Identifying Seasonality in Time Series by Applying Fast Fourier Transform

This paper concerns the computation of nonlinear crest distributions for irregular Stokes waves, and a numerical algorithm based on the Fast Fourier Transform (FFT) technique has been developed for carrying out the nonlinear computations. In order to further improve the computational efficiency, a new Transformed Rayleigh procedure is first proposed as another alternative for computing the nonlinear wave crest height distributions, and the corresponding computer code has also been developed. In the proposed Transformed Rayleigh procedure, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The numerical algorithm based on the FFT technique and the proposed Transformed Rayleigh procedure have been applied for calculating the wave crest distributions of a sea state with a Bretschneider spectrum and a sea statewith the surface elevation datameasured at the Poseidon platform. It is demonstrated in these two cases that the numerical algorithm based on the FFT technique and the proposed Transformed Rayleigh procedure can offer better predictions than those from using the empirical wave crest distribution models. Meanwhile, it is found that our proposed Transformed Rayleigh procedure can compute nonlinear crest distributions more than 25 times faster than the numerical algorithm based on the FFT technique.

This paper presents a method for the computation of the Stokes formula using the Fast Hartley Transform CFHT) techniques. The algorithm is most suitable for the computation of real sequence transform, while the Fast Fourier Transform (FFT) techniques are more suitable for the computa ton of complex sequence transform. A method of spherical coordinate transformation is presented in this paper. By this method the errors, which are due to the approximate term in the convolution of Stokes formula, can be effectively eliminated. Some numerical tests are given. By a comparison with both FFT techniques and numerical integration method, the results show that the resulting values of geoidal undulations by FHT techniques are almost the same as by FFT techniques, and the computational speed of FHT techniques is about two times faster than that of FFT techniques.

The purpose of the current study is to detect the squirrel cage induction machine under the Broken Rotor Bars fault (BRBs). In this context, most of the studies were starting by using the Fast Fourier Transform (FFT) technique and applied to the various signals extracted from the motor as the stator phases currents. Unfortunately, FFT technique has some drawbacks such as suffering from the spectral leakage, also, it needs large data points to give clear results about the state of the machine. In addition, most of the induction motors are using speed control devices (the inverters), these devices reduce the effectiveness of FFT because it leads to the appearance of an additional harmonics, and it produces a further spectrum noises. To overcome these limitations, the Multiple Signal Classification (MUSIC) algorithm have been applied to replace the FFT. In particular, MUSIC algorithm allows to minimize the computation of the signal data without losing its diagnostic effectiveness, on the other hand, this technique allows to remove the noise that accompanies the signal. In this paper, the simulation results evidence the robustness of the MUSIC technique to detect the BRBs when the machine is operating under different conditions.

An application of radar sensor in self-driven vehicles, to be used in detecting obstacles and providing accurate information about the vehicle’s ambient environment to activate appropriate control commands. There is need for the sensor to have a computing platform that can ensure real-time processing of the received signals. From previous works, appropriate algorithm, chip-set, memory, etc. capable of performing these tasks sufficiently, are the main challenges. This work model and simulate Radar Sensor signals; Radar signal for automated driving using Fast Fourier Transform (FFT) Technique. Analysis on the FFT Technique is carried out; in terms of its merits and demerits in this application. Applicability of Wavelet Transform (WT) technique for processing of Automotive Radar Signal (ARS) is demonstrated by offering WT Technique Solutions to FFT Problems for ARS by modeling and simulating the following: (a) 1-D Multi-signal WT Operations; (b) Solution to the Noise Problems – Wavelet Denoising; (c) Use of WT for Time-Frequency Reassignment and Mode Extraction with Synchrosqueezing; (d) Discrete Wavelet Transform (DWT) and Continuous Wavelet Transform (CWT) of an ARS with a Frequency Break. All simulations are done using the MATLAB R2017b software. The focused of this work is in the area of appropriate algorithm: to show how the WT technique and which of its tools, and how those tools could be used in developing appropriate algorithm for Automotive Radar Signal Processing (ARSP) as applied in self-driven vehicles.

This paper presents the calibration of pulse generator according to International Special Committee on Radio Interference (CISPR) 16-1-1 standard using Fast Fourier Transform (FFT) technique for Electromagnetic Compatibility (EMC) Testing. The pulse generator is configured to source a pulse signal for each CISPR frequency band A, B and C respectively and the signal is then split into two paths using a splitter. A delay line is inserted into one path of them as a trigger signal to allow the sampling head of digital sampling oscilloscope to capture the signal from the other path. After that, the data is recorded and transferred to the computer using Labview software via a GPIB interface. This signal waveform is now analyzed using FFT and calculated on Matlab to compare with the standard. Finally, the calibration results are shown with uncertainty budget.

The emergence of advanced cryptographic protocols has promoted the developments of many applications, such as secure multi-party computation (MPC). For this reason, new symmetric-key primitives have been designed to natively support the finite field $$\mathbb {F}_p$$ with odd characteristic for better efficiencies. However, some well-studied symmetric cryptanalytic methods and techniques over $$\mathbb {F}_2^n$$ cannot be applied to these new primitives over $$\mathbb {F}_p$$ directly. Considering less standard design approaches adopted in these novel MPC-friendly ciphers, these proposals are in urgent need of full investigations; generalizations of the traditional cryptanalytic tools and techniques to $$\mathbb {F}_p$$ will also contribute to better understand the security of these new designs. In this paper, we first show that the Fast Fourier Transform (FFT) technique for the estimations of correlation, introduced by Collard et al. at ICISC 2007, can be applied to $$\mathbb {F}_p$$ and significantly improves the complexity of Matsui’s Algorithm 2 over $$\mathbb {F}_p$$ . Then, we formalize the differential-linear (DL) cryptanalysis to $$\mathbb {F}_p$$ . Inspired by the differential-linear connectivity table (DLCT) introduced by Bar-On et al. at EUROCRYPT 2019, we also include the DLCT into the consideration, and find the relation between DLCT and differential distribution table (DDT) over $$\mathbb {F}_p$$ . Finally, we mount key recovery attacks on a version of HADESMiMC, which is a SHARK-like MPC-friendly block cipher proposed by Grassi et al. at EUROCRYPT 2020. We denote this version as HADESMiMC-128 in this paper. For linear cryptanalysis with the FFT technique, we can attack 7 rounds of HADESMiMC-128. For DL cryptanalysis, a 7-round key recovery attack of HADESMiMC-128 is also mounted but with better time and data complexity. It should be noted that the attacks are still far from threatening the security of the full 14-round HADESMiMC-128.

In two-phase bubbly flow, measurement of liquid and bubble velocity is a necessity to understand fluid characteristic. The conventional ultrasonic velocity profiler (UVP), which has been known as a nonintrusive measurement technique, can measure velocity profile of liquid and bubble simultaneously by applying a separation technique for both phases (liquid and bubble) and transparent test section is unnecessary. The aim of this study was to develop a new technique for separating liquid and bubble velocity data in UVP method to measure liquid and bubble velocity profiles separately. The technique employs only single resonant frequency transducer and a simple UVP system. An extra equipment is not required. Fast Fourier Transform (FFT) based frequency estimator paralleled with other signal processing techniques, which is called as proposed technique, was proposed to measure liquid and bubble velocity separately. The experimental facility of two-phase bubbly flow in the vertical pipe was constructed. Firstly, the Doppler frequency estimation by using the FFT technique was evaluated in single-phase liquid flow. Results showed that FFT technique showed a good agreement with autocorrelation and maximum likelihood estimator. Then, separation of liquid and bubble velocity was demonstrated experimentally in the two-phase bubbly flow. The proposed technique confirmed that liquid and bubble velocity could be measured efficiently.

The solutions to the geodetic boundary value problem of predicting geoid undulations from gravity observations are complicated by the non-level observation surface, thus requiring the use of Molodensky’s theory instead of Stokes’ theory. For practical computations, Molodensky’s equations, as well as Stokes’ equation, may be reformulated as convolution integrals that can be efficiently evaluated by Fast Fourier Transform (FFT) techniques. A link between the two approaches, to a first-order approximation, is provided by use of the classical terrain correction, which can also be evaluated by FFT techniques. The terrain correction is also required for terrain reductions, which smooth the gravity data using topographic density assumptions, yielding more reliable gridding of free-air gravity anomalies and smaller and smoother Molodensky corrections. These reductions can be used in a remove-restore fashion as pre- and post-processing steps, analogously to the direct and indirect effects of shifting the topographic masses below the geoid.

To improve the numerical efficiency, the Fast Fourier Transform (FFT) technique was facilitated in Parker–Oldenburg’s method for a regional gravimetric Moho recovery, which assumes the Earth’s planar approximation. In this study, we extend this definition for global applications while assuming a spherical approximation of the Earth. In particular, we utilize the FFT technique for a global Moho recovery, which is practically realized in two numerical steps. The gravimetric forward modeling is first applied, based on methods for a spherical harmonic analysis and synthesis of the global gravity and lithospheric structure models, to compute the refined gravity field, which comprises mainly the gravitational signature of the Moho geometry. The gravimetric inverse problem is then solved iteratively in order to determine the Moho depth. The application of FFT technique to both numerical steps reduces the computation time to a fraction of that required without applying this fast algorithm. The developed numerical producers are used to estimate the Moho depth globally, and the gravimetric result is validated using the global (CRUST1.0) and regional (ESC) seismic Moho models. The comparison reveals a relatively good agreement between the gravimetric and seismic models, with the RMS of differences (of 4–5 km) at the level of expected uncertainties of used input datasets, while without the presence of significant systematic bias.

The paper presents a comparison among three different techniques for harmonic analysis on the sphere and the ellipsoid. The EGM2008 global geopotential model has been used up to degree and order 360 in order to create gravity anomaly fields on both the sphere and the ellipsoid as the function fields of the current investigation. Harmonic analysis has then been carried out to compute the dimensionless potential coeficients using the created function fields. Three different harmonic analysis techniques have been applied: the least-squares technique, the Fast Fourier Transform (FFT) technique and the Gauss-Legendre numerical integration technique. The computed coeficients in spherical harmonics have then been compared with EGM2008 (in the frequency domain) and the computed fields on the sphere and the ellipsoid have been compared with fields created by EGM2008 up to degree and order 360 (in the space domain) in order to estimate the accuracy of the three different harmonic analysis techniques used within the current investigation. The results proved that the least-squares technique gives the best accuracy both in frequency and space domain. The FFT technique provides quite good results in a very short cpu time. The Gauss-Legendre technique gives the worst results among the presented techniques, but still the residuals in the space domain are negligibly small.

Block cipher ARIA was first proposed by some South Korean experts in 2003, and later, it was established as a Korean Standard block cipher algorithm by Korean Agency for Technology and Standards. In this paper, we focus on the security evaluation of ARIA block cipher against the recent zero-correlation linear cryptanalysis. In addition, Partial-sum technique and FFT (Fast Fourier Transform) technique are used to speed up the cryptanalysis, respectively. We first introduce some 4-round linear approximations of ARIA with zero-correlation, and then present some key-recovery attacks on 6/7-round ARIA-128/256 with Partial-sum technique and FFT technique.The key-recovery attack with Partial-sum technique on 6-round ARIA-128 needs 2^{123.6}known plaintexts (KPs), 2^{121} encryptions and 2^{90.3} bytes memory, and the attack with FFT technique requires 2^{124.1} KPs, 2^{121.5} encryptions and 2^{90.3}bytes memory. Moreover, applying Partial-sum technique, we can attack 7-round ARIA-256 with 2^{124.6} KPs, 2^{203.5} encryptions and 2^{152} bytes and 7-round ARIA-256 employing FFT technique, requires 2^{124.7} KPs, 2^{209.5} encryptions and 2^{152} bytes. Our results are the first zero-correlation linear cryptanalysis results on ARIA.

A comparison of a spectral analysis using the fast Fourier transform (FFT) and the maximum entropy method (MEM) was carried out in the case in which both methods can be performed, that is, when several time acquisitions can be recorded. A summary of the principles of the MEM is given. Then the main properties of this method are investigated, that is, influence of the MEM order on the spectrum accuracy, validity of the low-frequency plateau usually given by this technique, overlapping of spectra measured for different frequency bandwidths, and influence of a slow evolution of the amplitude of the signal fluctuations. The susceptibility to pitting corrosion of type 304 stainless steel and type 304 modified by molybdenum (Mo) by means of ion implantation was studied. The power spectral densities (PSD) measured with the FFT and MEM techniques are in reasonable agreement, except for low electrochemical current noises (ECN) buried in the parasitic noise generated by the power supply. In that case, the FFT technique is more appropriate than the MEM, which gave qualitative results only. The type 304 stainless steel showed a large metastable pitting leading to only a few macroscopic pits, whereas the type 304 Mo-implanted specimen showed a very low metastable pitting leading to many hemispheric pits covered by the Mo-implanted layer, under which localized corrosion occurred.

Active power measurement of an inverter-fed induction motor in a photovoltaic water pumping system is considered. An improved digital method based on FFT (fast Fourier transform) techniques is used. Measurement results show the advantages of this method over currently available power measurement apparatus. This technique is applied at the intermediate AC stage for inverter output power measurement corresponding to the power consumed by the motor. Thus, both motor and power converter behavior can be analyzed from the resulting power estimation according to efficiency or the electromechanical criterion. It is shown that the digital techniques used for the power measurement make it possible to obtain reliable results.

Forecasting is the first step to deal with the new generation of renewable energy systems. The accuracy of the forecasting techniques is very important. Time series technique is one of the powerful tools used for forecasting, but it works well with stationary data. In addition, non-stationary time series can cause unexpected behaviors or create a non-existing relationship between two variables. This work was motivated by the need of detecting the seasonality and trend for a given data. The trend and seasonality components are very important in dealing with forecasting. Based on the trend and seasonality we could use clustered regions and feed the clustered regions to a forecasting technique like ANN, WNN or Kalman Filtering. Then aggregating the forecasted data back again for a better performance. In this paper we use Fast Fourier Transform (FFT) in Box-Jenkins approach instead of Autocorrelation Function (ACF) for the seasonality and trend detection. The present study is validated using visual inspection, statistical tests and time series decomposition in identifying the trend and the seasonality by applying them to wind speed time series. The results of FFT technique and ACF are compared to the results of the most well-known techniques. The results show that some methods have minor limitations in determining either the trend or the seasonality compared to FFT.

ABSTRACTThe dominant upward‐continuation technique used in the potential‐field geophysics industry is the fast Fourier transform (FFT) technique. However, the spline‐based upward‐continuation technique presented in this paper has some advantages over the FFT technique. The spline technique can be used to carry out level‐to‐uneven surface 2D and 3D potential‐field upward continuation. An example of level‐to‐uneven surface upward continuation of 3D magnetic data using the spline technique is shown, and it is evident that the continued anomalies are very close to the theoretical values. The spacing can be irregular. Synthetic examples using the spline technique to continue noise‐contaminated gravity and magnetic data upward to an altitude of 15 km on irregular grids are shown. Gaussian noise with a zero mean and a standard deviation of 1% does not cause much error and can readily be tolerated. Through comparison with the FFT technique, it is found that for low‐altitude gravity and magnetic upward continuation, both the FFT technique and the spline technique are suitable; for high‐altitude upward continuation, the FFT technique is inaccurate, whereas the spline technique works very well. Also, upward continuation by the spline technique has a smaller edge effect than upward continuation by the FFT technique. The spline‐based upward continuation technique works fairly well even when the periphery of a grid is not quiet: it is rather robust in general. A real example shows that the spline technique can be employed to perform upward continuation of total‐field magnetic data and to de‐emphasize near‐surface noise.