
A Hadamard transformation and inverse transformation method comprising:
- a transformation step of performing a Hadamard transformation of an input signal using a Hadamard transform matrix;
- and
- a rounding step of rounding up the least significant bit of odd number of data in the transformed data transformed in said transformation step and rounding down the LSB of remaining odd number of data.
A Hadamard transformation method comprising:
- a transformation step of performing a Hadamard transformation using a Hadamard transform matrix;
- a rounding step of rounding up the least significant bit of odd number of transformation output in the transformation results output of said transformation step and rounding down the LSB of remaining odd number of transformation output;
- an inverse transformation step of performing an inverse Hadamard transformation of the transformation output rounded in said rounding step;
- and
- a reversion step of restoring the data to its original state by performing the same rounding as the rounding of said rounding step for the transformation results of said inverse transformation step.
A Hadamard transformation apparatus comprising:
- Hadamard transformation means;
- and
- rounding means for rounding up odd number of LSB of transformation output by said Hadamard transformation means and rounding down remaining odd number of transformation output LSB
A Hadamard transformation apparatus comprising:
- transformation means for performing a Hadamard transformation using a 4-point Hadamard transform matrix;
- rounding means for rounding up the least significant bit of odd-numbered transformation output in the transformation results output by said transformation means and rounding down the LSB of remaining odd-numbered transformation output;
- inverse transformation means for performing an inverse Hadamard transformation of the transformation output rounded by said rounding means;
- and
- reversion means for restoring the data to its original state by performing the same rounding as the rounding of said rounding means for the transformation results of said inverse transformation means.
A program that causes a computer to execute a Hadamard transformation method comprising:
- a transformation step of performing a Hadamard transformation of an input signal using a Hadamard transform matrix;
- and
- a rounding step of rounding up the least significant bit of each odd-numbered data in the transformed data transformed in said transformation step and rounding down the least significant bit of remaining odd-numbered data.
A computer-readable recording medium on which is recorded a program that causes a computer to execute a Hadamard transformation method comprising:
- a transformation step of performing a Hadamard transformation of an input signal using a Hadamard transform matrix;
- and
- a rounding step of rounding up the least significant bit of each odd-numbered data in the transformed data transformed in said transformation step and rounding down the least significant bit of remaining odd-numbered data.
A Hadamard transformation apparatus, comprising:
- calculation means for adding and subtracting 4 integer input data in accordance with a 4-point Hadamard transform matrix;
- addition means for adding predetermined values to the transformed results by said calculation means and outputting the added data;
- and
- rounding means for rounding down the least significant bit of the added data outputted by said addition means,
- wherein the predetermined values are 2Mi+Si (i=0, 1, 2, 3)
- wherein Mi is an integer number, Si is 0 or 1, and S0+S1+S2+S3=1 or 3.
A Hadamard transformation method, comprising the steps of:
- adding and subtracting 4 integer input data in accordance with a 4-point Hadamard transform matrix;
- adding predetermined values to the Hadamard transformed results and outputting the added data;
- and
- rounding down the least significant bit of the added data,
- wherein the predetermined values are 2Mi+Si (i=0, 1, 2, 3)
- wherein Mi is an integer number, Si is 0 or 1, and S0+S1+S2+S3=1 or 3.
A program that causes a computer to execute a Hadamard transformation method comprising the steps of:
- adding and subtracting 4 integer input data in accordance with a 4-point Hadamard transform matrix;
- adding predetermined values to the Hadamard transformed results and outputting the added data;
- and
- rounding down the least significant bit of the added data,
- wherein the predetermined values are 2Mi+Si (i=0, 1, 2, 3)
- wherein Mi is an integer number, Si is 0 or 1, and S0+S1+S2+S3=1 or 3.
A computer-readable recording medium on which is recorded a program that causes a computer to execute a Hadamard transformation method comprising the steps of:
- adding and subtracting 4 integer input data in accordance with a 4-point Hadamard transform matrix;
- adding predetermined values to the Hadamard transformed results and outputting the added data;
- and
- rounding down the least significant bit of the added data,
- wherein the predetermined values are 2Mi+Si (i=0, 1, 2, 3)
- wherein Mi is an integer number, Si is 0 or 1, and S0+S1+S2+S3=1 or 3.
Dependencies are inferred from the claim text.