Accurate Amplitude Estimation of a Noisy Sine-wave via Interpolated DFT Algorithm

Daniel Belega, Dario Petri, Dominique Dallet

Abstract

This paper analyses Mean Square Error (MSE) of a noisy sine-wave amplitude estimator based on the Discrete-Time Fourier Transform (DTFT) evaluated at the signal frequency estimated by the classical Interpolated Discrete Fourier Transform (IpDFT) algorithm. In order to reduce the contribution of the spectral image component on the returned estimates, the sine-wave is weighted by a Maximum Sidelobe Decay (MSD) window. An analytical expression for the estimator MSE is derived. For given Signal-to-Noise Ratio (SNR) and number of processed samples, that expression allows us to derive the minimum number of acquired sinewave cycles ensuring that the detrimental contribution of the image component on the estimation accuracy is negligible as compared with the effect of wideband noise. In such condition, both computer simulations and experimental results show that the analysed DTFT-based estimator outperforms the classical DFT-based estimator.

Keywords

amplitude estimation, Discrete-Time Fourier Transform (DTFT), error and statistical analysis, windowing

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DOI

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IMEKO TC

TC4 - Measurement of Electrical Quantities

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