Goertzel Algorithm Research Articles

Accurate and Efficient Path Delay Estimation in OMP Based Sparse Channel Estimation for OFDM With Equispaced Pilots

The orthogonal matching pursuit (OMP) algorithm has been widely adopted in sparse channel estimation, both in radio and underwater acoustic communications. Traditionally, the accuracy of path delay estimation in an OMP based channel estimator depends on the adopted delay grid. The finer the delay grid, the higher the estimation accuracy, but meanwhile the higher the computational complexity. In this letter, we propose a modified OMP based channel estimation scheme for orthogonal frequency division multiplexing with equispaced pilots, which utilizes the characteristic of the Hermitian inner product between the pilot-compensated frequency observation vector and the columns of the dictionary matrix to provide a closed-form estimate for the path delays. In addition, a two-step scheme facilitated by Goertzel's algorithm is proposed to search the samples in the closed-form estimation to further reduce the computational complexity. Simulation results and complexity analysis demonstrate the advantages of the proposed scheme in both estimation accuracy and computational complexity.

Efficient Detection Approach for DTMF Signal Detection

A novel tone detection approach, designated as the multi-frequency detecting (MFD) algorithm, is presented in this work as an alternative to conventional single point detection approaches but it is an efficient way to achieve the aim of further computational load reduction for a dual-tone multi-frequency (DTMF) signal detection. The idea is that an optimal phase search is performed over the frequency band of interest in each tone detection, and then the optimal frequency response of a detector is built accordingly. In this manner, a DTMF detection task is done following one-time detection computation. This proposal demonstrates an overall computational load reduction of 80.49% and 74.06% in comparison with a discrete Fourier transform (DFT) approach and the Goertzel algorithm, respectively. This detection complexity reduction is an advantage and an important issue for applying DTMF detection technique to embedded devices.

基于Goertzel算法的红外气体检测方法

基于Goertzel算法的红外气体检测方法

Применение дискриминаторных методов для оценки параметров режима энергорайонов с объектами распределенной генерации

The specific features of electrical operation modes in power districts containing distributed generating facilities under different conditions in terms of their circuit configurations and operation are analyzed. The analysis has revealed significant deviations of electric power quality indicators and occurrence of short-term fluctuations of operating parameters in a wide dynamic range under the conditions of fast electromechanical transients. The basic principles used to set up discriminator methods are outlined, and the possibility of using them in estimating the operating parameters under the conditions of deviations from normal electric power quality indicators and influence of various distorting factors is shown. Simplified and complete structural diagrams of the discriminator frequency and voltage measuring device are presented, and their advantages are shown. Application of the Goertzel algorithm for minimizing the computation effort in implementing the discrete Fourier transform is substantiated. The results from investigations into the dynamic characteristics of the discriminator measuring device for estimating the operating parameters as applied to emergency control are presented. It is shown that under harsh conditions for digital processing of signals with the level of interference components up to 15% of the voltage amplitude, the errors of estimating the voltage signal frequency and amplitude do not exceed 2,5%. Based on the simulation results, the effectiveness of using discriminator methods in digital processing of signals has been proven.

Finite state machine control and power quality enhancement using Goertzel filter for multifunctional battery energy storage system

This study presents the design and control of a multifunctional battery energy storage system (BESS) to provide reactive power and harmonics compensation in grid-connected and uninterrupted supply modes to loads during grid non-availability. The BESS comprises of a bidirectional DC–DC converter and a grid-connected voltage source converter (VSC). The bidirectional converter is controlled to provide the battery charging and to maintain constant DC link voltage. The VSC uses a multimode controller and the finite state machine (FSM) based logic for mode transitions. The multimode controller uses a sliding Goertzel transform based filter for grid-connected mode and voltage controller for standalone mode of operation. The FSM logic monitors the system parameters using a voltage and the rate of change of frequency for deciding the mode of operation and for smooth transition between these modes. Simulated and test results validate the effectiveness of the proposed control in achieving the set objectives.

Enrichment of Poly Vinyl Chloride (PVC) Biological uses Through Sodium Chloride Filler, Density Functional Theory (DFT) Supported Experimental Study

Samples of pristine poly vinyl chloride (PVC) and other samples of the same matrix containing a variable amount of inorganic sodium salt (sodium chloride NaCl) were prepared via simple casting route in a dimethyl sulfoxide (DMSO) solvent were prepared. Prepared samples were characterized via x-ray diffraction (XRD) measurements and Fourier transform infrared spectrophotometric measurements (FTIR) in combination with computational density functional theory approaches (DFT) into account for a detailed picture of the possible reaction mechanisms within the polymeric matrices. All measurements were performed on the possible basis set. Local density approximate (LDA) and generalized Goertzel algorithm (GGA) was also tested. A compatibility between computed and experimental results suggested that physical interaction was preferred in such matrix and nominate use of this new material to be used in the medical field as a result of dioxin illumination.

An improved sag detection approach based on modified Goertzel algorithm

ABSTRACTPower quality is one of the key features in developing electric networks. It has been noticed because of its impact on economy and reliability of electrical networks. There are several power quality phenomena which are categorised in recent standards and literatures. Among them, voltage sag is more common and destructive for electric networks and consumers. This article presents a new detection method to monitor voltage sag in different electric network conditions. Goertzel algorithm is shown to be effective and simple for sag measurement compared to available sag detection methods.In order to increase the detection speed and response time, the Goertzel algorithm is modified. This modification will add to the speed of sag detection. The feasibility of the proposed method is justified through a measurement set-up developed using the dSPACE R1104 Digital Signal Processor Platform. The experimental results prove that sag measurement speed is improved by twice using the proposed modified Goertzel algorithm in comparison with the original method and some established methods. The results also verify that the sag detection of the proposed method is not affected by harmonic distortion of the voltage waveform.

Using of Generalized Goertzel Algorithm for FDTD Calculation of the Transmission and Reflection Spectra of Periodic Structures

Finite-difference time-domain (FDTD) method is frequently used for calculation of transmission and reflection characteristics of periodic structures. We propose a hybrid FDTD technique for evaluation of the transmittance and reflectance spectra of periodic structures that significantly reduces the usage of computer memory and time of the calculation. In the considered case, calculation time and memory occupation were reduced up to 30% and 20%, respectively, compared to the standard FDTD procedure. Calculated results fit well in the experimentally measured data.

A synergistic method for vibration suppression of an elevator mechatronic system

Modern elevators are complex mechatronic systems which have to satisfy high performance in precision, safety and ride comfort. Each elevator mechatronic system (EMS) contains a mechanical subsystem which is characterized by its resonant frequency. In order to achieve high performance of the whole system, the control part of the EMS inevitably excites resonant circuits causing the occurrence of vibration. This paper proposes a synergistic solution based on the jerk control and the upgrade of the speed controller with a band-stop filter to restore lost ride comfort and speed control caused by vibration. The band-stop filter eliminates the resonant component from the speed controller spectra and jerk control provides operating of the speed controller in a linear mode as well as increased ride comfort. The original method for band-stop filter tuning based on Goertzel algorithm and Kiefer search algorithm is proposed in this paper. In order to generate the speed reference trajectory which can be defined by different shapes and amplitudes of jerk, a unique generalized model is proposed. The proposed algorithm is integrated in the power drive control algorithm and implemented on the digital signal processor. Through experimental verifications on a scale down prototype of the EMS it has been verified that only synergistic effect of controlling jerk and filtrating the reference torque can completely eliminate vibrations.

Amplitude Estimation Technique for Intermittent Contact Atomic Force Microscopy

This article describes how one of the biggest challenges in designing of high-speed intermittent contact atomic force microscope (AFM) is the construction of a fast amplitude detector. The measurement techniques commonly used in commercial microscopes, such as RMS to DC converters or lock-in amplifiers often do not provide sufficient bandwidth to perform high speed imaging. On the other hand, many techniques developed especially for high-speed AFM are characterized by poor signal-to-noise ratio. In this paper, a novel amplitude estimation method based on the generalized Goertzel algorithm is presented. The detection system, composed of 16-bit 100 mega-samples per second analog-to-digital converter and field-programmable gate array device, allows to measure the signal amplitude within the time comparable to one oscillation cycle of the AFM cantilever. The effectiveness and validity of the designed detector were investigated by computer simulation. High spatial resolution of the presented method implemented in the actual atomic force microscopy system is also demonstrated.

Design of a recursive single-bin DFT algorithm for sparse spectrum analysis

Discrete Fourier transform (DFT) is the basic means of spectrum analysis in the field of digital signal processing, and the fast Fourier transform (FFT) has become the most popular algorithm which decreases the computational complexity from quadratical to linearithmic. However, engineers are often challenged to detect a single or just a few of the frequency components. For this kind of sparse spectrum analysis, the FFT no longer has advantage because it always computes all the frequency components. This paper proposes a recursive single-bin DFT (RSB-DFT) algorithm to compute one specific frequency spectrum, whose theoretical derivation is elaborated and implementation steps are given as a flow diagram. A 16-point RSB-DFT calculation example is also given to exhibit computation process of the algorithm. An application example for bioimpedance spectroscopy (BIS) measurement demonstrates that the proposed RSB-DFT algorithm can compute specific single spectral lines accurately. The computation efficiency of the proposed RSB-DFT algorithm is demonstrated as the highest compared with the DFT, FFT, Goertzel algorithm, which means that the RSB-DFT algorithm has the potential to become an alternative and efficient tool for sparse spectrum analysis.

Quality-Guaranteed Event-Sensitive Data Collection and Monitoring in Vibration Sensor Networks

High-resolution vibration data collection with data quality guaranteeing is important in a class of applications like industrial machine and structural health monitoring. Applying wireless vibration sensor networks (WVSNs) to this class is challenging due to severe resource constraints (e.g., bandwidth and energy). State-of-the-art data reduction approaches (e.g., signal processing, in-network aggregation) suggested to improve these constraints do not satisfy application-specific requirements, e.g., high quality of data (QoD) collection or quality of monitoring (QoM). In this paper, we propose $v\text{Collector}$ , a general approach to vibration data collection and monitoring in a resource-constrained WVSN. We enable each sensor to reduce the amount of data (before transmission) in a decentralized manner in two stages: the data acquisition stage and data transmission stage. In the first, we propose a solution to low-complexity signal processing; each sensor analyzes signals using the fast Fourier transform (FFT) under the quadrature amplitude modulation (QAM) and then applies an idea from the Goertzel algorithm (first proposed by Goertzel in 1958) so that the sensor can reduce a significant amount of data without sacrificing the QoD. In the second stage, we propose a decision-making algorithm by which each sensor can make a decision on its acquired data (considered event-sensitive data if it has information about harmful vibrations ) so that event-insensitive data communication is reduced. Evaluation results (obtained by simulations using our empirical data traces and by a real system deployment) demonstrate that $v\text{Collector}$ significantly reduces energy consumption and guarantees QoM in a WVSN.

Online frequency estimation with applications to engine and generator sets

Frequency and spectral analysis based on the discrete Fourier transform is a fundamental task in signal processing and machine diagnostics. This paper aims at presenting computationally efficient methods for real-time estimation of stationary and time-varying frequency components in signals. A brief survey of the sliding time window discrete Fourier transform and Goertzel filter is presented, and two filter banks consisting of: (i) sliding time window Goertzel filters (ii) infinite impulse response narrow bandpass filters are proposed for estimating instantaneous frequencies. The proposed methods show excellent results on both simulation studies and on a case study using angular speed data measurements of the crankshaft of a marine diesel engine-generator set.

A performance comparison of static VAr compensator based on Goertzel and FFT algorithm and experimental validation.

The main objective of the present paper is to introduce a new approach for measuring and calculation of fundamental power components in the case of various distorted waveforms including those containing harmonics. The parameters of active, reactive, apparent power and power factor, are measured and calculated by using Goertzel algorithm instead of fast Fourier transformation which is commonly used. The main advantage of utilizing Goertzel algorithm is to minimize computational load and trigonometric equations. The parameters measured in the new technique are applied to a fixed capacitor–thyristor controlled reactor based static VAr compensation system to achieve accurate power factor correction for the first time. This study is implemented both simulation and experimentally.

PPG 신호의 동잡음 구간 검출에 관한 연구

Abstract: The biomedical information (heart rate, HRV, SpO 2 etc) from the Photoplethysmography (PPG) signal sec-tion can be estimated without the motion artifacts if the PPG signal section in the motion artifacts is detected accu-rately. But the PPG signal is easily exposed to the motion artifacts by the decrease of the medical instrument sizeand applying as portable or wearable. Besides, it is difficult to completely eliminate the motion artifacts from the PPGsignal without distortion and ensure reliability as well. In this paper, the method was suggested to determine themotion artifacts or not on the PPG signal of the section divided into intervals of constant length. By comparing thespectrum of each section, it can be determined whether the motion artifacts are or not after obtaining the spectrumof each section by the Goertzel algorithm. Moreover, an amount of computation while maintaining a high detectionrate can be reduced by using the Goertzel algorithm.Key words: Photoplethysmography (PPG), Goertzel algorithm, Motion artifacts

Performance improvement of the Goertzel algorithm in estimating of protein coding regions using modified anti-notch filter and linear predictive coding model

The aim of this paper is to improve the performance of the conventional Goertzel algorithm in determining the protein coding regions in deoxyribonucleic acid (DNA) sequences. First, the symbolic DNA sequences are converted into numerical signals using electron ion interaction potential method. Then by combining the modified anti-notch filter and linear predictive coding model, we proposed an efficient algorithm to achieve the performance improvement in the Goertzel algorithm for estimating genetic regions. Finally, a thresholding method is applied to precisely identify the exon and intron regions. The proposed algorithm is applied to several genes, including genes available in databases BG570 and HMR195 and the results are compared to other methods based on the nucleotide level evaluation criteria. Results demonstrate that our proposed method reduces the number of incorrect nucleotides which are estimated to be in the noncoding region. In addition, the area under the receiver operating characteristic curve has improved by the factor of 1.35 and 1.12 in HMR195 and BG570 datasets respectively, in comparison with the conventional Goertzel algorithm.

Area and Power Optimized DTMF Detection by Using Different FPGA's

Rapid improvements in communication technologies, different applications in communications by FPGA technology. This paper explains about the Dual tone multi frequency detection (DTMF) by using different FPGA's. Fast Fourier Transform (FFT) is one of the approach to detect the DTMF tones. But it requires more hardware and also power consuming. So this paper proposes Split Goertzel Algorithm is optimized solution compared to Fast Fourier Transform. By using resource sharing approach (RSA) better optimized solution is achieved compared to Split Goertzel Algorithm. For functional verification Mentor graphics Modelsim software is used. Xilinx ISE 14.7 is used for Simulation & Synthesis respectively. To test the FPGA inside results the Xilinx Chopscope is used. The Spartan 3e, Spartan 6 & Zybo zynq 7000 series family FPGA boards are used in this paper and the corresponding results are showed as a table.

Phase Difference Measurement Based on Recursive DFT with Spectrum Leakage Considered

This paper investigates spectrum leakage influence on the performance of discrete Fourier transform (DFT) based phase difference measurement and proposes a novel method with spectrum leakage considered. In the proposed method, spectrum is firstly corrected by interpolation algorithm to remove the influence of short range leakage. To avoid negative frequency interference caused by the long range leakage, real-time phase difference is calculated in succession by a recursive DFT based algorithm with negative frequency contribution. And then, precision of the proposed method is theoretically demonstrated in detail. Furthermore, the method is applied to Coriolis mass flowmeter (CMF). Simulation and experimental results show that the accuracy of phase difference measurement has largely improved, as compared with the existing method based on the sliding Goertzel algorithm.

Off-Line Parameter Identification of Permanent Magnet Synchronous Motor Using a Goertzel Algorithm

Generally, internal parameters of the motors and generators can be divided to the resistance and inductance components. They can become a cause of the changing internal parameters because they have sensitive characteristics due to external conditions. The changed parameters can generate the outputs which include error values from the speed and current controllers. Also, it can bring the temperature increase and mechanical damage to the system. Therefore, internal parameters of the motors and generators need to obtain their values according to the external conditions because it can prevent the mechanical damage caused by the changed parameters. In this paper, the off-line parameter identification method is verified using the Goertzel algorithm. The motor used in the simulation and experiments is an interior permanent magnet synchronous motor (IPMSM), and the proposed algorithm is verified by the simulation and experimental results.

Detection of Protein Coding Regions using Goertzel Algorithm

Processing and interpretation of genomic sequence by DSP (digital signal processing) tools has attracted many researchers in last two decades particularly, the protein coding regions (exons) detection have been a challenging task in bioinformatics. The three base periodicity (TBP) or period-3 property of exonic regions form basis for most researchers for identification purpose. Many DSP based model dependent and model independent techniques have been applied for identification but still improvement is needed. In this article, a simple model independent technique using Goertzel algorithms proposed for exonic regions detection. The potential of the proposed method have been evaluated on the basis of performance parameters like sensitivity, specificity and correlation coefficient and found that the proposed method provides better performance than conventional DFT methods.