Patent ID: 7129962

Claim:
Computer-readable media tangibly embodying a program of instructions executable by a computer to perform a method of transforming an ordered set of N first coefficients representative of a signal in a first domain into an ordered set of M second coefficients representative of the signal in a second domain, the method comprising: accessing an ordered set of N ordered sets of M pre-computed factors each, the n th ordered set of pre-computed factors, 1≦n≦N, being associated with the n th one of the first coefficients; and selecting one of a magnification factor and a reduction factor for applying to the ordered set of N first coefficients in order to avoid one of overflow and underflow during the transforming of the set of N first coefficients to the M second coefficients, said one of a magnification factor and a reduction factor being selected by: a) determining a sum of absolute values of the first coefficients; b) determining a maximum absolute value amongst the pre-computed factors; c) computing a product of the sum of absolute values obtained in (a) and the maximum absolute value obtained in (b): d) comparing the product obtained in (c) to a maximum value to which a machine-readable representation can be assigned; e) if said product exceeds said maximum value to which a machine-readable representation can be assigned, selecting one of the magnification factor and the reduction factor to a value such that a product of the selected one of the magnification factor and the reduction factor with the product obtained in (c) does not exceed said maximum value to which a machine-readable representation can be assigned; otherwise, selecting a factor of unity; applying the selected one of the magnification factor and the reduction factor to each of the N first coefficients, thereby to obtain an ordered set of N scaled first coefficients; computing a set of N ordered sets of M intermediate values each, the j th element, 1≦j≦M, of the k th ordered set of intermediate values, 1≦k≦N, being a scalar product of the k th scaled first coefficient with the j th element of the k th ordered set of pre-computed factors; cumulatively adding corresponding elements of the ordered sets of intermediate values, thereby to form an ordered set of N scaled second coefficients; and inversely applying the selected one of the magnification factor and the reduction factor to each element of the ordered set of scaled second coefficients, thereby to obtain the ordered set of second coefficients.