Fast Fourier Research Articles

Integrated Neural Network Approach for Enhanced Vital Signal Analysis Using CW Radar

This study introduces a novel approach for analyzing vital signals using continuous-wave (CW) radar, employing an integrated neural network model to overcome the limitations associated with traditional step-by-step signal processing methods. Conventional methods for vital signal monitoring, such as electrocardiograms (ECGs) and sphygmomanometers, require direct contact and impose constraints on specific scenarios. Conversely, our study primarily focused on non-contact measurement techniques, particularly those using CW radar, which is known for its simplicity but faces challenges such as noise interference and complex signal processing. To address these issues, we propose a temporal convolutional network (TCN)-based framework that seamlessly integrates noise removal, demodulation, and fast Fourier transform (FFT) processes into a single neural network. This integration minimizes cumulative errors and processing time, which are common drawbacks of conventional methods. The TCN was trained using a dataset comprising preprocessed in-phase and quadrature (I/Q) signals from the CW radar and corresponding heart rates measured via ECG. The performance of the proposed method was evaluated based on the L1 loss and accuracy against the moving average of the estimated heart rates. The results indicate that the proposed approach has the potential for efficient and accurate non-contact vital signal analysis, opening new avenues in health monitoring and medical research. Additionally, the integration of CW radar and neural networks in our framework offers a robust and scalable solution, enhancing the practicality of non-contact health monitoring systems in diverse environments. This technology can be leveraged in healthcare robots to provide continuous and unobtrusive monitoring of patients’ vital signs, enabling timely interventions and improving overall patient care.

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.

Spectral analysis based blind frequency offset estimation for digital subcarrier multiplexing systems with adjustable roll-off factors and various modulation formats.

We proposed a blind frequency offset estimation (FOE) method for digital subcarrier multiplexing (DSM) signals. By utilising spectral information from the DSM signal and analysing the correlation between the frequency offset (FO) and the summed power of the signal spectrum, the proposed FOE method can accurately and effectively handle various modulation schemes assigned to each subcarrier. The proposed FOE method exhibits a flexibility to the roll-off factor of the root raised cosine (RRC) spectral shaping and can achieve a high level of accuracy in FOE under different roll-off factors and subcarrier numbers, with an FOE error of less than 30 MHz under a fast Fourier transform (FFT) size of 2048. Additionally, the proposed FOE method has advantages in terms of the computational complexity compared to the existing method. The performance of the proposed FOE method is experimentally verified for 48Gbaud 16QAM DSM signals in a coherent detection system.

Intelligent fault diagnosis of rolling bearings in strongly noisy environments using graph convolutional networks

SummaryRolling bearings often function under complex and non‐stationary conditions, where significant noise interference complicates fault diagnosis by obscuring fault characteristics. This paper presents an innovative fault diagnosis technique using graph convolutional networks (GCN) to address these challenges. Vibration signals are first transformed into the frequency domain through fast Fourier transform (FFT), creating a detailed graph where nodes and edges encapsulate fault signals. The GCN method then extracts complex node features from this graph, enabling a classifier, comprising a fully connected layer and Softmax function, to accurately identify fault types. Experimental results demonstrate the superior performance of the proposed GCN‐based fault diagnosis method, achieving an accuracy of 99.79%. This significantly surpasses traditional machine learning methods (85.4%), deep learning models (92.3%), and other graph neural network approaches (94.1%). Notably, the method shows exceptional resilience to noise, maintaining high accuracy even with 20% added noise, underscoring its robustness for practical industrial applications. The transformation of vibration signals into the frequency domain using FFT, followed by constructing a detailed graph structure, enables the GCN to effectively capture and represent intricate fault characteristics, thus enhancing accurate fault classification. These findings highlight the method's practical applicability and potential for deployment in advanced industrial settings characterized by high noise levels and complexity.

Analysis of spatiotemporal variation in land surface temperature on the Tibetan Plateau from 2001 to 2020

ABSTRACT With global climate warming intensifying, the Land Surface Temperature (LST) variation on the Tibetan Plateau (TP) has become a hot topic in environmental studies. This letter employs spatial analysis to identify LST distribution characteristics, the Pettitt test to detect abrupt changes, and Fast Fourier Transform (FFT) to analyse periodic variations. Analysing mean annual and seasonal LST from 2001 to 2020, the results indicate the following: (1) Over the past 20 years, the TP’s LST increased slowly at 0.08°C per decade, with significant seasonal variations. Warming trends dominate in spring, summer, and autumn, shifting from the northern to the southwestern plateau. Autumn shows the most significant warming at 0.31°C per decade, while winter shows a cooling trend at −0.46°C per decade. (2) The Pettitt test reveals no statistically significant abrupt changes in mean annual and seasonal LST, though potential change points were detected in 2013 for mean annual LST, and in 2005, 2006, 2014, and 2017 for summer, spring, autumn, and winter, respectively. This indicates relative stability in interannual temperature changes, with some asynchronous seasonal variations. FFT analysis indicates dominant short-term variability with a period of 3.33 years and secondary cycles of 10 and 5 years.

CLASS-OneLoop: accurate and unbiased inference from spectroscopic galaxy surveys

The power spectrum is the most commonly applied summary statistics to extract cosmological information from the observed three-dimensional distribution of galaxies in spectroscopic surveys. We present CLASS-OneLoop, a new numerical tool, fully integrated into the Boltzmann code CLASS, enabling the calculation of the one-loop power spectrum of biased tracers in spectroscopic surveys. Built upon the Eulerian moment expansion framework for redshift-space distortions, the implemented model incorporates a complete set of nonlinear biases, counterterms, and stochastic contributions, and includes the infrared resummation and the Alcock-Paczynski effect. The code features an evaluation of the loops by either direct numerical integration or Fast Fourier Transform, and employs a fast-slow parameter decomposition, which is essential for accelerating MCMC runs. After presenting performance and validation tests, as an illustration of the capabilities of the code, we apply it to fit the measured redshift-space halo power spectrum wedges on a ΛCDM subset of the AbacusSummit simulation suite and considering scales up to kmax = 0.3 h/Mpc. We find that the one-loop model adeptly recovers the fiducial cosmology of the simulation, while a simplified model commonly used in the literature for sensitivity forecasts yields significantly biased results. Furthermore, we conduct Monte Carlo Markov Chain (MCMC) forecasts for a DESI-like survey, considering a model with a dynamical dark energy component. Our results demonstrate the ability to independently constrain cosmological and nuisance parameters, even in the presence of a large parameter space with twenty-nine variables.

Anisotropic mechanism of material removal and ductile-brittle transition in sapphire scratching based on acoustic emission signal

Sapphire exhibits typical anisotropy due to its unique crystal structure, and there are significant property differences in different processing areas during the machining of curved sapphire component, making it essential to investigate the anisotropy in the removal process of sapphire materials for efficient curved surface machining. In this study, the force and acoustic emission (AE) signals were monitored at different scratch stages and orientations, and the anisotropic characteristics of ductile-brittle transition (DBT) depths, material removal morphology, and subsurface crack propagation direction were analyzed. The results indicate that the anisotropy of force signals and DBT depths is mainly reflected in the differences between crystal planes. In addition, the removal morphology of materials with different crystal orientations showed smooth scratch grooves with unclear anisotropic characteristics during the ductile removal (DR) stage, while the crack propagation direction with different scratch orientations during the DBT stage showed significant anisotropic characteristics. The brittle removal (BR) stage is characterized by brittle spalling in the form of shell-like, blocky, and fishbone spalling, and there is a significant anisotropic difference in the spalling shapes on both sides of the scratch. The original AE signals, Fast Fourier Transform (FFT), and Short Time Fourier Transform (STFT) results show that the AE frequencies of different crystal planes are different, and the differences in different scratch orientations on the same crystal plane are reflected in the peak amplitude. Finally, the propagation directions of subsurface cracks with different directions are anisotropic due to different scratching crystal planes, and propagate mainly along directions of 15°, 29°, 32°, 58°, and 105°.

Few-shot bearing fault diagnosis by semi-supervised meta-learning with graph convolutional neural network under variable working conditions

Aiming at the problems of low accuracy and weak generalization ability in fault diagnosis caused by complex working conditions and limited fault samples of bearings, a few-shot bearing fault diagnosis method by semi-supervised meta-learning with simplifying graph convolutional neural network (semi-meta-sgc) is proposed. Firstly, the time domain signal is converted into the frequency domain by fast Fourier transform (FFT). Secondly, considering each spectrum sample as a node, a k-nearest neighbor (KNN) graph is constructed according to the adjacencies between nodes, thus transforming the bearing fault classification into a graphical node classification. Then, relying on meta-learning, graph convolutional neural network, and semi-supervised learning, a high-accuracy node classifier is obtained by using a small number of training samples to achieve the classification of bearing faults under variable working conditions. Finally, the proposed method is verified by four cases and compared with other methods. The results show that this method has higher recognition accuracy and generalization performance.

Anomalous geomagnetic activities before the Karangasem - Bali, Indonesia earthquakes on December 13, 2022

Abstract A series of earthquakes occurred on Bali Island, Indonesia, on December 13, 2022. The United States Geological Survey (USGS) recorded four shallow earthquakes around Karangasem - Bali with magnitude (M) > 4 at that time. The largest was the M 5.2 earthquake, which occurred at 10:38:21.67 UTC with 10 km of depth. We analyzed the anomalous geomagnetic activities during these earthquakes by utilizing the geomagnetic data from the Bayan geomagnetic station located on Lombok Island, less than 100 km from the earthquake’s epicenters. We conducted the polarization ratio analysis by applying the Fast Fourier Transform (FFT) on the five hours of night geomagnetic data (16:00 - 21:00 UTC). The spectral power values of X, Y, and Z geomagnetic data at frequencies 0.04 - 0.06 Hz were calculated and compared with the disturbance storm time (Dst) to find their correlation. The Pearson correlation analysis indicates that they are significantly uncorrelated. Finally, we calculated the Sz/Sg to analyze the geomagnetic anomalies and found them 6 - 11 days before the earthquakes at frequencies 0.04 - 0.06 Hz. We consider that these anomalies are possibly caused by the M 5.2 earthquake since it had the highest magnitude, Es, and Kls values.

Application of Lock-in Amplifier Technique in Signal Blind Source Separation

Abstract In the realm of signal processing, frequency error stands as a critical challenge that cannot be overlooked, particularly in scenarios characterized by noise disturbances and constantly changing environmental variables, as it significantly undermines the precision of waveform separation. Faced with a spectrum of frequency error phenomena stemming from hardware instability, such as clock drift, transmission distortion, and environmental changes, this paper proposes a waveform separation scheme centered around a core closed-loop control architecture aimed at addressing such challenges. Leveraging the high-performance STM32F407 microcontroller platform, the system harnesses the powerful algorithmic advantages of Fast Fourier Transform (FFT) to precisely locate and delineate the spectral characteristics of signals. Furthermore, we creatively integrate lock-in amplifier technology into the meticulously designed closed-loop control system, coupled with state-of-the-art zero-crossing detection algorithms for in-depth optimization. The research findings demonstrate outstanding signal-to-noise ratio performance within predefined target frequency bands for the separation device based on lock-in amplifier technology, showcasing not only remarkable resilience against interference but also the ability to accurately separate and reconstruct target signal components with high fidelity from complex and dynamic signal environments. This significantly enhances the robustness and accuracy of the entire system.

3D reverse-time migration for pure P-wave in orthorhombic media

Compared with the transverse isotropic (TI) medium, the orthorhombic anisotropic medium has both horizontal and vertical symmetry axes and it can be approximated as a set of vertical fissures developed in a group of horizontal strata. Although the full-elastic orthorhombic anisotropic wave equation can accurately simulate seismic wave propagation in the underground media, a huge computational cost is required in seismic modeling, migration, and inversion. The conventional coupled pseudo-acoustic wave equations based on acoustic approximation can be used to significantly reduce the cost of calculation. However, these equations usually suffer from unwanted shear wave artifacts during wave propagation, and the presence of these artifacts can significantly degrade the imaging quality. To solve these problems, we derived a new pure P-wave equation for orthorhombic media that eliminates shear wave artifacts while compromising computational efficiency and accuracy. In addition, the derived equation involves pseudo-differential operators and it must be solved by 3D FFT algorithms. In order to reduce the number of 3D FFT, we utilized the finite difference and pseudo-spectral methods to conduct 3D forward modeling. Furthermore, we simplified the equation by using elliptic approximation and implemented 3D reverse-time migration (RTM). Forward modeling tests on several homogeneous and heterogeneous models confirm that the accuracy of the new equation is better than that of conventional methods. 3D RTM imaging tests on three-layer and SEG/EAGE 3D salt models confirm that the ORT media have better imaging quality.

Enhancing Inductive IR Thermography by Using FFT-Equalization, Motion Tracking Detection and VDSR Super-resolution Processing

Among non-destructive inspection techniques, infrared thermography stands out as a promising technology that enables real-time inspection of large areas without the need for physical contact. In this study, we employed the dynamic induction thermography method, which is one of the active infrared thermography techniques, to detect defects on the back side of the S275 material specimen. This technique involves creating relative movement between the IR camera and the specimen. We acquired sequence images at different moving speeds using the induction thermography technique, and then used the FFT with Gaussian filtering to solve for non-uniform heat sources. To further enhance the resolution, we applied the VDSR technique, which is based on deep neural networks. The effectiveness of this approach was validated both qualitatively and quantitatively. Finally, we utilized the MOT algorithm to automatically detect defects in the image with the highest thermal contrast, which was captured at a speed of 15 mm/s. In this study, we demonstrate the effectiveness of thermal equalization using the GF-based FFT algorithm, as well as the superresolution conversion achieved through the VDSR-based deep neural network. Additionally, we present a mechanism for automated slit detection using the MOT algorithm.

Verification of the AIS service availability model based on dynamic data streams recorded from three receiving stations in the Polish coastal area

The reliability aspects of the operation of radio navigation systems constitute a crucial element for the safety of maritime navigation.. Technological progress in ship traffic monitoring is achieved through the design of ship systems and shore infrastructure equipped with Automatic Identification System (AIS) devices. One of the issues with AIS operation is the limited availability of the service in the form of data streams with an extended data age recorded on the receiving side. Another problem is the emission and reception by ships of incomplete positional reports without navigational parameters. Such situations render the system operationally unfit in terms of processed information. Therefore, it is essential to investigate the operational characteristics of radio navigation systems and develop tools to monitor the AIS service status on the receiving side. This article presents the development of a model for the availability of an AIS for vessels based on the determined mean time of the occurrence of incomplete navigation parameter values in AIS messages and the results of research in the domain of time and frequency using a mathematical method of the Fast Fourier Transform (FFT). The study results refer to six basic navigation parameters and show a varying service availability factor for the navigation parameters under study, i.e. the latitude (LAT), longitude (LON), speed over ground (SOG), course over ground (COG), heading (HDT), and the rate of turn (ROT). The data recorded by three receiving AIS stations on the Polish coast, i.e. PLKOL, PLSZZ, and PLSWI, were used as a key source of practical knowledge on the limitations of the AIS service availability. The experiment observed interruptions in the regular transmission of data from navigation equipment in the AIS service operational zone. As a result, the functional relationship was described based on the spectral analysis of the frequency of occurrence of times between the service repair (Time To Repair, TTR), and the model was proposed to be applied to the study of other variables. The presented model is a tool that allows for improving the monitoring of vessel traffic in terms of reliability, which directly affects the improvement of maritime traffic safety.

Feature selection based on snake optimizer for defect or damage classification in composite rolls via ultrasonic Rayleigh waves

Defects or damages on the surface or subsurface of composite rolls directly affect the quality of the rolled products, and their periodic inspection and accurate identification can provide a reference for the repair or replacement of composite rolls. Ultrasonic Rayleigh waves can non-destructively assess the surface or subsurface of composite rolls, during which similar original signals are perhaps generated for the defects or damages with different types or sizes, making it difficult to distinguish their types. Machine learning is proposed to solve these problems, and feature selection based on the ultrasonic Rayleigh waves mainly utilizes traditional methods such as ReliefF. However, these unsupervised methods have not been combined with specific classification algorithms. In this study, swarm intelligence optimization algorithms, including snake optimizer (SO), dung beetle optimizer (DBO), and grasshopper optimization algorithm (GOA), are investigated based on the support vector machine (SVM). Note that the utilized original signals are received on the left and right sides of defects or damages, and they are processed by segmentation, fast Fourier transform (FFT), and wavelet packet decomposition to build original feature sets. It is illustrated that Rayleigh waves passing through the defects or damages carry more valuable information about the types. In contrast, the ultrasonic waves reflected from the defects or damages can provide information about the types that the former does not contain. Furthermore, for the intelligent classification of defects or damages in composite rolls using ultrasonic Rayleigh waves, SO is more suitable for SVM and has certain advantages.

Nonstationary random vibration analysis of hysteretic systems with fractional derivatives by FFT-based frequency domain method

Nonstationary random vibration problems of nonlinear fractional systems are challenging and drawing increasing attention. This study presents an efficient numerical method for the random vibration analysis of large-scale nonlinear fractional systems subjected to fully nonstationary excitations. Firstly, the fast Fourier transform (FFT)-based frequency domain method originally proposed for the nonstationary random vibration analysis of linear integer-order systems is extended to linear fractional systems, in which the explicit expression of dynamic responses of fractional systems is derived based on the load superposition principle and Newmark method. Secondly, an equivalent linearization analysis framework is constructed to solve the nonstationary responses of hysteretic systems with fractional derivatives, in which the nonstationary response analyses of equivalent linear systems are accomplished by the FFT-based frequency domain method. The presented method can account for nonstationary excitations with arbitrary forms of evolutionary power spectrum, even of the non-separable one. Two numerical examples are used to confirm its superior performance in terms of accuracy and computational efficiency.

Fast Fourier Transform periodic interpolation method for superposition sums in a periodic unit cell

We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic array. Under the same umbrella, FFT-PIM allows computing the potential for 1D, 2D, and 3D periodicities for dynamic problems involving the Helmholtz potential and static problems involving Coulomb potential, including problems with and without a periodic phase shift. The computational complexity of the FFT-PIM is of O(Nlog⁡N) for N spatially coinciding sources and observer points. The FFT-PIM uses rapidly converging series representations of the Green's function serving as a kernel in the superposition sum. Based on these representations, the FFT-PIM splits the potential into its near-zone component, which includes a small number of images surrounding the unit cell of interest, and far-zone component, which includes the rest of an infinite number of images. The far-zone component is evaluated by projecting the non-uniform sources onto a sparse uniform grid, performing superposition sums on this sparse grid, and interpolating the potential from the uniform grid to the non-uniform observation points. The near-zone component is evaluated using an FFT-based method, which is adapted to efficiently handle non-uniform source-observer distributions within the periodic unit cell. The FFT-PIM can be used for a broad range of applications, such as periodic problems involving integral equations for wave propagation in electromagnetics and acoustics, micromagnetic solvers, and density functional theory solvers.

Efficient modeling of fractional Laplacian viscoacoustic wave equation with fractional finite-difference method

The fractional viscoacoustic/viscoelastic wave equation, which accurately quantifies the frequency-independent anelastic effects, has been the focus of seismic industry in recent years. The pseudo-spectral (PS) method stands as one of the most widely used numerical methods for solving the fractional wave equation. However, the PS method often suffers from low accuracy and efficiency, particularly when modeling wave propagation in heterogeneous media. To address these issues, we propose a novel and efficient fractional finite-difference (FD) method for solving the wave equation with fractional Laplacian operators. This method develops an arbitrary high-order FD operator via the generating function of our fractional FD (F-FD) scheme, enhancing accuracy with L2-optimal FD coefficients. Similar to classic FD methods, our F-FD method is characterized by straightforward programming and excellent 3D extensibility. It surpasses the PS method by eliminating the need for Fast Fourier Transform (FFT) and inverse-FFT (IFFT) operations at each time step, offering significant benefits for 3D applications. Consequently, the F-FD method proves more adept for wave-equation-based seismic data processes like imaging and inversion. Compared with existing F-FD methods, our approach uniquely approximates the entire fractional Laplacian operator and stands as a local numerical algorithm, with an adjustable F-FD operator order based on model parameters for enhanced practicality. Accuracy analyses confirm that our method matches the precision of the PS method with a correctly ordered F-FD operator. Numerical examples show that the proposed method has good applicability for complex models. Finally, we have carried out reverse time migration on the Marmousi-2 model, and the imaging profiles indicate that the proposed method can be effectively applied to seismic imaging, demonstrating good practicability.

A Deep Learning-Based Emergency Alert Wake-Up Signal Detection Method for the UHD Broadcasting System.

With the increasing frequency and severity of disasters and accidents, there is a growing need for efficient emergency alert systems. The ultra-high definition (UHD) broadcasting service based on Advanced Television Systems Committee (ATSC) 3.0, a leading terrestrial digital broadcasting system, offers such capabilities, including a wake-up function for minimizing damage through early alerts. In case of a disaster situation, the emergency alert wake-up signal is transmitted, allowing UHD TVs to be activated, enabling individuals to receive emergency alerts and access emergency broadcasting content. However, conventional methods for detecting the bootstrap signal, essential for this function, typically require an ATSC 3.0 demodulator. In this paper, we propose a novel deep learning-based method capable of detecting an emergency wake-up signal without the need for an ATSC 3.0. The proposed method leverages deep learning techniques, specifically a deep neural network (DNN) structure for bootstrap detection and a convolutional neural network (CNN) structure for wake-up signal demodulation and to detect the bootstrap and 2 bit emergency alert wake-up signal. Specifically, our method eliminates the need for Fast Fourier Transform (FFT), frequency synchronization, and interleaving processes typically required by a demodulator. By applying a deep learning in the time domain, we simplify the detection process, allowing for the detection of an emergency alert signal without the full suite of demodulator components required for ATSC 3.0. Furthermore, we have verified the performance of the deep learning-based method using ATSC 3.0-based RF signals and a commercial Software-Defined Radio (SDR) platform in a real environment.

Investigation of super-resolution in microsphere-assisted microscopy with the Poynting vector of the dipole model.

In this paper, the Fourier spectrum of an image in microsphere-assisted microscopy (MAM) and the wavenumber decomposition of the Poynting vector of the dipole model are compared for the first time to study the super-resolution performance within several wavelengths in MAM. Firstly, an experiment using microsphere-assisted microscopy is performed, and the fast Fourier transformation (FFT) spectra of the images along the distance are studied. Then the Poynting vector in the point dipole field is theoretically investigated based on the spectral decomposition of dyadic Green's function. Our study finds that the result of decomposition of the Poynting vector corresponds with the propagation results of components with different transverse wavenumbers kρ in an experiment. Even when kρ reaches 1.7k0, the waves can still arrive outside one wavelength. Our work is the first effort (to our knowledge) to associate the Fourier spectrum and the decomposition of the Poynting vector together, and it may contribute to the quantitative exploration of super-resolution performance in MAM in the future.

Utilizing fast Fourier transform in the processing of biomedical signals: An analytical approach

Fast Fourier Transform (FFT) is an indispensable tool in biomedical engineering, which optimizes the computational process of the traditional Discrete Fourier Transform (DFT) and effectively reduces the computational complexity. This paper first introduces the basic principle of FFT and its importance in biomedical signal processing. It focuses on the application of FFT in the analysis of electrocardiogram (ECG) and electroencephalogram (EEG) signals, such as the diagnosis of arrhythmia and the analysis of sleep quality, as well as the importance of FFT in removing biomedical signal noise. In addition, the paper explores FFT discussing its challenges and future directions in biomedical engineering, including the development of new algorithms and integration with machine learning techniques. Finally, the article summarizes the applications of FFTs in biomedical engineering and their importance. It emphasizes the need for continued research and development of FFTs and their related techniques in the biomedical field.