A non-iterative approach to frequency estimation of a complex exponential in noise by interpolation of fourier coefficients

Minhas, Shahab Faiz; Gaydecki, Patrick

doi:10.1109/icdsp.2013.6622758

Cited by 3 publications

(2 citation statements)

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“…Numerous efforts have been made in the past to achieve fast and accurate frequency recovery through DFT interpolation. Existing solutions can be roughly divided into two categories: direct methods [11], [12], [13], [14], [15], [16], [17], [18] and iterative schemes [19], [20], [21], [22], [23], [24]. The former operate by reprocessing the maximum DFT coefficient and its neighbours that are available from the coarse search stage.…”

Section: Introductionmentioning

confidence: 99%

“…Using the fixedpoint theorem, it is shown that both schemes converge after two iterations, thereby requiring four auxiliary DFT samples to complete the fine tuning stage. Methods to reduce the processing load without sacrificing the system performance are reported in [20], [21], and [22]. More recently, Fan and Qi [23] have proposed an iterative scheme (denoted as FQE) based on interpolation of three DFT coefficients, namely the central DFT peak and two auxiliary spectral lines with arbitrary shifts of ±qΔf .…”

Section: Introductionmentioning

confidence: 99%

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Frequency Estimation by Interpolation of Two Fourier Coefficients: Cramér-Rao Bound and Maximum Likelihood Solution

D’Amico

Morelli

Moretti

2022

IEEE Trans. Commun.

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Sinusoidal frequency estimation in the presence of white Gaussian noise plays a major role in many engineering fields. Significant research in this area has been devoted to the fine tuning stage, where the discrete Fourier transform (DFT) coefficients of the observation data are interpolated to acquire the residual frequency error ε. Iterative interpolation schemes have recently been designed by employing two q-shifted spectral lines symmetrically placed around the DFT peak, and the impact of q on the estimation accuracy has been theoretically assessed. Such analysis, however, is available only for some specific algorithms and is mostly conducted under the assumption of a vanishingly small frequency error, which makes it inappropriate for the first stage of any iterative process. In this work, further investigation on DFT interpolation is carried out to examine some issues that are still open. We start by evaluating the Cramér-Rao bound (CRB) for frequency recovery by interpolation of two q-shifted spectral lines and assess its dependence on ε and q. Such a bound is of primary importance to check whether existing schemes can provide efficient estimates at any iteration or not. After determining the optimum value of q for a given ε, we eventually derive the maximum likelihood (ML) DFT interpolator. Since the latter exhibits the best performance at any step of the iteration process, it might attain the desired accuracy just at the end of the first iteration, which is especially advantageous in terms of computational load and processing time.

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