Patent ID: 8447591

Claim:
A method of deriving reversible integer-input/integer-output implementations of a lapped transform for processing an input audio signal partitioned in subframes of plural different sizes, the method comprising: factorizing the lapped transform into combinations of overlap windowing transforms for an overlap region overlapping adjacent subframes and block transforms for the subframes, wherein said factorizing comprises, forming a representation of the lapped transform for a given subframe as a rectangular linear transform matrix A, having a form of [ A i ⁡ ( j - 1 ) A ij A i ⁡ ( j + 1 ) A i ⁡ ( j + 2 ) A ( i + 1 ) ⁢ ( j - 1 ) A ( i + 1 ) ⁢ j A ( i + 1 ) ⁢ ( j + 1 ) A ( i + 1 ) ⁢ ( j + 2 ) ] ⁢ where each subblock in the matrix is a N/2×N/2 matrix for a size N of the subframe and i, j are indices of the matrix subblocks, and further wherein the matrix has a property that A i(j−1) A (i+1)(j−1) −1 =A ij A (i+1)j −1 ; factoring the rectangular linear transform matrix A into an overlap windowing transform matrix C in a form of [ C ( i - 1 ) ⁢ ( j - 1 ) C ( i - 1 ) ⁢ j C i ⁡ ( j - 1 ) C ij ] and block transform matrix B in form of [ B ij B i ⁡ ( j + 1 ) B ( i + 1 ) ⁢ j B ( i + 1 ) ⁢ ( j + 1 ) ] , wherein said factoring comprises solving the relations: C i(j−1) =B ij −1 A i(j−1) C ij =B ij −1 A ij B (i+1)j =A (i+1)(j−1) B ij A i(j−1) −1 ; at an audio processor, receiving input of an audio signal with said subframe; and with the audio processor, applying the overlap windowing transform matrix C to said subframe and its preceding adjacent subframe; and with the audio processor, applying the block transform matrix B to said subframe.