An Accurate and Efficient Frequency Estimation Algorithm by Using FFT and DTFT

Liu, Jinyu; Fan, Lei; Jin, Jiyu; Wang, Xinzhe; He, Wei

doi:10.23919/ccc50068.2020.9188660

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…The root mean square error (RMSE) of a suggested algorithm is much lower than that of Candan, a rational combination of three spectrum lines (RCTSL), and Aboutanios and Mulgrew (A&M) algorithms and close to the Hybrid A&M and q-shift estimator (HAQSE) algorithm. When the SNR is between 5 dB and 100 dB, the suggested approach outperforms the competitor algorithms [3].…”

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Razzaq

Hussain

2022

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Deep learning (DL) and machine learning (ML) are widely used in many fields but rarely used in the frequency estimation (FE) and slope estimation (SE) of signals. Frequency and slope estimation for frequency-modulated (FM) and single-tone sinusoidal signals are essential in various applications, such as wireless communications, sound navigation and ranging (SONAR), and radio detection and ranging (RADAR) measurements. This work proposed a novel frequency estimation technique for instantaneous linear FM (LFM) sinusoidal wave using deep learning. Deep neural networks (DNN) and convolutional neural networks (CNN) are classes of artificial neural networks (ANNs) used for the frequency and slope estimation for LFM signals under additive white Gaussian noise (AWGN) and additive symmetric alpha stable noise (SαSN). DNN is composed of input, output, and two hidden layers, where several nodes in the first and second hidden layers are 25 and 8, respectively. CNN is the content input layer; many hidden layers include convolution, batch normalization, ReLU, max pooling, fully connected, and dropout. The output layer consists of a fully connected softmax and classification layers. SαS distributions are impulsive noise disturbances found in many communication environments such as marine systems, their distribution lacks a closed-form probability density function (PDF), except for specific cases, and infinite second-order statistics, hence geometric SNR (GSNR) is used in this work to determine the effect of noise in a mixture of Gaussian and SαS noise processes. DNN is a machine learning classifier with few layers for reducing FE and SE complexity. CNN is a deep learning classifier, designed with many layers, and proved to be more accurate than DNN when dealing with big data and finding optimal features. Simulation results show that SαS noise can be much more harmful to the FE and SE of FM signals than Gaussian noise. DL and ML can significantly reduce FE complexity, memory cost, and power consumption as compared to the classical FE based on time–frequency analysis, which are important requirements for many systems, such as some Internet of Things (IoT) sensor applications. After training CNN for frequency and slope estimation of LFM signals, the performance of CNN (in terms of accuracy) can give good results at very low signal-to-noise ratios where time–frequency distribution (TFD) fails, giving more than 20 dB difference in the GSNR working range as compared to the classical spectrogram-based estimation, and over 15 dB difference with Viterbi-based estimate.

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Section: Introductionmentioning

confidence: 97%

“…Ref. [3] proposes an algorithm for frequency estimation of sinusoidal FM signals using interpolation of the fast Fourier transform (FFT) and discrete-time Fourier transform (DTFT), relying on N-point FFT to find the position of the maximum FFT. Three spectral lines located within the main lobe are used to estimate the frequency.…”

Section: Introductionmentioning

confidence: 99%

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Razzaq

Hussain

2022

Information

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“…When there are multiple targets, the signal beat frequency is a multi-frequency signal. There are basically two ways to estimate the frequencies of a multi-frequency signal: time-domain methods and frequency-domain methods [ 7 , 8 ]. The frequency-domain methods are based on the fast Fourier transform (FFT) [ 9 , 10 ].…”

Section: Introductionmentioning

confidence: 99%

Enhanced Root-MUSIC Algorithm Based on Matrix Reconstruction for Frequency Estimation

Zhu

Zhang

et al. 2023

Sensors

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In recent years, frequency-modulated continuous wave (FMCW) radar has been widely used in automatic driving, settlement monitoring and other fields. The range accuracy is determined by the estimation of the signal beat frequency. The existing algorithms are unable to distinguish between signal components with similar frequencies. To address this problem, this study proposed an enhanced root-MUSIC algorithm based on matrix reconstruction. Firstly, based on the sparsity of a singular value vector, a convex optimization problem was formulated to identify a singular value vector. Two algorithms were proposed to solve the convex optimization problem according to whether the standard deviation of noise needed to be estimated, from which an optimized singular value vector was obtained. Then, a signal matrix was reconstructed using an optimized singular value vector, and the Hankel structure of the signal matrix was restored by utilizing the properties of the Hankel matrix. Finally, the conventional root-MUSIC algorithm was utilized to estimate the signal beat frequency. The simulation results showed that the proposed algorithm improved the frequency resolution of multi-frequency signals in a noisy environment, which is beneficial to improve the multi-target range accuracy and resolution capabilities of FMCW radar.

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“…Many researchers have proposed their estimators of single-tone sinusoid in the background of AWGN. These estimators can be categorized into time domain estimators [6][7][8][9][10][11] and frequency domain estimators [12][13][14][15][16][17][18][19][20][21][22][23][24]. Time domain estimators include autocorrelation methods [6,7], maximum likelyhood methods [8,9] and least square methods [10,11].…”

Section: Introductionmentioning

confidence: 99%

DFT-Based Frequency Estimation of Multiple Sinusoids

Liu

Fan

et al. 2022

IEEE Access

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An accurate frequency estimation method of multi-component sinusoidal signal in additive white Gaussian noise (AWGN) is proposed. The algorithm is implemented in the frequency domain and based on discrete Fourier transform (DFT). The maximum DFT spectral line and two Discrete-Time Fourier Transform (DTFT) samples located on the same side of the maximum DFT spectral line are used to estimate the frequency of a sinusoidal component. And this algorithm is utilized in both the coarse estimation and the fine estimation. Simulation results show that compared with the competing estimators, the presented method is closer to the Cramer-Rao lower bound (CRLB). And it is almost independent of the frequency displacement. The numerical complexity of the presented method is similar with the competing DFT-based algorithms.

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An Accurate and Efficient Frequency Estimation Algorithm by Using FFT and DTFT

Cited by 10 publications

References 13 publications

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Enhanced Root-MUSIC Algorithm Based on Matrix Reconstruction for Frequency Estimation

DFT-Based Frequency Estimation of Multiple Sinusoids

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