Fast Fourier Transform Algorithm Research Articles

PyWolf: A PyOpenCL implementation for simulating the propagation of partially coherent light

We present PyWolf, an open-source software capable of performing numerical simulations of partially coherent light propagation from two-dimensional light sources. PyWolf computes the evolution of a user-defined cross-spectral density function in the Fresnel and far field approximations, which enables the retrieval of second-order optical quantities of interest such as the spectral degree of coherence and spectral density for a given frequency. The open-source tool kit PyOpenCL is used to increase the computation speed. We present examples of propagation of different source models and optical systems to validate our implementation. Performance results for the computation speed when using parallel computation through PyOpenCL is shown. Source models and propagation systems can be easily added to PyWolf, which has a graphical user interface built with PyQt5. This software can be of great utility for partially coherent light simulation problems that are difficult to treat analytically. Program summaryProgram Title: PyWolfCPC Library link to program files:https://doi.org/10.17632/frjscxypkd.1Developer's repository link:https://github.com/tiagoecmagalhaes/PyWolfLicensing provisions: GPLv3Programming language: PythonExternal routines: NumPy, SciPy, Matplotlib, PyOpenCL, PyQt5Nature of problem: Numerical simulations of the propagation of partially coherent light from planar sources in the Fresnel or far field approximations. Computation time can be improved by using optimized versions of the Fast Fourier Transform (FFT) algorithm, but other calculations can only be increased through parallel computation.Solution method: We use the open-source toolkit PyOpenCL to perform parallel computation on time-consuming calculations. The user can easily modify and add more features to the software, such as source models and propagation methods. A graphical user interface is also built using PyQt5 which enables the user to set input parameters, including the user's custom models, view the simulation results, export data, and save and load sessions.

Digital Implementation of Harmonic and Unbalanced Load Compensation for Voltage Source Inverter to Operate in Grid Forming Microgrid

Voltage source inverter (VSI) is a good candidate for grid forming microgrid because it provides constant amplitude, frequency, and sinusoidal shape voltage at point of common coupling (PCC). As the microgrid is separated from utility grid, voltage quality of the PCC is easily affected by the type of load. To ensure power quality in grid operation, a three-phase VSI providing automatic voltage compensation for unbalanced or nonlinear load is presented in this paper. To maintain voltage quality at a certain level, the Fast Fourier Transform (FFT) algorithm is embedded in a proportional-resonant (PR) controller to mitigate the total harmonic distortion (THD) at PCC. In the meantime, any change of voltage magnitude that is caused by the unbalanced load could be reduced as well. To further enhance the transient response with the change of load, a predictive current (PC) controller is integrated into the PR controller. All the control strategies are implemented by digital approach. The effectiveness of proposed controls is verified through experiments on a testbed of the three-phase stand-alone system.

A New Multichannel Parallel Real-time FFT Algorithm for a Solar Radio Observation System Based on FPGA

The real-time fast Fourier transform (FFT) is the essential algorithm for signal processing in a solar radio receiver. However, field-programmable gate array (FPGA) computation resources have become the limitation of real-time processing of signals with increasing time and spectral resolutions. It is necessary to design a real-time parallel FFT algorithm with reduced resource occupation in the development of future receiving systems. In this paper, we developed a multichannel parallel FFT algorithm named the multichannel parallel real-time fast Fourier transform (MPR-FFT), which can greatly reduce FPGA resource occupation while increasing the real-time processing speed. In this algorithm, the 4L simultaneous N-point FFTs are first converted into L simultaneous 4N-point FFTs. Fusion processing is then performed to obtain the 4 ∗ L ∗ N-point spectrum. This method has been used in developing a solar radio spectrometer, which works in the frequency range of 0.5–15 GHz in the Chashan Observatory. In this spectrometer, 16 channel MPR-FFT with 8k-point data is realized in a Xilinx UltraScale KU115 FPGA. The MPR-FFT algorithm reduced the computational resources to a large extent compared to the Cooley-Tukey-based parallel FFT method; for instance, the Look-Up-Table, Look-Up-Table RAM, Flip-Flop, and Digital Signal Process slices were reduced by 37%, 50%, 17%, and 2.48%, respectively. Although the MPR-FFT consumes 14 block RAM resources more than the Cooley-Tukey-based parallel FFT, the MPR-FFT algorithm presents an overall reduction in resource usage.

A fast frequency estimation algorithm and its application in transformer terminal unit

To accurately obtain the frequency of voltage and current signals and form the basis for the analysis of power quality in the Transformer Terminal Unit (TTU), a Hanning window and interpolation algorithm is proposed to estimate the signal frequency. The principle of the algorithm is introduced, and the computer program is written. At the same time, the voltage signals with different frequencies are numerically generated and the real voltage is measured, and the signal frequency is estimated by using the algorithm. The results reveal that the proposed method can accurately estimate the signal frequency for TTU, and the maximum error of frequency estimation is only 2 mHz when the signal frequency varies in the range of 49.8-50.2 Hz. However, the maximum error estimated by the FFT algorithm is up to 0.2 Hz. The computation time of the Hanning window and interpolation algorithm is only 1.29 times that of the Fast Fourier Transform algorithm. The work lays the foundation for accurate and rapid estimation of voltage and current signal frequency in TTU.

A Deep Learning Approach to Design and Discover Sustainable Cementitious Binders: Strategies to Learn From Small Databases and Develop Closed-form Analytical Models

To reduce the energy-intensity and carbon footprint of Portland cement (PC), the prevailing practice embraced by concrete technologists is to partially replace the PC in concrete with supplementary cementitious materials [SCMs: geological materials (e.g., limestone); industrial by-products (e.g., fly ash); and processed materials (e.g., calcined clay)]. Chemistry and content of the SCM profoundly affect PC hydration kinetics; which, in turn, dictates the evolutions of microstructure and properties of the [PC + SCM] binder. Owing to the substantial diversity in SCMs’ compositions–plus the massive combinatorial spaces, and the highly nonlinear and mutually-interacting processes that arise from SCM-PC interactions–state-of-the-art computational models are unable to produce a priori predictions of hydration kinetics or properties of [PC + SCM] binders. In the past 2 decades, the combination of Big data and machine learning (ML)—commonly referred to as the fourth paradigm of science–has emerged as a promising approach to learn composition-property correlations in materials (e.g., concrete), and capitalize on such learnings to produce a priori predictions of properties of materials with new compositions. Notwithstanding these merits, widespread use of ML models is hindered because they: 1) Require Big data to learn composition-property correlations, and, in general, large databases for concrete are not publicly available; and 2) Function as black-boxes, thus providing little-to-no insights into the materials laws like theory-based analytical models do. This study presents a deep learning (DL) model capable of producing a priori, high-fidelity predictions of composition- and time-dependent hydration kinetics and phase assemblage development in [PC + SCM] pastes. The DL is coupled with: 1) A fast Fourier transformation algorithm that reduces the dimensionality of training datasets (e.g., kinetic datasets), thus allowing the model to learn intrinsic composition-property correlations from a small database; and 2) A thermodynamic model that constrains the model, thus ensuring that predictions do not violate fundamental materials laws. The training and outcomes of the DL are ultimately leveraged to develop a simple, easy-to-use, closed-form analytical model capable of predicting hydration kinetics and phase assemblage development in [PC + SCM] pastes, using their initial composition and mixture design as inputs.

Rolling contact on a viscoelastic multi-layered half-space

This paper’s purpose is the contact of a rolling body on a viscoelastic multi-layered half-space. Firstly, the contact is formulated with the classical definition of the gap and the pressure states in the contact zone and outside. L layers are considered on a substrate, L being any positive integer. Secondly, the influence coefficients related to an elastic multi-layered half-space are found, using the Papkovich–Neuber potentials. Tractions and displacements continuity is assumed at the interfaces, and then a construction of matrix systems corresponding to a unit pressure and a unit shear imposed at the top surface, leads to the general problem to solve. Further, the solution for any kind of pressure and/or shear distributions at the contact surface is inferred by convolution with the influence coefficients found earlier, using the Fast Fourier Transform (FFT) algorithms. Throughout the steps, an Elastic/Viscoelastic correspondence is used in order to take into account not only the change of behaviour of the half-space during time, but also to superpose the load history. Conjugate Gradient Method (CGM) algorithms are used to solve the variational problem that yields from the contact problem definition. In the present paper, a parametric study is performed to highlight the effects of the elastic modulus and the relaxation time on some relatively simple cases of rolling contact.

Computation of range velocity and direction of arrival in FMCW radar

Frequency Modulated Continuous Wave (FMCW) radar is widely used in applications to find the range, velocity and angle of the target objects from the radar. The transmitted signal is in the form of chirp where the frequency increases linearly with time. After hitting the target object, the signal is received by the receiver antenna which contains the information about the range, velocity and angle of target object. The information is extracted using different signal processing algorithms like Fast Fourier Transform algorithm (FFT) and Multiple Signal Classification (MUSIC) algorithm. When Fast Fourier Transform (FFT) algorithm is used to estimate the Direction of Arrival (DOA), the angular resolution is less, as it is dependent on the number of points in FFT and number of receivers used. As Additive White Gaussian Noise (AWGN) gets added to the received signal, and in cases of low Signal to Noise Ratio (SNR), the angle estimation using FFT algorithm becomes difficult as many peaks were obtained in spectrum due to addition of noise. MUSIC algorithm uses Eigen value decomposition method and denoising occurs by suppressing the peaks due to noise. The angular resolution is also increased and this algorithm works good in noisy environment. The simulation was carried out in MATLAB and the results were also verified using the same.

An Evolutionary Normalization Algorithm for Signed Floating-Point Multiply-Accumulate Operation

In the era of digital signal processing, like graphics and computation systems, multiplication-accumulation is one of the prime operations. A MAC unit is a vital component of a digital system, like different Fast Fourier Transform (FFT) algorithms, convolution, image processing algorithms, etcetera. In the domain of digital signal processing, the use of normalization architecture is very vast. The main objective of using normalization is to perform comparison and shift operations. In this research paper, an evolutionary approach for designing an optimized normalization algorithm is proposed using basic logical blocks such as Multiplexer, Adder etc. The proposed normalization algorithm is further used in designing an 8 × 8 bit Signed Floating-Point Multiply-Accumulate (SFMAC) architecture. Since the SFMAC can accept an 8-bit significand and a 3-bit exponent, the input to the said architecture can be somewhere between −(7.96872)10 to + (7.96872)10. The proposed architecture is designed and implemented using the Cadence Virtuoso using 90 and 130 nm technologies (in Generic Process Design Kit (GPDK) and Taiwan Semiconductor Manufacturing Company (TSMC), respectively). To reduce the power consumption of the proposed normalization architecture, techniques such as “block enabling” and “clock gating” are used rigorously. According to the analysis done on Cadence, the proposed architecture uses the least amount of power compared to its current predecessors.

Multifeature Fusion-Based Hand Gesture Sensing and Recognition System

With the development of the radar sensing technology, hand gesture sensing and recognition has attracted much attention. This letter adopts a frequency-modulated continuous wave (FMCW) radar to achieve short-range hand gesture sensing and recognition. Specifically, the range, Doppler, and angle parameters of hand gestures are measured by fast Fourier transformation (FFT) and multiple signal classification (MUSIC) algorithm, respectively. The mixup (MP) algorithm combined with augmentation (AU) algorithm using a weight factor is applied to expand the hand gesture data. Then, a complementary multidimensional feature fusion network-based hand gesture recognition (CMFF-HGR) is designed to extract the features and achieve HGR. Finally, a series of experiments are carried out to verify the effectiveness of the proposed approach, and the results show that the recognition accuracy is higher than the existing alternatives with low computational complexity.

Series Arc Fault Breaker in Low Voltage Using Microcontroller Based on Fast Fourier Transform

Series Arc Fault is one of the disturbances of arcing jump is caused by gas ionization between two ends of damaged conductors or broken wire forming a gap in the insulator. Series arc fault is the primary driver of electrical fire. However, lack of knowledge of the disturbance of series arc fault causes the problem of electrical fire not be mitigated. Magnitude current is not capable to detect of series arc fault. Therefore, this paper proposes fast fourier transform (FFT) to detect series AC arc fault in low voltage using microcontroller ARM STM32F7NGH in real time. A cheap and high speed of microcontroller ARM STM32F7NGH can be used for FFT computation to transform signal in time domain to frequency domain. Moreover, in this paper, protection of series AC arc fault is proposed in the real time mode. In this experimental process, some various experiments are tested to evaluate the reliability of FFT and protection with various load starts from 1 A, 2 A, 3 A, 4 A in resistive load. The result of this experiment shows that series AC arc fault protection with STM32F7 microcontroller and FFT algorithm can be utilized to ensure series AC arc fault properly.

Dimension-reduction of stochastic wave forces and probability density evolution analysis of wave-excited pile foundation

This paper discusses the reasonable description and simulation of the continuous stochastic wave force field at probabilistic level. Firstly, in order to overcome the challenge of high-dimensional random variables inherent in the conventional Monte Carlo sampling (MCS), the dimension-reduction (DR) simulations of stochastic processes are addressed based on both the non-deterministic spectral amplitude (NSA) method and the deterministic spectral amplitude (DSA) method. In the proposed method, merely one or two elementary random variables are required to describe the continuous stochastic wave force field at the level of probability density. Simultaneously, the simulation efficiency of the proposed scheme is significantly enhanced by employing the Fast Fourier Transform (FFT) algorithm. In addition, the DR simulations for continuous stochastic wave force field are conducted in accordance with the linear Morison's equation (LME) and the nonlinear Morison's equation (NLME). Finally, the stochastic wave force field acting on a single pile foundation is generated by the proposed method, followed by the refined linear dynamic analysis and reliability assessment of the employed single pile foundation combining the probability density evolution method (PDEM). The effectiveness, accuracy and engineering practicability of the DR methods are sufficiently illustrated by comparison with the MCS methods thereafter. The analysis results also show that the DR methods are of significance robustness in reliability assessment of offshore engineering structures.

High-performance computation of pricing two-asset American options under the Merton jump-diffusion model on a GPU

This paper is concerned with fast, parallel and numerically accurate pricing of two-asset American options under the Merton jump-diffusion model, which gives rise to a two-dimensional partial integro-differential complementarity problem (PIDCP) with a nonlocal two-dimensional integral term. Following method-of-lines approach, the solution to the PIDCP can be computed quite accurately by a robust numerical technique that combines Ikonen–Toivanen splitting with an alternating direction implicit scheme. However, we observed that computing the numerical solution with this technique becomes extremely time consuming, mainly due to the handling of the integral term. In this paper we parallelize this technique by applying a parallel fast Fourier transformation algorithm to all matrix-vector multiplications involving the huge and dense integral approximation matrix by exploiting its block Toeplitz with Toeplitz block structure. We also parallelize other computationally intensive steps of this technique by applying a recently developed parallel cyclic reduction algorithm for pentadiagonal systems. Our solutions computed on a graphics processing unit (GPU) using CUDA® platform are compared for accuracy with those available in the literature. It is observed that by solving the PIDCP parallelly we could bring down the computational times from several hours to a few seconds in certain cases in our experiments.

Enhancement of vital signals based on low-rank, sparse representation for UWB through-wall radar

ABSTRACT The life detection radar plays an important role in earthquake rescue, but the vital signal acquired in practice is often submerged in noise. Improving the signal-to-noise ratio (SNR) of through-wall vital signals is still a challenging task. In this paper, we propose a new vital signal enhancement algorithm based on low-rank, sparse representation. The proposed algorithm decomposes the acquired time-frequency image of echo signals into low-rank and sparse components. The low-rank component captures vital signals, and the environmental noise is contained in the sparse component. The proposed algorithm is compared with the traditional Fast Fourier transform (FFT) algorithm and singular value decomposition (SVD) enhanced algorithm through simulation and experimental data verification. Visual images and quantitative data prove that the output SNR of the proposed vital enhancement algorithm is better than that of the FFT and SVD algorithms.

Broadband Spectral Analysis Algorithm with High-Frequency Resolution for Elimination of Overlap Interference between Adjacent Channels

Spectral lines can be analysed to determine the physical properties of molecular clouds and the astrochemical processes in the formation area of massive stars. To improve the observation technology of radio astronomy, this paper proposes and compares two spectral analysis algorithms (improved weighted overlap-add (IWOLA) + FFT and IWOLA + weighted overlap-add (WOLA)). The proposed algorithms can obtain an ultra-high-frequency resolution for real-valued wideband signals, eliminate the signal overlapping interference between adjacent channels, substantially decrease the required hardware resources, especially multipliers, adders, and memory resources, and reduce the system design complexity. The IWOLA + FFT algorithm consists of an improved weighted overlap-add (IWOLA) filter bank, fast Fourier transform (FFT), a specific decimation for the output data from the IWOLA filter bank, and a selection for part of the output data from the FFT. The IWOLA + WOLA algorithm consists of the same modules as the IWOLA + FFT algorithm, with the second-stage FFT replaced by the modules of the weighted overlap-add (WOLA) filter bank and the accumulation for each sub-band. Based on an analysis of the underlying principles and characteristics of both algorithms, the IWOLA + FFT algorithm demonstrated a spectrum with a high frequency resolution and a comparable performance to an ultra-large-scale FFT, based on two smaller FFTs and a flexible architecture instead of a ultra-large-scale FFT. The IWOLA + WOLA algorithm contains the same function as the IWOLA + FFT algorithm and demonstrates a higher performance. The proposed algorithms eliminated the interference between the adjacent channels within the entire Nyquist frequency bandwidth. The simulation results verify the accuracy and spectral analysis performances of the proposed algorithms.

Performance Analysis of Associate Radix-2, Radix- 4 and Radix-8 based FFT using Folding Technique

Abstract : In recent years, as a result of advancing VLSI technology, Orthogonal Frequency Division Multiplexing (OFDM) has received a great deal of attention and has been adopted in many new generation wideband data communication systems such as IEEE 802.11a, IEEE 802.16e, HiPerLAN/2, Digital Audio/Video Broadcasting (DAB/DVB), and for 4G Radio mobile communications. This is because of its high bandwidth efficiency as the use of orthogonal waveforms with overlapping spectra. The immunity to multipath fading channel and the capability for parallel signal processing make it a promising candidate for the next generation mobile communication systems. The modulation and demodulation of OFDM based communication systems can be efficiently implemented with an FFT and IFFT, which has made the FFT valuable for those communication systems. The complexity of an OFDM system highly depends upon the computation of Fast Fourier Transform (FFT) algorithm. With the advent of new technology in the fields of VLSI and communication, there is also an ever growing demand for high speed processing and low area design. It is also a well-known fact that the multiplier unit forms an integral part of processor design. Due to this regard, high speed multiplier architectures become the need of the day.

Circadian Rhythm Analysis Using Wearable Device Data: Novel Penalized Machine Learning Approach.

BackgroundWearable devices have been widely used in clinical studies to study daily activity patterns, but the analysis remains a major obstacle for researchers.ObjectiveThis study proposes a novel method to characterize sleep-activity rhythms using actigraphy and further use it to describe early childhood daily rhythm formation and examine its association with physical development.MethodsWe developed a machine learning–based Penalized Multiband Learning (PML) algorithm to sequentially infer dominant periodicities based on the Fast Fourier Transform (FFT) algorithm and further characterize daily rhythms. We implemented and applied the algorithm to Actiwatch data collected from a cohort of 262 healthy infants at ages 6, 12, 18, and 24 months, with 159, 101, 111, and 141 participants at each time point, respectively. Autocorrelation analysis and Fisher test in harmonic analysis with Bonferroni correction were applied for comparison with the PML. The association between activity rhythm features and early childhood motor development, assessed using the Peabody Developmental Motor Scales-Second Edition (PDMS-2), was studied through linear regression analysis.ResultsThe PML results showed that 1-day periodicity was most dominant at 6 and 12 months, whereas one-day, one-third–day, and half-day periodicities were most dominant at 18 and 24 months. These periodicities were all significant in the Fisher test, with one-fourth–day periodicity also significant at 12 months. Autocorrelation effectively detected 1-day periodicity but not the other periodicities. At 6 months, PDMS-2 was associated with the assessment seasons. At 12 months, PDMS-2 was associated with the assessment seasons and FFT signals at one-third–day periodicity (P<.001) and half-day periodicity (P=.04), respectively. In particular, the subcategories of stationary, locomotion, and gross motor were associated with the FFT signals at one-third–day periodicity (P<.001).ConclusionsThe proposed PML algorithm can effectively conduct circadian rhythm analysis using time-series wearable device data. The application of the method effectively characterized sleep-wake rhythm development and identified the association between daily rhythm formation and motor development during early childhood.

Hand character gesture recognition based on a single millimetre‐wave radar chip

In this work, a new method for hand character gesture recognition based on a single millimetre-wave radar chip is proposed. Most current radar-based gesture recognition approaches use Doppler spectrograms or the feature extraction of Doppler spectrograms. In contrast, the authors propose using the trajectory points of gesture movements. Compared with the previous methods, the variations in the gesture movement speed, distance and direction during data acquisition have relatively little impact on the generated trajectories. The character trajectories drawn by gestures in the air output a fixed shape, and this fixed output facilitates the classification of gestures at a later stage. In this work, a single millimetre-wave radar is used to collect data and a three-dimensional fast Fourier Transform (3D-FFT) algorithm is used to obtain the gesture trajectories. For the trajectory points, a trajectory conversion image method is proposed and finally the improved Xception network proposed in this work is used for image recognition. Compared with traditional methods, the proposed method does not require large-scale data acquisition to facilitate different users. This work is concluded by recognising hand character gestures and comparing them with other commonly used classification methods to verify the gesture recognition accuracy of the proposed method.

A FFT accelerated high order finite difference method for elliptic boundary value problems over irregular domains

For elliptic boundary value problems (BVPs) involving irregular domains and Robin boundary condition, no numerical method is known to deliver a fourth order convergence and O(Nlog⁡N) efficiency, where N stands for the total degree-of-freedom of the system. Based on the matched interface and boundary (MIB) and fast Fourier transform (FFT) schemes, a new finite difference method is introduced for such problems, which involves two main components. First, a ray-casting MIB scheme is proposed to handle different types of boundary conditions, including Dirichlet, Neumann, Robin, and their mix combinations. By enclosing the concerned irregular domain by a large enough cubic domain, the ray-casting MIB scheme generates necessary fictitious values outside the irregular domain by imposing boundary conditions along the normal direction of the boundary, so that a high order central difference discretization of the Laplacian can be formed. Second, an augmented MIB formulation is built, in which Cartesian derivative jumps are reconstructed on the boundary as auxiliary variables. By treating such variables as unknowns, the discrete Laplacian can be efficiently inverted by the FFT algorithm, in the Schur complement solution of the augmented system. The accuracy and efficiency of the proposed augmented MIB method are numerically examined by considering various elliptic BVPs in two and three dimensions. Numerical results indicate that the new algorithm not only achieves a fourth order of accuracy in treating irregular domains and complex boundary conditions, but also maintains the FFT efficiency.

Evaluating FFT-based algorithms for strided convolutions on ARMv8 architectures

Convolutional Neural Networks (CNNs) have been widely adopted in many kinds of artificial intelligence applications. Most of the computational overhead of CNNs is spent on convolutions. An effective approach to reducing the overhead is transforming convolutions in the time domain into multiplications in the frequency domain by means of Fast Fourier Transform (FFT) algorithms, known as FFT-based fast algorithms for convolutions. However, current FFT-based fast implementations only work for unit-strided convolutions with stride as 1, and cannot be directly applied to strided convolutions with stride size greater than 1, which are usually used as the first layer of CNNs and as an effective alternative to the pooling layers for downsampling.In this paper, we first introduce rearrangement- and sampling-based methods for applying FFT-based fast algorithms to strided convolutions, and the arithmetic complexities of these two methods and the direct method are compared in detail. Then, the highly optimized parallel implementations of the two methods on ARMv8-based many-core CPU are presented. Lastly, we benchmark these implementations against two GEMM-based implementations on this ARMv8 CPU. Our experimental results with convolutions of different kernels, feature maps, and batch sizes show that the rearrangement-based method generally exceeds the sampling-based one under the same optimizations in most cases, and these two methods can get much better performance than GEMM-based ones when the kernels, feature maps and batch sizes are large. The experimental results on the convolutional layers in popular CNNs further demonstrate the conclusions above.

Feature selection to classify lameness using a smartphone-based inertial measurement unit.

Background and objectivesGait can be severely affected by pain, muscle weakness, and aging resulting in lameness. Despite the high incidence of lameness, there are no studies on the features that are useful for classifying lameness patterns. Therefore, we aimed to identify features of high importance for classifying population differences in lameness patterns using an inertial measurement unit mounted above the sacral region.MethodsFeatures computed exhaustively for multidimensional time series consisting of three-axis angular velocities and three-axis acceleration were carefully selected using the Benjamini–Yekutieli procedure, and multiclass classification was performed using LightGBM (Microsoft Corp., Redmond, WA, USA). We calculated the relative importance of the features that contributed to the classification task in machine learning.ResultsThe most important feature was found to be the absolute value of the Fourier coefficients of the second frequency calculated by the one-dimensional discrete Fourier transform for real input. This was determined by the fast Fourier transformation algorithm using data of a single gait cycle of the yaw angular velocity of the pelvic region.ConclusionsUsing an inertial measurement unit worn over the sacral region, we determined a set of features of high importance for classifying differences in lameness patterns based on different factors. This completely new set of indicators can be used to advance the understanding of lameness.