scholarly journals Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples

2015 ◽  
Vol 22 (3) ◽  
pp. 403-416 ◽  
Author(s):  
Xin Liu ◽  
Yongfeng Ren ◽  
Chengqun Chu ◽  
Wei Fang
Keyword(s):  
Fourier Transform ◽  
Frequency Estimation ◽  
Signal To Noise Ratio ◽  
Golden Section ◽  
Least Square ◽  
Estimation Accuracy ◽  
Tone Frequency ◽  
Single Tone ◽  
Dc Component ◽  
Fitting Error

Abstract This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512.

An ENOB Evaluation Method for an Acquisition Channel

2019 ◽  
Vol 28 (11) ◽  
pp. 1950185
Author(s):  
Xin Liu ◽  
Yan Liu ◽  
Zengshou Dong
Keyword(s):  
Evaluation Method ◽  
Golden Section ◽  
Dynamic Performance ◽  
Performance Testing ◽  
Sine Wave ◽  
Least Square ◽  
Test Method ◽  
Single Tone ◽  
Fitting Procedure ◽  
Dc Component

Three-parameter and four-parameter sine-wave fitting algorithms are powerful tools for estimating the parameters of the excited single-tone sine-wave for ADC. In the dynamic performance testing processes of instruments, the angle frequency, amplitude, phase and dc component of the input sine-wave are all unknown, so the fitting procedure is nonlinear. This paper proposes and analyzes a test method based on iteration Interpolated Discrete Fourier Transform (IpDFT) and sine-wave fitting method for evaluating the effective number of bit (ENOB) of the acquisition channel. Mathematical expressions of the Least-square fitting residual error and the proposed ENOB evaluation based on iteration IpDFT method are derived. These expressions are then particularized for acquisition circuit output noise composed of single-tone and additive white noise. Simulation results show that the DFT-based golden section searching algorithm (DGSSA) is an effective algorithm under coherent and non-coherent sampling conditions. The accuracy of the derived expressions and estimated parameters are verified through both the computer simulations and experimental results.

FFT-Based Moving Average Maximum Likelihood Single-tone Frequency Estimation

2011 ◽  
Vol 30 (4) ◽  
pp. 831-835
Author(s):  
Yu-chun Huang ◽  
Zai-lu Huang ◽  
Ben-xiong Huang ◽  
Shu-hua Xu
Keyword(s):  
Maximum Likelihood ◽  
Frequency Estimation ◽  
Moving Average ◽  
Tone Frequency ◽  
Single Tone ◽  
Average Maximum

scholarly journals Phase Clustering Based Modulation Classification Algorithm for PSK Signal over Wireless Environment

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Qi An ◽  
Zi-shu He ◽  
Hui-yong Li ◽  
Yong-hua Li
Keyword(s):  
Frequency Estimation ◽  
Signal To Noise Ratio ◽  
Frequency Offset ◽  
Estimation Accuracy ◽  
Modulation Classification ◽  
Electronic Warfare ◽  
Wireless Communication Network ◽  
Shift Keying ◽  
Analytical Formulas ◽  
Fractional Function

Promptitude and accuracy of signals’ non-data-aided (NDA) identification is one of the key technology demands in noncooperative wireless communication network, especially in information monitoring and other electronic warfare. Based on this background, this paper proposes a new signal classifier for phase shift keying (PSK) signals. The periodicity of signal’s phase is utilized as the assorted character, with which a fractional function is constituted for phase clustering. Classification and the modulation order of intercepted signals can be achieved through its Fast Fourier Transform (FFT) of the phase clustering function. Frequency offset is also considered for practical conditions. The accuracy of frequency offset estimation has a direct impact on its correction. Thus, a feasible solution is supplied. In this paper, an advanced estimator is proposed for estimating the frequency offset and balancing estimation accuracy and range under low signal-to-noise ratio (SNR) conditions. The influence on estimation range brought by the maximum correlation interval is removed through the differential operation of the autocorrelation of the normalized baseband signal raised to the power ofQ. Then, a weighted summation is adopted for an effective frequency estimation. Details of equations and relevant simulations are subsequently presented. The estimator proposed can reach an estimation accuracy of10-4even when the SNR is as low as-15 dB. Analytical formulas are expressed, and the corresponding simulations illustrate that the classifier proposed is more efficient than its counterparts even at low SNRs.

scholarly journals Multidimensional Single-Tone Frequency Estimation Based on QR Decomposition

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 68153-68159
Author(s):  
Hui Cao ◽  
Long-Ting Huang ◽  
Yuntao Wu ◽  
Qi Liu
Keyword(s):  
Frequency Estimation ◽  
Qr Decomposition ◽  
Tone Frequency ◽  
Single Tone
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