Fourier Transform Algorithm Research Articles

Advanced Frequency Analysis of Signals with High-Frequency Resolution

In today’s era, it is important to analyze and utilize various signals in industrial or laboratory applications. Measured signals provide critical information about the controlled system, which can be contained precisely within a narrow frequency range. Many methods and algorithms exist to process such signals in both the time and frequency domains. In particular, signal processing in the frequency domain is primary in industrial practice because dominant components within a specific narrow frequency band are sought. The discrete Fourier transformation (DFT) algorithm is the tool used in practice to find these frequency components. The DFT algorithm provides the full frequency spectrum with a higher number of calculation steps, and its spectrum frequency resolution is low. Therefore, research has focused on finding a method to achieve high-frequency spectrum resolution. An important factor in selecting the technique was that such an algorithm should be implementable on a microprocessor-based system under harsh industrial conditions. Research results showed that the DFT ZOOM method meets these requirements. The frequency zoom has many advantages but requires some modification. It is implemented in high-performance analyzers, but a thorough and detailed description of the respective algorithm is lacking in technical articles and literature. This article mathematically and theoretically describes the modified frequency zoom algorithm in detail. The steps of the frequency zoom, from creating an analytical signal through frequency shifting and decimation to the frequency analysis of the signal, are realized. The algorithm allows for the analysis of a signal with high-frequency resolution in a limited frequency band. A significant modification of DFT ZOOM is that of using the Hilbert transform to create an analytic signal. This resolves the aliasing issue caused by the overlap between fundamental and sideband spectra. Results from processing deterministic and stochastic signals using the modified DFT ZOOM are presented. The presented experimental results contribute to a more detailed frequency analysis of the signal. As part of this scientific research, the issues of frequency zoom were thoroughly addressed, solving the partial problems of this algorithm, both in theory and in the context of signal theory.

Uncertainty of the initial phase estimation of a sinewave in the presence of phase noise, additive noise or jitter

This paper presents the derivation of a simple analytical expression for the precision of the initial phase estimates obtained through a least-squares procedure. That expression depends on number of samples, phase noise standard deviation and additive noise standard deviation. This study is applicable to the estimates obtained through the sine fitting algorithm with known frequency and to the Discrete Fourier Transform algorithm. The analytical expression supplied was verified using a Monte Carlo simulation with numerically created data. The non-ideal phenomena treated in this work is the presence of jitter in the sampling instant, phase noise in the oscillator and additive noise in the system both of which must be normally distributed with a known value of standard deviation. It is useful information for an engineer in order to choose the proper number of samples to acquire to achieve a desired level of precision on the estimates made and thus carry out an efficient data acquisition with no unnecessary samples thus optimizing the test duration.

Numerical and Experiment Analysis of Sapphire Sandwich-Structure Fabry-Perot Pressure Sensor through Fast Fourier Transform and Mean Square Error Demodulation Algorithm.

Pressure sensors prepared from sapphire exhibit excellent characteristics, including high-temperature resistance, high hardness, and resistance to electromagnetic interference. A Fast Fourier Transform and Mean Square Error (FFT-MSE) demodulation algorithm was employed to demodulate a sapphire sandwich-structure Fabry-Perot (F-P) pressure sensor. Through simulation analysis, the experimental results indicated that the demodulation error of the air cavity length in the range of 206 μm to 216 μm was less than 0.0008%. Compared to single demodulation methods and combined demodulation methods based on FFT or Minimum Mean Square Error (MMSE), the method proposed in this work reduced the demodulation error by more than three times and increased accuracy by more than six times. The algorithm was utilized to demodulate the sapphire sandwich-structure F-P pressure sensor, and the test results indicated that the fitting error of the sensor was less than 0.025% within the pressure range of 0 MPa to 10 MPa. The repeatability error was less than 0.066%, the zero-point deviation was 1.26%, and the maximum stability deviation was 0.0063% per 30 min. The algorithm effectively demodulated the actual cavity length variation in the sapphire sandwich-structure F-P pressure sensor, providing a solution for the performance evaluation of the sapphire sandwich-structure F-P pressure sensor.

High-Speed Schlieren Imaging And PIV Of Unsteady Free Jet Injection With Plume Formation

This work aims to investigate Schlieren image correlation velocimetry for flow field quantification of gaseous jet injection in non-manipulable apparatus like flow chambers. Such flow cases often struggle using tracer-based methods: Seeding particles may locally cause technical problems, or the plant design prevents the principal opportunity of tracer adding, both of which lead to a reduced method repertory. This is specifically the case under flow conditions, where contamination of apparatus internals by seeding particles should be avoided completely. Therefore, in this paper, we explore a seedless, refraction-based method to quantify the velocity field of a jet plume. As an experimental flow case, we examine a transient jet release into a closed compartment under nearly atmospheric conditions. For simplification and greater clarity, the laboratory model geometry is kept essentially two-dimensional, thus we chose a flat-jet nozzle as injection device. The experimental investigations cover high-speed Schlieren imaging and laser sheet visualization, followed by digital image correlation. Combining the traditionally qualitative Schlieren approach for flow visualization with Fast Fourier Transform and cross-correlation algorithms, we calculated the velocity vector field of an unsteady jet plume formation. Furthermore, we determined the axial jet velocity profile at steady-state conditions. Our research findings highlight the applicability of Schlieren image correlation velocimetry to quantify gaseous jet formation at encased flow sections spatially. Concluding, the results coincide with data from particle image velocimetry measurements and point out the potential of expanding flow diagnostics to hitherto hardly explored (industrial) flow cases.

Frequency and damping factor estimation of real-valued damped sinusoids by means of an improved two-point Interpolated DFT algorithm

The contribution of this paper is two-fold. Firstly, the well-known two-point Interpolated Discrete Fourier Transform (IpDFT) algorithm based on a Maximum Sidelobe Decay (MSD) window is generalized to the estimation of the frequency and the damping factor of a real-valued damped sinusoids. Analytical expressions for the detrimental contributions on the obtained estimators due to the image frequency component and wideband noise are then derived and their accuracies are verified through computer simulations. Secondly, leveraging on the derived expression, an improved version of the IpDFT algorithm is proposed which ensure more accurate estimates by compensating the contribution of the image frequency component. The performance of the improved IpDFT algorithm is compared with those provided by various state-of-the-art algorithms through meaningful computer simulations.

Direct Position Determination of Non-Gaussian Sources for Multiple Nested Arrays: Discrete Fourier Transform and Taylor Compensation Algorithm.

This paper delves into the problem of direct position determination (DPD) for non-Gaussian sources. Existing DPD algorithms are hindered by their high computational complexity from exhaustive grid searches and a disregard for the received signal characteristics by multiple nested arrays (MNAs). To address these issues, the paper proposes a novel DPD algorithm for non-Gaussian sources with MNAs: the Discrete Fourier Transform (DFT) and Taylor compensation algorithm. Initially, the fourth-order cumulant matrix of the received signal is computed, and the vectorizing method is applied. Subsequently, a computationally efficient DPD cost function is proposed by leveraging a normalized DFT matrix to reduce complexity. Finally, first-order Taylor compensation is utilized to enhance the accuracy of the localization results. The superiority of the proposed algorithm is demonstrated through numerical simulation results.

A short time series rolling bearing fault diagnosis method based on FMTF-CNN

The signal characteristics are extracted directly from the convolutional level when the Convolutional Neural Network (CNN) is used as a fault diagnosis method in most instances. Some scholars have proposed to use the Markov Transition Field (MTF) to extract the signal characteristics before convolution. However, for time-domain signals, the fault characteristics extraction is difficult, and the training process of the neural network parameters is slow. Therefore, in this paper, based on Fast Fourier Transform (FFT) and MTF algorithm, the Fourier Markov Transition Field (FMTF) characteristics extraction method in frequency domain is proposed, and a large number of experiments are carried on the public bearing data set of Jiangnan University. The final verification shows that the FMTF-CNN method has higher accuracy, faster training process and more accurate characteristics extraction than the traditional MTF-CNN diagnosis method.

Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm.

Quasi-continuous-phase metasurfaces overcome the side effects imposed by high-order diffraction on imaging and can impart optical parameters such as amplitude, phase, polarization, and frequency to incident light at sub-wavelength scales with high efficiency. Structured-light three-dimensional (3D) imaging is a hot topic in the field of 3D imaging because of its advantages of low computation cost, high imaging accuracy, fast imaging speed, and cost-effectiveness. Structured-light 3D imaging requires uniform diffractive optical elements (DOEs), which could be realized by quasi-continuous-phase metasurfaces. In this paper, we design a quasi-continuous-phase metasurface beam splitter through a vector iterative Fourier transform algorithm and utilize this device to realize structured-light 3D imaging of a target object with subsequent target reconstruction. A structured-light 3D imaging system is then experimentally implemented by combining the fabricated quasi-continuous-phase metasurface illuminated by the vertical-cavity surface-emitting laser and a binocular recognition system, which eventually provides a new technological path for the 3D imaging field.

Wide-angle digital holography with aliasing-free recording

High-quality wide-angle holographic content is at the heart of the success of near-eye display technology. This work proposes the first digital holographic (DH) system enabling recording wide-angle scenes assembled from objects larger than the setup field of view (FOV), which can be directly replayed without 3D deformation in the near-eye display. The hologram formation in the DH system comprises free space propagation and Fourier transform (FT), which are connected by a rectangular aperture. First, the object wave propagates in free space to the rectangular aperture. Then, the band-limited wavefield is propagated through the single lens toward the camera plane. The rectangular aperture can take two sizes, depending on which DH operates in off-axis or phase-shifting recording mode. An integral part of the DH solution is a numerical reconstruction algorithm consisting of two elements: fringe processing for object wave recovery and wide-angle propagation to the object plane. The second element simulates propagation through both parts of the experimental system. The free space part is a space-limited angular spectrum compact space algorithm, while for propagation through the lens, the piecewise FT algorithm with Petzval curvature compensation is proposed. In the experimental part of the paper, we present the wide-angle DH system with FOV 25°×19°, which allows high-quality recording and reconstruction of large complex scenes.

Assembly accuracy analysis and phase optimization of aero-engine multistage rotors considering surface morphology and non-uniform contact deformation

The assembly accuracy of multistage rotors is crucial to guarantee the quality and performance of aero engines. However, traditional assembly accuracy analysis methods usually oversimplify geometric deviations as the degrees of freedom (DOF) variations relative to the ideal position, ignoring real surface morphology and the resulting non-uniform contact deformation. Therefore, this paper proposes an assembly accuracy analysis method that integrates the effects of surface morphology and non-uniform contact deformation on error propagation process, and further adopts a phase optimization method to improve the assembly accuracy of multistage rotors. Specifically, the surface morphology of rotor end faces is generated using the random midpoint displacement method. The Conjugate Gradient-Fast Fourier Transform (CG-FFT) algorithm is employed to calculate the non-uniform contact deformation. According to the simulation results, a fitting deformation surface (FDS) is constructed to determine the assembly position and orientation. On this basis, a novel error propagation model is established and the mounting phase of each stage rotor is optimized by a genetic algorithm (GA). A case study of a specific rotor system is carried out to verify the proposed error propagation model and give the optimized assembly combination with the objective of minimum coaxiality. This research effectively improves the prediction and actual assembly accuracy of aero-engine multistage rotors and provide a theoretical basis for the precision assembly of multistage rotors in aero-engine applications.

Numerical modeling of edge inhomogeneity in a macro cantilever beam

This study explores the inhomogeneity problem near the edge of a cantilever beam. Common in gears and turbine blades, inhomogeneities under local edge contact, coupled with macroscale bending effects, result in extreme and complex stress concentration. This model employs the Conjugate Gradient Method to combines the macroscopic beam theory and microscopic elasticity. The Eshelby inclusion method for simulating inhomogeneities. The Hetényi image method is used for address edge contacts in the beam. Enhanced by the Discrete Convolution fast Fourier Transform algorithm, the model’s accuracy and efficiency are validated with the Finite element method. Parametric analysis highlights the influence of distance between indenter and edge, stress components distribution and potential failure in cross-scale challenges.

Numerical Simulation of Flows Using the Fourier Pseudospectral Method and the Immersed Boundary Method

The present work proposes the application of a computational methodology based on the coupling of the Fourier Pseudospectral Method (FPSM) and the Immersed Boundary Method (IBM) for conducting flow simulations over slender airfoils. This methodology, termed IMERSPEC, leverages the benefits of both high accuracy and low computational cost inherent in pseudospectral methods, thanks to the utilization of the Fast Fourier Transform algorithm. IBM is employed to impose non-periodic boundary conditions in the Navier–Stokes equations, addressing the requirement of periodicity at boundaries for FPSM convergence and to accurately represent the immersed slender airfoil in the flow. The aerodynamic behavior of the analyzed profiles was assessed by calculating lift and drag coefficients, which were then compared with existing literature results. Consistently favorable outcomes were observed, particularly in flows at lower Reynolds numbers, demonstrating the effectiveness of the IMERSPEC methodology for simulating complex flows computationally. Additionally, weight functions, fundamental to IBM, are employed flexibly for aerodynamic force calculations. Specifically, within the same simulation, a Cubic function is utilized for drag calculation while a Hat function is employed for lift calculation, yielding results more closely aligned with the literature’s findings. This approach offers an alternative to previously proposed methods for IBM implementation.

Higher-order spectral representation method: New algorithmic framework for simulating multi-dimensional non-Gaussian random physical fields

This study derives a novel higher-order spectral representation method (HOSRM) to represent and simulate multi-dimensional fourth-order non-Gaussian random physical fields. The method primarily extends the traditional second-order spectral representation method (SRM) for simulating non-Gaussian random physical fields by introducing higher-order cumulant function tensors and trispectrum tensors, thereby accomplishing the modeling of fourth-order non-Gaussian random physical fields (symmetric nonlinear physical fields) from a frequency domain perspective. In an endeavor to enhance the simulation efficiency of this theoretical framework, the Fast Fourier Transform (FFT) algorithm is astutely amalgamated into the simulation. This integration contributes significantly to the augmentation of computational efficiency. Furthermore, exhaustive derivations and proofs are presented for the first-order, second-order, and fourth-order ensemble properties of simulated fourth-order non-Gaussian random physical fields. Subsequently, the reliability and accuracy of the proposed algorithm framework are validated through numerical simulations of two two-dimensional and two three-dimensional non-Gaussian random physical fields. The findings demonstrate that the simulated sample function effectively captures the probability characteristics of the random field, including mean, variance, and kurtosis. Finally, an in-depth analysis of numerical simulation results highlights the difference between the proposed method and the traditional second-order spectral representation method, which further underscores the distinctive attributes and potential superiority of the proposed method.

Millimeter wave-based patient setup verification and motion tracking during radiotherapy.

Position verification and motion monitoring are critical for safe and precise radiotherapy (RT). Existing approaches to these tasks based on visible light or x-ray are suboptimal either because they cannot penetrate obstructions to the patient's skin or introduce additional radiation exposure. The low-cost mmWave radar is an ideal solution for these tasks as it can monitor patient position and motion continuously throughout the treatment delivery. To develop and validate frequency-modulated continuous wave (FMCW) mmWave radars for position verification and motion tracking during RT delivery. A 77GHz FMCW mmWave module was used in this study. Chirp Z Transform-based (CZT) algorithm was developed to process the intermediate frequency (IF) signals. Absolute distances to flat Solid Water slabs and human shape phantoms were measured. The accuracy of absolute distance and relative displacement were evaluated. Without obstruction, mmWave based on the CZT algorithm was able to detect absolute distance within 1mm for a Solid Water slab that simulated the reflectivity of the human body. Through obstructive materials, the mmWave device was able to detect absolute distance within 5mm in the worst case and within 3.5mm in most cases. The CZT algorithm significantly improved the accuracy of absolute distance measurement compared with Fast Fourier Transform (FFT) algorithm and was able to achieve submillimeter displacement accuracy with and without obstructions. The surface-to-skin distance (SSD) measurement accuracy was within 8mm in the anterior of the phantom. With the CZT signal processing algorithm, the mmWave radar is able to measure the absolute distance to a flat surface within 1mm. But the absolute distance measurement to a human shape phantom is as large as 8mm at some angles. Further improvement is necessary to improve the accuracy of SSD measurement to uneven surfaces by the mmWave radar.

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, in particular beam-coupling impedance, can significantly affect Schottky spectra when large bunch charges are involved. In such conditions, the available interpretation methods are difficult to apply directly to the measured spectra, thus preventing the extraction of beam and machine parameters, which is possible for lower bunch charges. To study the impact of impedance on such spectra, we introduce a method for building Schottky spectra from macro-particle simulations performed with the PyHEADTAIL code, applied to LHC beam conditions. In this case, the use of a standard Fast Fourier Transform (FFT) algorithm to recover the spectral content of the beam becomes computationally intractable memory-wise, because of the relatively short bunch length compared to the large revolution period. To circumvent this difficulty, a semi-analytical method was developed to efficiently compute the Fourier transform. The simulated Schottky spectrum is then compared against theoretical formulas and measurements of Schottky signals previously obtained with lead ion beams in the LHC where impedance effects are expected to be limited. Furthermore, this study provides preliminary interpretations of the impact of beam-coupling impedance on proton Schottky spectra by incorporating longitudinal and transverse resonator-like impedance models into the simulations. A theoretical framework is also introduced for the case of the longitudinal impedance, allowing the extension of the existing theoretical formalism.

Research on High-Performance Fourier Transform Algorithms Based on the NPU

Backpack computers require powerful, intelligent computing capabilities for field wearables while taking energy consumption into careful consideration. A recommended solution for this demand is the CPU + NPU-based SoC. In many wearable intelligence applications, the Fourier Transform is an essential, computationally intensive preprocessing task. However, due to the unique structure of the NPU, the conventional Fourier Transform algorithms cannot be applied directly to it. This paper proposes two NPU-accelerated Fourier Transform algorithms that leverage the unique hardware structure of the NPU and provides three implementations of those algorithms, namely MM-2DFT, MV-2FFTm, and MV-2FFTv. Then, we benchmarked the speed and energy efficiency of our algorithms for the gray image edge filtering task on the Huawei Atlas200I-DK-A2 development kits against the Cooley-Tukey algorithm running on CPU and GPU platforms. The experiment results reveal MM-2DFT outperforms OpenCL-based FFT on NVIDIA Tegra X2 GPU for small input sizes, with a 4- to 8-time speedup. As the input image resolution exceeds 2048, MV-2FFTv approaches GPU computation speed. Additionally, two scenarios were tested and analyzed for energy efficiency, revealing that cube units of the NPU are more energy efficient. The vector and CPU units are better suited for sparse matrix multiplication and small-scale inputs, respectively.

Is Acoustic modal analysis a reliable substitution for Osstell® device in dental implant stability assessment? An experimental and finite element analysis study.

Different methods have been proposed to investigate the fixation stability of dental implants, each of which has its limitations. Among these methods, resonance frequency analysis (RFA) has been widely utilized to measure dental implant stability. This study aimed to assess dental implants with two non-destructive RFA and acoustic modal analysis (AMA) validated with a finite element simulation of the fundamental natural frequency (NF) of the bone analog-implant structure. A total number of 18 implants were inserted into two Polyurethane (PU) bone blocks with different densities (0.16 g/cc and 0.32 g/cc). AMA was used to measure NF; First, the sound originating from the axial tapping of the implant was recorded with a simple microphone. Secondly, a fast Fourier transformation algorithm was conducted to determine the NF of the implant-bone analog structure. In parallel, the ISQ (Implant Stability Quotient) value was measured using the Osstell® device. Finally, using finite element analysis (FEA), the implant-bone analog structure was modeled for validation. Doubling the bone analog density resulted in an average increase of 82% and 47% in the NF and ISQ using AMA and Osstell®, respectively (P-value<0.05). Furthermore, a strong linear relationship (R2= 0.93) was observed between the measured NF and ISQ values in the linear regression analysis. The NF of the dental implant predicted by FEA was overestimated by about 15.2% and 15.0% than those in the low- and high-density PUs, respectively. Moreover, the FEA predicted an increase of 83% in NF by increasing the bone analog density from 0.16 to 0.32 g/cc. Having required the minimum process combined with easily available equipment makes it an ideal method for fixation strength studies. The good correspondence between the ISQ values and NFs, in addition to the good accuracy and reliability of the later method, confirms its application for fixation stability assessment.

Reliability of a semi-tethered front crawl sprint performance test in adolescent swimmers.

This study aimed to evaluate the test-retest reliability of a sprint performance test with semi-tethered front crawl swimming to indirectly assess the current potential to perform at maximal anaerobic effort in adolescent swimmers. Eight adolescent swimmers participated in this study (gender: females (n = 4) aged 13.0 ± 0.8 years, body height 1.6 ± 0.0m, body mass 50.1 ± 4.5kg; and males (n = 4) aged 13.3 ± 1.3 years, body height 1.7 ± 0.1m, body mass 59.0 ± 8.2kg. The testing protocol consisted of two trials of 25m semi-tethered front crawl swimming with maximal effort and with 1kg resisted isotonic load. Velocity data were recorded automatically by the 1080 Sprint device for 15m (between 3m and 18m). The Fast Fourier Transform algorithm filtered raw instantaneous swimming velocity data in distance (time) function. A third-degree polynomial was used to extract the individual velocity profile, from which the following variables were chosen for test-retest reliability and the assessment of sprint performance: ttrial15, vmax, vmin, tvto max, tvat max, Dto vmax, Dat vmax, fatigue index. Parameters such as vmax, vmin, and ttrial15 were estimated from swimming velocity profiles and considered as reliable. The CV showed low variance <5%; while ICC2,1 demonstrated respectively good (ICC2,1: 0.88), very good (ICC2,1: 0.95), and excellent (ICC2,1: 0.98) rate of relative reliability; and the Bland-Altman index revealed an acceptable agreement (LoA ≤5%) between two measurements. The sprint performance test based on semi-tethered front crawl swimming confirmed that ttrial15, vmax, and vmin were reliable variables to indirectly indicate a potential to perform the maximal anaerobic effort among adolescent swimmers. The evaluation of the swimming velocity profiles allows coaches to monitor the adaptive changes of performance during the training process.

Seasonality of COVID-19 incidence in the United States.

The surges of Coronavirus Disease 2019 (COVID-19) appeared to follow a repeating pattern of COVID-19 outbreaks regardless of social distancing, mask mandates, and vaccination campaigns. This study aimed to investigate the seasonality of COVID-19 incidence in the United States of America (USA), and to delineate the dominant frequencies of the periodic patterns of the disease. We characterized periodicity in COVID-19 incidences over the first three full seasonal years (March 2020 to March 2023) of the COVID-19 pandemic in the USA. We utilized a spectral analysis approach to find the naturally occurring dominant frequencies of oscillation in the incidence data using a Fast Fourier Transform (FFT) algorithm. Our study revealed four dominant peaks in the periodogram: the two most dominant peaks show a period of oscillation of 366 days and 146.4 days, while two smaller peaks indicate periods of 183 days and 122 days. The period of 366 days indicates that there is a single COVID-19 outbreak that occurs approximately once every year, which correlates with the dominant outbreak in the early/mid-winter months. The period of 146.4 days indicates approximately 3 peaks per year and matches well with each of the 3 annual outbreaks per year. Our study revealed the predictable seasonality of COVID-19 outbreaks, which will guide public health preventative efforts to control future outbreaks. However, the methods used in this study cannot predict the amplitudes of the incidences in each outbreak: a multifactorial problem that involves complex environmental, social, and viral strain variables.

Moving Target Detection Algorithm for Millimeter Wave Radar Based on Keystone-2DFFT

Millimeter wave radar has the advantage of all-day and all-weather capability for detection, speed measurement. It plays an important role in urban traffic flow monitoring and traffic safety monitoring. The conventional 2-dimensional Fast Fourier Transform (2DFFT) algorithm is performed target detection in the range-Doppler domain. However, the target motion will induce the range walk phenomenon, which leads to a decrease in the target energy and the performance of the target detection and speed measurement. To solve the above problems, this paper proposes a moving vehicle detection algorithm based on Keystone-2DFFT for a traffic scene. Firstly, this paper constructs and analyzes the Frequency Modulated ContinuousWave (FMCW) moving target signal model under traffic monitoring scenario’s radar observation geometry. The traditional 2DFFT moving target detection algorithm is briefly introduced. Then, based on mentioned signal model, an improved moving vehicle detection algorithm based on Keystone-2DFFT transform is proposed. The method first input the echo, then the range walk is removed by keystone transformation. the keystone transformation is achieved via Sinc interpolation. Next is transform data into range-Doppler domain to perform detection and speed estimation. The algorithm is verified by simulation data and real data.