Patent ID: 7408997

Claim:
A modulation and demodulation system of n sub-carrier frequencies, where n is a positive integer, and an oversampling parameter α, where α is a positive integer, comprising: a modulation circuit comprising: 2n numbers of a modulation ROM having a 2αn wide address, a size of the modulation ROM based on the oversampling parameter, the modulation ROM storing columns of elements independently in a modulation ROM matrix in the address according to a sampling order, where the elements are a value of trigonometric sine and cosine of the sub-carrier frequencies; and a demodulation circuit comprising: 2n numbers of a first demodulation ROM (ROM 1 ) having a 2αn wide address, the ROM 1 having rows and columns of 2αn and 2n, respectively, the ROM 1 storing elements of a combined matrix, wherein the combined matrix is generated by arranging in a matrix an α number of inverse matrices according to the oversampling parameter, each of the α number of inverse matrices are the inverse of respective portions of the modulation ROM.