Analytical solutions for frequency estimators by interpolation of DFT coefficients

Generalization of interpolation DFT algorithms and frequency estimators with high image component interference rejection

“…These effects will lead to significant errors in spectral analysis such as parameter estimation [2,3]. In order to obtain accurate estimates of signal parameters, a lot of solutions were proposed [4][5][6][7][8][9][10][11][12][13][14]. The interpolation discrete Fourier transform (IpDFT) algorithm is one of the most popular algorithms.…”

Frequency estimation by two- or three-point interpolated Fourier algorithms based on cosine windows

“…The sum of the two procedure outputs then provides the desired frequency estimate. Various methods have been proposed in the scientific literature for fine-search implementation of either complex sinusoids [2][3][4][5][6][7][8][9][10][11] or real sinusoids [1,[12][13][14][15][16][17][18][19][20] by interpolating two or more DFT complex samples or modules. In particular, more than two DFT samples are used when estimating the frequency of a real sinusoid in order to reduce the effect of the spectral interference from the image component [17][18][19][20], but at the cost of an increased wideband noise sensitivity of the related frequency estimator [19].…”

“…Two-or three-point interpolated Fourier algorithms are often used when estimating the frequency of a complex sinusoid [2][3][4][5][6][7][8][9][10]. The effect of wideband noise on the estimates returned by two interpolation points algorithms is minimized when using the Aboutanios and Mulgrew (AM) algorithm [8].…”

High-precision frequency estimation of real sinusoids with reduced computational complexity using a model-based matched-spectrum approach

“…Frequency estimation is a standard problem in the signal processing field with a plethora of applications ranging from radar and satellite/mobile communications to general audio or speech processing and metrology [1][2][3][4][5]. The theoretical basis for the optimal frequency estimation, based on the maximum-likelihood (ML) criterion, of a discrete-time complex sinusoid embedded in noise was established in [6].…”