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PRONY'S METHOD FOR PROCESSING OF DATA WITH WHITE OR COLOUR NOISE

Z Uang

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Abstract

In this paper Prony's method is extended to the processing of the data with white and / or colour noise. When the observed noise is white, the observation process obeys the ARMA model in which the AR coefficients equal the MA coefficients, and two kinds of modified Yule-Walker normal equations, which yield the unbiased estimates of the AR coefficients, are derived. For the colour observed noise, a new concept of the two-step autoregression procedure is developed, through which the colour noise can be whitened. Finally, the theoretical results are checked by simulative calculations on a DJS 108 Ⅱ computer.

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What this paper is about

In this paper Prony's method is extended to the processing of the data with white and / or colour noise. When the observed noise is white, the observation process obeys the ARMA model in which the AR coefficients equal the MA coefficients, and two kinds of modified Yule-Walker normal equations, which yield the unbiased estimates of the AR coefficients, are derived. For the colour observed noise, a new concept of the two-step autoregression procedure is developed, through which the colour noise can be whitened. Finally, the theoretical results are checked by simulative calculations on a DJS 108 Ⅱ computer.

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Available abstract

In this paper Prony's method is extended to the processing of the data with white and / or colour noise. When the observed noise is white, the observation process obeys the ARMA model in which the AR coefficients equal the MA coefficients, and two kinds of modified Yule-Walker normal equations, which yield the unbiased estimates of the AR coefficients, are derived. For the colour observed noise, a new concept of the two-step autoregression procedure is developed, through which the colour noise can be whitened. Finally, the theoretical results are checked by simulative calculations on a DJS 108 Ⅱ computer.

Key concepts: White noise, Autoregressive model, Noise (video), Mathematics, Colors of noise, Statistics, Autoregressive–moving-average model, Applied mathematics

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