Accurate and instant frequency estimation from noisy sinusoidal waves by deep learning

We used a deep learning network to find the frequency of a noisy sinusoidal wave. A three-layer neural network was designed to extract the frequency of sinusoidal waves that had been combined with white noise at a signal-to-noise ratio of 25 dB. One hundred thousand waves were prepared for training and testing the model. We designed a neural network that could achieve a mean squared error of 4 × 10−5 for normalized frequencies. This model was written for the range 1 kHz ≤ f ≤ 10 kHz but also shown how to easily be generalized to other ranges. The algorithm is easy to rewrite and the final results are highly accurate. The trained model can find frequency of any previously-unseen noisy wave in less than a second.

[1]  Trevon Badloe,et al.  Optimisation of colour generation from dielectric nanostructures using reinforcement learning. , 2019, Optics express.

[2]  Geoffrey Ye Li,et al.  ComNet: Combination of Deep Learning and Expert Knowledge in OFDM Receivers , 2018, IEEE Communications Letters.

[3]  Daniel Belega,et al.  Frequency estimation via weighted multipoint interpolated DFT , 2008 .

[4]  Jian Huang,et al.  Ballistic missile detection via micro-Doppler frequency estimation from radar return , 2012, Digit. Signal Process..

[5]  Jiwen Lu,et al.  PCANet: A Simple Deep Learning Baseline for Image Classification? , 2014, IEEE Transactions on Image Processing.

[6]  Daniel S. Kermany,et al.  Identifying Medical Diagnoses and Treatable Diseases by Image-Based Deep Learning , 2018, Cell.

[7]  Geoffrey Ye Li,et al.  Power of Deep Learning for Channel Estimation and Signal Detection in OFDM Systems , 2017, IEEE Wireless Communications Letters.

[8]  Jeonghyun Kim,et al.  Finding the optical properties of plasmonic structures by image processing using a combination of convolutional neural networks and recurrent neural networks , 2019, Microsystems & Nanoengineering.

[9]  Kai-Bor Yu,et al.  Total least squares approach for frequency estimation using linear prediction , 1987, IEEE Trans. Acoust. Speech Signal Process..

[10]  Junsuk Rho,et al.  Designing nanophotonic structures using conditional deep convolutional generative adversarial networks , 2019, Nanophotonics.

[11]  Bram van Ginneken,et al.  A survey on deep learning in medical image analysis , 2017, Medical Image Anal..

[12]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[13]  L. C. Palmer,et al.  Coarse frequency estimation using the discrete Fourier transform (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[14]  Tara N. Sainath,et al.  Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups , 2012, IEEE Signal Processing Magazine.

[15]  J Pou,et al.  Variable-Frequency Grid-Sequence Detector Based on a Quasi-Ideal Low-Pass Filter Stage and a Phase-Locked Loop , 2010, IEEE Transactions on Power Electronics.

[16]  S. Stankovic,et al.  Multiwindow S-method for instantaneous frequency estimation and its application in radar signal analysis , 2010, IET Signal Processing.

[17]  Dong Yu,et al.  Deep Learning and Its Applications to Signal and Information Processing [Exploratory DSP] , 2011, IEEE Signal Processing Magazine.

[18]  Loi Lei Lai,et al.  Real-time frequency and harmonic evaluation using artificial neural networks , 1999 .

[19]  Qirong Jiang,et al.  A Novel Phase-Locked Loop Based on Frequency Detector and Initial Phase Angle Detector , 2013 .

[20]  Richard Bamler,et al.  Doppler frequency estimation and the Cramer-Rao bound , 1991, IEEE Trans. Geosci. Remote. Sens..

[21]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .

[22]  Cagatay Candan,et al.  A Method For Fine Resolution Frequency Estimation From Three DFT Samples , 2011, IEEE Signal Processing Letters.

[23]  Geoffrey Ye Li,et al.  Deep Learning-Based CSI Feedback Approach for Time-Varying Massive MIMO Channels , 2018, IEEE Wireless Communications Letters.

[24]  Jian Li,et al.  Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares , 2010, IEEE Transactions on Aerospace and Electronic Systems.

[25]  Aurobinda Routray,et al.  A novel Kalman filter for frequency estimation of distorted signals in power systems , 2002, IEEE Trans. Instrum. Meas..