[특허]Signal processing apparatus and method for iteratively determining Arithmetic Fourier Transform

Signal processing apparatus and method for iteratively determining Arithmetic Fourier Transform 원문보기

IPC분류정보
국가/구분	United States(US) Patent 등록
국제특허분류(IPC7판)	G06F-015/332
출원번호	US-0792348 (1991-11-14)
발명자 / 주소	Tufts Donald W. (Greenwich RI)
출원인 / 주소	The Board of Governors for Higher Education, State of Rhode Island and Providence Plantations (Providence RI 02)
인용정보	피인용 횟수 : 27 인용 특허 : 0

초록 ▼

A signal processing apparatus and method for iteratively determining the inverse Arithmetic Fourier Transform (AFT) of an input signal by converting the input signal, which represents Fourier coefficients of a function that varies in relation to time, space, or other independent variable, into a set of output signals representing the values of a Fourier series associated with the input signal. The signal processing apparatus and method utilize a process in which a data set of samples is used to iteratively compute a set of frequency samples, wherein each computational iteration utilizes error information which is calculated between the initial data and data synthesized using the AFT. The iterative computations converge and provide AFT values at the Farey-fraction arguments which are consistent with values given by a zero-padded Discrete Fourier Transform (DFT), thus obtaining dense frequency domain samples without interpolation or zero-padding.

대표청구항 ▼

A signal processing method for converting an input signal, which represents Fourier coefficients of a function that varies in relation to an independent variable, into a set of output signals respectively representing the values of a Fourier series associated with said input signal, said method comprising the steps of: (a) generating from a signal data source a data signal vector comprising plural sets of samples of an input signal received within an analysis period of said independent variable; (b) generating from a first matrix multiplier means a frequency domain signal vector representative of an approximation of said frequency domain signal vector by multiplying said data signal vector by a predetermined transform signal matrix, wherein said first matrix multiplier means performs a predetermined number of computational iterations, and said frequency domain signal vector comprises plural sets of frequency samples of said input signal; (c) performing via a second matrix multiplier means an inverse transformation on said frequency domain signal vector by multiplying said frequency domain signal vector by an Arithmetic Fourier Transform signal matrix to produce a synthesized data signal vector representative of an approximation of said data signal vector; (d) generating from a subtractor an error signal vector by determining the difference between said generated data signal vector and said synthesized data signal vector; (e) converting via a third matrix multiplier means said error signal vector into a frequency domain improvement signal vector by multiplying said error signal vector by the transpose of said Arithmetic Fourier Transform signal matrix, and by a predetermined scaling value; (f) generating from an accumulator an updated frequency domain signal vector by adding said frequency domain improvement signal vector to said frequency domain signal vector; (g) utilizing said updated frequency domain signal vector as a replacement signal vector for said frequency domain signal vector, repeating steps (c) through (f) for said predetermined number of computational iterations; and (h) producing said output signals representative of said calculated frequency domain signal vector.

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Signal processing apparatus and method for iteratively determining Arithmetic Fourier Transform 원문보기

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Signal processing apparatus and method for iteratively determining Arithmetic Fourier Transform 원문보기

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