The JM-Filter to Detect Specific Frequency in Monitored Signal

The Discrete Fourier Transform (DFT) is a mathematical procedure that stands at the center of the processing inside a digital signal processor. It has been widely known and argued in relevant literature that the Fast Fourier Transform (FFT) is useless in detecting specific frequencies in a monitored signal of length N because most of the computed results are ignored. In this paper, we present an efficient FFT-based method to detect specific frequencies in a monitored signal, which will then be compared to the most frequently used method which is the recursive Goertzel algorithm that detects and analyses one selectable frequency component from a discrete signal. The proposed JM-Filter algorithm presents a reduction of iterations compared to the first and second order Goertzel algorithm by a factor of r, where r represents the radix of the JM-Filter. The obtained results are significant in terms of computational reduction and accuracy in fixed-point implementation. Gains of 15 dB and 19 dB in signal to quantization noise ratio (SQNR) were respectively observed for the proposed first and second order radix-8 JM-Filter in comparison to Goertzel algorithm.

[1]  I. Carugati,et al.  Frequency Adaptive PLL for Polluted Single-Phase Grids , 2012, IEEE Transactions on Power Electronics.

[2]  Hung Tien Bui.  Pipelined FPGA design of the Goertzel algorithm for exon prediction , 2012, 2012 IEEE International Symposium on Circuits and Systems.

[3]  Ming Ding,et al.  An achievable performance upper bound for discrete multitone equalization , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[4]  D. Straussnigg,et al.  Universal Tone Detection Based on the Goertzel Algorithm , 2006, 2006 49th IEEE International Midwest Symposium on Circuits and Systems.

[5]  E. Jacobsen,et al.  The sliding DFT , 2003, IEEE Signal Process. Mag..

[6]  Chih-Chyau Yang,et al.  High-speed area-efficient recursive DFT/IDFT architectures , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[7]  Miguel O. Arias-Estrada,et al.  Input and/or Output Pruning of Composite Length FFTs Using a DIF-DIT Transform Decomposition , 2009, IEEE Transactions on Signal Processing.

[8]  Deyun Wei,et al.  Novel Tridiagonal Commuting Matrices for Types I, IV, V, VIII DCT and DST Matrices , 2014, IEEE Signal Processing Letters.

[9]  P.D. Cristea,et al.  Genomic signal processing , 2004, 7th Seminar on Neural Network Applications in Electrical Engineering, 2004. NEUREL 2004. 2004.

[10]  Visar Berisha,et al.  A Frequency/Detector Pruning Approach for Loudness Estimation , 2009, IEEE Signal Processing Letters.

[11]  G. Goertzel.  An Algorithm for the Evaluation of Finite Trigonometric Series , 1958 .

[12]  Ching-Hsing Luo,et al.  Low Computational Complexity, Low Power, and Low Area Design for the Implementation of Recursive DFT and IDFT Algorithms , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  P.K. Meher,et al.  Novel Recursive Solution for Area-Time Efficient Systolization of Discrete Fourier Transform , 2007, 2007 International Symposium on Signals, Circuits and Systems.

[14]  Chin-Teng Lin,et al.  VLSI Architecture for the Low-Computation Cycle and Power-Efficient Recursive DFT/IDFT Design , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[15]  W. Steenaart,et al.  Overflow analysis of a fixed-point implementation of the Goertzel algorithm , 1989 .

[16]  Markku Renfors,et al.  Recursive Algorithms for Modulated and Extended Lapped Transforms , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Yong Xu,et al.  An Inductive Hybrid UPQC for Power Quality Management in Premium-Power-Supply-Required Applications , 2020, IEEE Access.

[18]  Ricardo del Corazón Grau-Ábalo,et al.  Detection of Coding Regions in Large DNA Sequences Using the Short Time Fourier Transform with Reduced Computational Load , 2006, CIARP.

[19]  Daniel Massicotte,et al.  Fast method to detect specific frequencies in monitored signal , 2010, 2010 4th International Symposium on Communications, Control and Signal Processing (ISCCSP).

[20]  Chun-Su Park,et al.  Fast, Accurate, and Guaranteed Stable Sliding Discrete Fourier Transform [sp Tips&Tricks] , 2015, IEEE Signal Processing Magazine.

[21]  Daniel Massicotte,et al.  The radix-r one stage FFT kernel computation , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[22]  Olivier Romain,et al.  Sparse channelizer for FPGA-based simultaneous multichannel DRM30 receiver , 2015, IEEE Transactions on Consumer Electronics.

[23]  Ksh Milan Singh.  Simultaneous Estimation of Moving-Vibration Parameters by Sliding Goertzel Algorithm in PLL Technique , 2019, IEEE Transactions on Instrumentation and Measurement.

[24]  Miguel O. Arias-Estrada,et al.  Using a Scaling Factor in O(1/N) for the fixed-point implementation of the second-order goertzel filter , 2012, 2012 IEEE International Symposium on Circuits and Systems.

[25]  Frede Blaabjerg,et al.  Condition Monitoring of DC-Link Capacitors Using Goertzel Algorithm for Failure Precursor Parameter and Temperature Estimation , 2020, IEEE Transactions on Power Electronics.

[26]  Yi-Hu Xu,et al.  An Efficient Pruning Algorithm for IFFT/FFT Based on NC-OFDM in 5G , 2018, 2018 Second International Conference on Inventive Communication and Computational Technologies (ICICCT).

[27]  Daniel Massicotte,et al.  Low Complexity Frequency Monitoring Filter for Fast Exon Prediction Sequence Analysis , 2019, 2019 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[28]  Wen-Ho Juang,et al.  Low-Computation-Cycle, Power-Efficient, and Reconfigurable Design of Recursive DFT for Portable Digital Radio Mondiale Receiver , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Frede Blaabjerg,et al.  A Self-commissioning Notch Filter for Active Damping in a Three-Phase LCL -Filter-Based Grid-Tie Converter , 2014, IEEE Transactions on Power Electronics.

[30]  Marian Verhelst,et al.  A 128∶2048/1536 point FFT hardware implementation with output pruning , 2014, 2014 22nd European Signal Processing Conference (EUSIPCO).

[31]  Guangkai Sun,et al.  Application of laser ultrasonic technique for non-contact detection of structural surface-breaking cracks , 2015 .

[32]  M. Arkan,et al.  Induction motor fault detection by space vector angular fluctuation , 2000, Conference Record of the 2000 IEEE Industry Applications Conference. Thirty-Fifth IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy (Cat. No.00CH37129).

[33]  Albertina Castro,et al.  Overflow analysis in the fixed-point implementation of the first-order Goertzel algorithm for complex-valued input sequences , 2009, 2009 52nd IEEE International Midwest Symposium on Circuits and Systems.

[34]  Yu-Wei Lin,et al.  A dynamic scaling FFT processor for DVB-T applications , 2004, IEEE Journal of Solid-State Circuits.

[35]  Yue Wang,et al.  Sparse Discrete Fractional Fourier Transform and Its Applications , 2014, IEEE Transactions on Signal Processing.

[36]  Truong Q. Nguyen,et al.  On the Fixed-Point Accuracy Analysis of FFT Algorithms , 2008, IEEE Transactions on Signal Processing.

[37]  Deni Torres Román,et al.  Unified commutation-pruning technique for efficient computation of composite DFTs , 2015, EURASIP J. Adv. Signal Process..

[38]  Don Ferguson,et al.  Radio frequency identification tags , 1996 .

[39]  Jingtao Hu,et al.  Sensorless Speed Estimation of an Inverter-Fed Induction Motor Using the Supply-Side Current , 2019, IEEE Transactions on Energy Conversion.