Fast Fourier Transform Coefficients Research Articles

Statistical and spectral analysis of wind over a strategic location

Abstract In the present work, we explored the inherent characteristics of the wind over a complex terrain site ‘Ranchi’ situated near a strategic location of the monsoon trough with various mathematical and statistical tools, i.e., time-series analysis, Fast Fourier transform (FFT), FFT coefficients, wavelet decomposition, and Weibull distribution. The time-series analysis showed a rapid day-to-day variability with a seasonal variation with a peak during summer. Fourier coefficients were concentrated for the winter/post-monsoon, indicating lower wind conditions, while wide spreads of the points indicate agility, i.e., high wind during the summer. The spectral features obtained using FFTs infer that wind has a prominent peak at a frequency f=0.00106724 (day−1) and f=0.00266809 (day−1). The power spectrum and wavelet decomposition show that the prominent frequencies correspond to yearly, eight, six, and four months. Weibull probability density function, cumulative probability distributions, and probability profiles are studied. Results show that the Weibull distribution function reasonably models the probability distribution of daily wind speed. Weibull scale parameter varied between 0.26 and 1.33 m/s, and the shape parameter ranged between 1.09 and 2.88. Results from various analyses indicate that the seasonal variation of wind speed over Ranchi is mainly associated with the development of monsoon trough over the site.

Riemannian manifold on stream data: Fourier transform and entropy-based DDoS attacks detection method

The means to achieve DDoS (distributed denial of service) attacks are becoming increasingly automated and diverse. A problem that automated attack tools cannot address, at least for now, is the inevitable repetitive or periodic nature of traffic data, which are important features for the effective detection of DDoS attacks. Some researchers have proposed to detect DDoS attacks by analyzing the frequency domain information or information entropy of network communication signals or network packets. However, they still suffer from insufficient accuracy and slow response time when dealing with large-scale attack data and multiple-packet types of attacks. Therefore, we hope to develop a detection method that can detect large-scale and multiple types of DDoS. This paper proposes a new DDoS detection method based on fast Fourier transform (FFT) and information entropy. This method (FFT and entropy-based DDoS detection method [FEDDM]) focuses on the periodicity of DDoS network traffic. First, we consider each piece of network traffic data as a network behavior. Then, we prove that the network traffic data conforms to the Riemann flow structure. We define the concept of work of stream data and treat it as a feature. The effect of stream data on the communication capacity can be considered as the work performed by the stream data on the channel. In addition, to improve the efficiency and accuracy of detection, we use the FFT coefficients and information entropy of work as features to train the neural network (NN) to detect DDoS attacks. This method is lightweight, faster, and more generally applicable. The experiment proved the advantage of this method using the latest CICDDoS2019 dataset. In the simulation, the detection accuracy of NetBIOS, SNMP, syn, and WebDDoS is more than 99.99%, which proves our method.

Robust Blind Speech Watermarking via FFT-Based Perceptual Vector Norm Modulation With Frame Self-Synchronization

Watermarking is an important measure for protecting proprietary digital multimedia data. This paper presents a novel approach to achieving robust and imperceptible blind speech watermarking on a frame-by-frame basis. The proposed method employs two modules operating in the fast Fourier transform (FFT) domain. The first module is referred to as downward progressive quantization index modulation. It modulates the vector norms drawn from FFT coefficients according to a guideline deduced from human auditory masking properties. The second module is referred to as boundary-constrained iterative adjustment. It provides a smooth transition across frames in the resulting speech waveform. Experiment results confirm the imperceptibility of the proposed modulation scheme in terms of the mean opinion score - listening quality objective (MOS-LQO) based on the perceptual evaluation of speech quality (PESQ) metric. The proposed watermarking method matched and exceeded the performance of five state-of-the-art methods in terms of robustness against common speech processing attacks.

Condition Analysis of a High-Speed Train Based on Similarity Ratio and MDBN

In order to make full use of the complementary information of multichannel vibration signals, this paper proposes a method of channel selection based on the similarity ratio and constructs a multichannel deep belief network (MDBN) for condition analysis of a high-speed train. First, fast Fourier transform (FFT) coefficients of the signals of all channels are extracted. Then, the similarity ratio of FFT coefficients of each channel is calculated, and a number of channels with a large similarity ratio are selected. Finally, the MDBN model is constructed to learn the features of the selected multichannel data and recognize conditions, and the feature fusion of multichannel data is realized in the common layer. The experimental results show that the similarity ratio is effective to select the channels with rich feature information, the feature learning ability of MDBN is better than DBN, and the condition recognition rate of MDBN is higher than other state-of-the-art methods.

Statistical modeling for fast Fourier transform coefficients of operational vibration measurements with non-Gaussianity using complex-valued t distribution

Abstract Frequency-domain operational vibration responses have been widely applied in structural health monitoring (SHM). Characterizing and quantifying their uncertainties are of fundamental importance for enhancing the robustness of SHM technologies. The classic complex Gaussian distribution is being increasingly used to model the distributions of fast Fourier transform (FFT) coefficients due to its elegant and convenient mathematical nature. However, the field-test data analysis of engineering structures under operational vibrations in this study emphasize the possibility of non-Gaussianity of some observations. The higher peaks and heavier tails than those of a Gaussian distribution emerge as observable features. As a member of the general family of elliptically symmetric distributions, the t distribution has been widely recognized as a useful extension of the Gaussian distribution for the robust statistical modeling of data sets with heavier-than-normal tails. In this paper, we consider using the complex-valued t distribution to characterize the FFT coefficients with high kurtosis and heavy tails. The probability density function (PDF) of multivariate proper complex t random variables are derived based on the equivalent counterparts in the real-valued domain. The marginal PDFs of the real part, the imaginary part, the magnitude, and the phase of a univariate complex-valued t random variable are also derived analytically based on advanced integration techniques. The field test data of different engineering structures provide an illustration of the performance of complex Gaussian and complex t probabilistic models at different frequencies evaluated via the K-S test, goodness-of-fit test, and probability plots.

Wall Thinning Characterization of Composite Reinforced Steel Tube Using Frequency-Domain PEC Technique and Neural Networks

Resin fiber composites reinforcement is used to recover the original mechanical properties of steel tubes subjected to corrosion wall thinning. Pulsed Eddy Current (PEC) technique can perform nondestructive evaluation of this kind of component, due to its capability to penetrate nonmagnetic insulation. Despite the evaluation capability, distinguishing inner surface from outer surface defects is not an easy task for time-domain PEC technique. In this paper, Fast Fourier transform (FFT) in combination with multilayer perceptron (MLP) neural network classifiers are applied to PEC signals and used to detect defects (wall thinning) and also to indicate their position. The tested sample is a carbon steel tube, with 17 mm of composite reinforcement, where two defects were manufactured, one at the inner and another at the outer surface. An automated scanner system is used to obtain C-scan maps, showing the thinning areas. Two feature extraction methods are used to produce the input features for the neural network classifier: the coefficients of the FFT; and the parameters of an exponential curve fitted to the FFT coefficients. The results indicate that the MLP neural network correctly recognized the presence of wall thinning and its location with detection efficiencies of 97.4 and 97.0%, respectively. The PEC technique analysis in frequency-domain associated with a neural network classifier seems to be a promising alternative to identify the position of defects in composite reinforced steel tubes.

Fixed-Point Analysis and Parameter Optimization of the Radix-<formula formulatype="inline"><tex Notation="TeX">$2^{k}$</tex> </formula> Pipelined FFT Processor

The radix- $2^{k}$ algorithm plays a crucial role in the pipelined implementation of fast Fourier transform (FFT). This paper presents a fixed-point analysis and hardware evaluation of radix- $2^{k}$ FFT under the framework of the single-path delay feedback (SDF) and multi-path delay commutator (MDC) pipelined structure. The investigation is carried out with variable operating word-lengths to ensure the generality. Furthermore, the main streams to fulfill FFT coefficients weighting, namely, the approach using complex multipliers and the one adopting memoryless CORDIC units, are both considered in the analysis. Based on these derivations, a joint optimization of radix- $2^{k}$ algorithm and operating word-length is discussed to achieve a reasonable trade-off between computational accuracy and hardware expenditure. Simulations and experiments indicates that the derived SQNR is reliable to unfold the quantization effects of fixed-point radix- $2^{k}$ FFT. In addition, the proposed joint optimization strategy is capable of providing better solutions to implement the radix- $2^{k}$ FFT processor efficiently.

효과적인 다중 차량 추적을 위한 객체 특징 추출 및 매칭

A vehicle tracking system makes it possible to induce the vehicle movement path for avoiding traffic congestion and to prevent traffic accidents in advance by recognizing traffic flow, monitoring vehicles, and detecting road accidents. To track the vehicles effectively, those which appear in a sequence of video frames need to identified by extracting the features of each object in the frames. Next, the identical vehicles over the continuous frames need to be recognized through the matching among the objects` feature values. In this paper, we identify objects by binarizing the difference image between a target and a referential image, and the labelling technique. As feature values, we use the center coordinate of the minimum bounding rectangle(MBR) of the identified object and the averages of 1D FFT(fast Fourier transform) coefficients with respect to the horizontal and vertical direction of the MBR. A vehicle is tracked in such a way that the pair of objects that have the highest similarity among objects in two continuous images are regarded as an identical object. The experimental result shows that the proposed method outperforms the existing methods that use geometrical features in tracking accuracy.

Audio watermarking in transform domain based on singular value decomposition and Cartesian-polar transformation

This paper presents an audio watermarking scheme in fast Fourier transform (FFT) domain based on singular value decomposition (SVD) and Cartesian-polar transformation (CPT). In our proposed scheme, initially the original audio is segmented into nonoverlapping frames. FFT is applied to each frame and low frequency FFT coefficients are selected. SVD is applied to the selected FFT coefficients of each frame represented in a matrix form. The highest singular values of each frame are selected and are decomposed into two components using CPT. Watermark information is embedded into each of these CPT components using an embedding function. Experimental results indicate that the proposed watermarking scheme is highly robust against various signal processing attacks. In addition, the proposed scheme has a high data payload. Moreover, it outperforms state-of-the-art audio watermarking methods in terms of imperceptibility, robustness, and data payload.

Low-Power Analog Processing for Sensing Applications: Low-Frequency Harmonic Signal Classification

A low-power analog sensor front-end is described that reduces the energy required to extract environmental sensing spectral features without using Fast Fouriér Transform (FFT) or wavelet transforms. An Analog Harmonic Transform (AHT) allows selection of only the features needed by the back-end, in contrast to the FFT, where all coefficients must be calculated simultaneously. We also show that the FFT coefficients can be easily calculated from the AHT results by a simple back-substitution. The scheme is tailored for low-power, parallel analog implementation in an integrated circuit (IC). Two different applications are tested with an ideal front-end model and compared to existing studies with the same data sets. Results from the military vehicle classification and identification of machine-bearing fault applications shows that the front-end suits a wide range of harmonic signal sources. Analog-related errors are modeled to evaluate the feasibility of and to set design parameters for an IC implementation to maintain good system-level performance. Design of a preliminary transistor-level integrator circuit in a 0.13 μm complementary metal-oxide-silicon (CMOS) integrated circuit process showed the ability to use online self-calibration to reduce fabrication errors to a sufficiently low level. Estimated power dissipation is about three orders of magnitude less than similar vehicle classification systems that use commercially available FFT spectral extraction.

Voiced-Unvoiced-Silence Detection Algorithm using Perceptron Neural Network

This paper proposes a detection algorithm for each section which detects the voiced section, unvoiced section, and the silence section at each frame using a multi-layer perceptron neural network. First, a power spectrum and FFT (fast Fourier transform) coefficients obtained by FFT are used as the input to the neural network for each frame, then the neural network is trained using these power spectrum and FFT coefficients. In this experiment, the performance of the proposed algorithm for detection of the voiced section, unvoiced section, and silence section was evaluated based on the detection rates using various speeches, which are degraded by white noise and used as the input data of the neural network. In this experiment, the detection rates were 92% or more for such speech and white noise when training data and evaluation data were the different.

A New Feature Fusion Method for Handwritten Character Recognition Based on 3D Accelerometer

In this paper, a new feature fusion method for Handwritten Character Recognition based on single tri-axis accelerometer has been proposed. The process can be explained as follows: firstly, the short-time energy (STE) features are extracted from accelerometer data. Secondly, the Frequency-domain feature namely Fast Fourier transform Coefficient (FFT) are also extracted. Finally, these two categories features are fused together and the principal component analysis (PCA) is employed to reduce the dimension of the fusion feature. Recognition of the gestures is performed with Multi-class Support Vector Machine. The average recognition results of ten Arabic numerals using the proposed fusion feature are 84.6%, which are better than only using STE or FFT feature. The performance of experimental results show that gesture-based interaction can be used as a novel human computer interaction for consumer electronics and mobile device.

An efficient locally pipelined FFT processor

The fast Fourier transform (FFT) is a very important algorithm in digital signal processing. The locally pipelined (LPPL) architecture is an efficient structure for FFT processor designing in a real-time embedded system. Two basic building blocks, to the LPPL FFT processor, the butterfly in pipeline, and address generating, are discussed in this brief. Based on the feedback to butterfly-2, a novel approach for pipelined architecture, the radix-2 single-path deep delay feedback architecture is proposed. For length-N discrete Fourier transform computation, the dominant hardware requirements are minimal for complex multipliers log/sub 4/N-1 and adders 2log/sub 4/N. As an integral need of the LPPL FFT processor design, address generating and coefficient store-load structures are also presented.

Classification of EMG Signals Using PCA and FFT

In this study, the fast Fourier transform (FFT) analysis was applied to EMG signals recorded from ulnar nerves of 59 patients to interpret data. The data of the patients were diagnosed by the neurologists as 19 patients were normal, 20 patients had neuropathy and 20 patients had myopathy. The amount of FFT coefficients had been reduced by using principal components analysis (PCA). This would facilitate calculation and storage of EMG data. PCA coefficients were applied to multilayer perceptron (MLP) and support vector machine (SVM) and both classified systems of performance values were computed. Consequently, the results show that SVM has high anticipation level in the diagnosis of neuromuscular disorders. It is proved that its test performance is high compared with MLP.

Fast Fourier transform based image compression algorithm optimized for speckle interferometer measurements

In the framework of European Space Agency (ESA) FluidPac satellite mission, we have developed a fast, lossy image compression algorithm (ICA) based on a slight variation of the classical 2-D fast Fourier transform (FFT). In essence, given a monochrome picture, the ICA calculates (almost) its Fourier spectrum. It then applies a low-pass filter to eliminate all Fourier coefficients beyond a certain user-defined cutoff frequency. Finally, it further compresses by encoding the surviving FFT coefficients in a more memory efficient manner. The proposed scheme works best with pictures where the high-frequency data are of little value. This is precisely the case with electronic speckle pattern interferometer (ESPI) images. The ICA low-pass filter removes the speckle noise while preserving the useful scientific information: the interference fringe pattern. We have, however, also applied the FluidPac ICA to pictures generated by classical interferometers, photographic equipment, particle tracing instruments, and IR cameras. The results are extremely encouraging.

A Neural Network Based Hybrid Technique for Data Compression of Stereopairs.(Dept.E)

This paper presents a new hybrid technique for efficient compression of stereopairs . The proposed technique encompasses three processing stages: a phase difference disparity interpreter, a neural network based image compressor / decompressor, and a stereopair reconstructor. The main advantage of the proposed technique lies in a threefold data compression. The first data compression stage is realized by using the Fast Fourier Transform (FFT) for computation of the disparity. Data compression is achieved by sending both the disparity and the compressed right image. The second data compression stage is achieved by clamping the significant part of the FFT coefficients of the right image to the input layer of the neural network for further data compression. This has the advantage of reducing the number of neurons in the input layer of the neural compressor. The third data compression stage is encompassed in the data compression of the previously FFT - compressed right image through the neural net data compressor. At the receiver, the disparity, the displaced subimage and the compressed right image are used to reconstruct the left image: Experiments are performed on both random and real stereopairs. The compression ratio of the neural network depends on the number of neurons in the hidden layer. The FFT of the input parterns is used to increase the compression ratio and to speed up the learning of the neural network. Correspondence analysis is performed using the spin model to obtain the disparity map of the stereopair. System design parameters affecting the performance of the correspondence analyzer are studied to achieve optimal stereopais interpretation. This process makes it possible to transmit only the displaced regions in the left image. Another data compression step is achieved through the contour of the disparity map.

Separation of action potentials in multiunit intrafascicular recordings.

Classification of action potentials in multiunit recordings was based on the use of various types of features to uniquely characterize action potentials from different cells. We compared classification results obtained using three types of descriptive features: digitized data points, amplitude and duration (time domain) parameters, and fast Fourier transform (FFT) coefficients. Digitized data points used as descriptive features provided good classification success and required minimal computation. Time-domain features gave comparable results but required more computation. FFT coefficients were less effective than the other features. As the signal-to-noise ratio of the recordings increased, smaller differences in feature values could be discriminated.

Effects of FFT coefficient quantization on bin frequency response

A method is presented for analyzing the effets of quantization of coefficients on the frequency response of any frequency bin of the fast Fourier transform (FFT) algorithm. Although more detail is easily obtained, we concentrate on predicting the locations and sizes of all spurious sidelobes in the frequency response which are above any specified level. Certain sidelobes are present due to the particular window or weighting function that is being used. Spurious sidelobes or artifacts are extra sidelobes which are introduced if the FFT coefficients are quantized.