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Open AccessArticle

Harmonic Parameter Estimation Based on the ApFFT/ApDTFT Spectral Scenario with Low Mutual Interference

by Qi Zhang, Xiangdong Huang, Xiao Ma and Hongwei Fang

Electronics 2026, 15(9), 1784; https://doi.org/10.3390/electronics15091784 - 22 Apr 2026

Viewed by 373

In order to improve the accuracy of multi-tone parameter estimation, we propose a scheme derived from a novel spectral scenario based on all-phase Fast Fourier Transform (apFFT)/all-phase discrete-time Fourier Transform (apDTFT). This scheme is constructed based on the following architecture. Firstly, we theoretically extend the original discrete apFFT analysis to the proposed continuous apDTFT analysis, so that two excellent spectral properties (suppression of spectral leakage and phase invariance) hold across the entire frequency axis. Secondly, on the basis of apFFT/apDTFT, we design a single-tone interpolator and its improved version with frequency-shift iteration. Thirdly, we derive a multi-tone harmonic estimator, which can further reduce the mutual spectral interference under the apFFT-/apDTFT-based spectral scenario. Both numerical and experimental results demonstrate that, even with one fewer sample, the proposed apFFT-/apDTFT-based estimator achieves higher accuracy across individual harmonics and inter-harmonics than the FFT-/DTFT-based estimator. Full article

(This article belongs to the Section Circuit and Signal Processing)

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17 pages, 3374 KB

Open AccessTechnical Note

A Novel Real-Time Multi-Channel Error Calibration Architecture for DBF-SAR

by Jinsong Qiu, Zhimin Zhang, Yunkai Deng, Heng Zhang, Wei Wang, Zhen Chen, Sixi Hou, Yihang Feng and Nan Wang

Remote Sens. 2025, 17(16), 2890; https://doi.org/10.3390/rs17162890 - 19 Aug 2025

Cited by 2 | Viewed by 1793

Abstract

Digital Beamforming SAR (DBF-SAR) provides high-resolution wide-swath imaging capability, yet it is affected by inter-channel amplitude, phase and time-delay errors induced by temperature variations and random error factors. Since all elevation channel data are weighted and summed by the DBF module in real time, conventional record-then-compensate approaches cannot meet real-time processing requirements. To resolve the problem, a real-time calibration architecture for Intermediate Frequency DBF (IFDBF) is presented in this paper. The Field-Programmable Gate Array (FPGA) implementation estimates amplitude errors through simple summation, time-delay errors via a simple counter, and phase errors via single-bin Discrete-Time Fourier Transform (DTFT). The time-delay and phase error information are converted into single-tone frequency components through Dechirp processing. The proposed method deliberately employs a reduced-length DTFT implementation to achieve enhanced delay estimation range adaptability. The method completes calibration within tens of PRIs (under 1 s). The proposed method is analyzed and validated through a spaceborne simulation and X-band 16-channel DBF-SAR experiments. Full article

(This article belongs to the Section Remote Sensing Image Processing)

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18 pages, 2178 KB

Open AccessArticle

Performance Optimization in Frequency Estimation of Noisy Signals: Ds-IpDTFT Estimator

by Miaomiao Wei, Yongsheng Zhu, Jun Sun, Xiangyang Lu, Xiaomin Mu and Juncai Xu

Sensors 2023, 23(17), 7461; https://doi.org/10.3390/s23177461 - 28 Aug 2023

Cited by 3 | Viewed by 2703

Abstract

This research presents a comprehensive study of the dichotomous search iterative parabolic discrete time Fourier transform (Ds-IpDTFT) estimator, a novel approach for fine frequency estimation in noisy exponential signals. The proposed estimator leverages a dichotomous search process before iterative interpolation estimation, which significantly reduces computational complexity while maintaining high estimation accuracy. An in-depth exploration of the relationship between the optimal parameter p and the unknown parameter

δ

forms the backbone of the methodology. Through extensive simulations and real-world experiments, the Ds-IpDTFT estimator exhibits superior performance relative to other established estimators, demonstrating robustness in noisy conditions and stability across varying frequencies. This efficient and accurate estimation method is a significant contribution to the field of signal processing and offers promising potential for practical applications. Full article

(This article belongs to the Special Issue Audio, Image, and Multimodal Sensing Techniques)

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11 pages, 2127 KB

Open AccessArticle

Accurate Frequency Estimator for Real Sinusoid Based on DFT

by Zhanhong Liu, Lei Fan, Jinyu Liu, Nian Liu, Jiyu Jin and Jun Xing

Electronics 2022, 11(19), 3042; https://doi.org/10.3390/electronics11193042 - 24 Sep 2022

Cited by 10 | Viewed by 2856

Abstract

An accurate frequency estimator for real sinusoid based on Discrete Fourier Transform (DFT) is proposed. The proposed estimator is based on the interpolation of the maximum DFT spectral line and two Discrete-Time Fourier Transform (DTFT) spectral lines and can operate with both the rectangular window and the maximum sidelobe decay (MSD) window. In the coarse estimation step, the proposed estimator with the MSD window is used. According to the value of the coarse estimate, the negative frequency spectral component is removed. In the fine estimation step, the proposed estimator with the rectangular window is utilized to achieve the Cramer–Rao lower bound (CRLB). Simulation results show that the performance of this algorithm is better than that of the AM algorithm, Candan algorithm, Djukanovic algorithm, and FDIAM algorithm. Full article

(This article belongs to the Section Circuit and Signal Processing)

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23 pages, 569 KB

Open AccessArticle

Comparative Study of AC Signal Analysis Methods for Impedance Spectroscopy Implementation in Embedded Systems

by Ahmed Yahia Kallel, Zheng Hu and Olfa Kanoun

Appl. Sci. 2022, 12(2), 591; https://doi.org/10.3390/app12020591 - 7 Jan 2022

Cited by 25 | Viewed by 6570

Abstract

For embedded impedance spectroscopy, a suitable method for analyzing AC signals needs to be carefully chosen to overcome limited processing capability and memory availability. This paper compares various methods, including the fast Fourier transform (FFT), the FFT with barycenter correction, the FFT with windowing, the Goertzel filter, the discrete-time Fourier transform (DTFT), and sine fitting using linear or nonlinear least squares, and cross-correlation, for analyzing AC signals in terms of speed, memory requirements, amplitude measurement accuracy, and phase measurement accuracy. These methods are implemented in reference systems with and without hardware acceleration for validation. The investigation results show that the Goertzel algorithm has the best overall performance when hardware acceleration is excluded or in the case of memory constraints. In implementations with hardware acceleration, the FFT with barycentre correction stands out. The linear sine fitting method provides the most accurate amplitude and phase determinations at the expense of speed and memory requirements. Full article

(This article belongs to the Special Issue Impedance Spectroscopy and Its Application in Measurement and Sensor Technology)

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19 pages, 430 KB

Open AccessArticle

Four Particular Cases of the Fourier Transform

by Jens V. Fischer

Mathematics 2018, 6(12), 335; https://doi.org/10.3390/math6120335 - 18 Dec 2018

Cited by 10 | Viewed by 17729

Abstract

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense. Full article

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