Fast Fourier Transform Computation Research Articles

Preliminary insights on fast GNSS signal capture using SFT and FFT frequency shift

Global Navigation Satellite Systems (GNSS) are the cornerstone of modern navigation and positioning technology. In this paper, we introduce an innovative approach to GNSS signal acquisition, specifically designed to enhance the performance and speed of the signal lock-on process with real-world applications in mind. Our proposed algorithm leverages advanced mathematical tools, including Fast Fourier Transform (FFT) and Inverse FFT, to streamline the acquisition process. Notably, it eliminates the need for an Intermediate Frequency (IF) down mixer, simplifying hardware and potentially reducing power consumption in GNSS receivers. One key breakthrough is using the FFT's "circle shift" to handle Doppler frequency offsets resulting from relative satellite-receiver motion. This method significantly reduces the computational burden during Doppler frequency search, ensuring a faster and more efficient lock-on to satellite signals. Furthermore, we exploit the sparse nature of GNSS signals in the reverse FFT calculation, utilizing a Sparse Fourier Transform (SFT) for efficient processing. This innovation allows quicker reverse FFT computations, pivotal in the acquisition process. Through extensive simulations, we demonstrate the superior performance of our improved algorithm. Its speed and reliability make it well-suited for many practical GNSS applications, such as vehicle navigation, precision agriculture, surveying, and geolocation services. By enhancing acquisition efficiency, our approach contributes to more accurate, responsive, and energy-efficient GNSS positioning, benefiting users in both civilian and industrial sectors.

An ultra-precise Fast Fourier Transform

The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency) amplitude and phase while suppressing spectral leakage.

IMPLEMENTATION OF FAST FOURIER TRANSFORM (FFT) FOR INFANT CRYING DETECTION

Babies cry based on the discomfort felt by the baby which is a reflex such as when a hungry baby will suck his hand and then he will start crying, hunger can be interpreted from the baby's crying. At each of the baby's cries, when each crying pattern was responded to with the solution applied to the previous baby, each baby would stop crying. For this reason, to carry out this solution, a research was carried out to identify the pattern recognition of the sound of a baby's cry using the fast fourier transform (FFT) method with several different frequency ranges. The voice recording process is stored in digital form in the form of frequency-based sound spectrum waves, where signals that were previously in the time domain will be changed in the frequency domain. The sounds that will be distinguished in this study include the sounds of crying babies, adults, and colliding objects. This can be obtained through several stages, namely sound sample recording, sampling, signal cutting, frame blocking, final normalization, hamming window, and finally the FFT calculation process. From these series of stages, the results of the frequency range of baby crying are 101-1863 Hz, for adults the frequency range is 101-1376 Hz and for the sound of colliding objects 101-2233 Hz.

An ultra-precise Fast Fourier Transform

The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies, amplitudes and phases; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase while suppressing spectral leakage.

F3Net: Fast Fourier Filter Network for Hyperspectral Image Classification

In the hyperspectral image (HSI) classification, there are numerous deep learning-based research routes that have emerged recently. Among them, two methodologies attract our attention. One is CNN-based classification and the other is transformer-based classification. The essence of these two methodologies is to interchange information locally or at a long distance for HSI pixels in the spatial or spectral-spatial domain. There are two principles underlying this essence—the information mixing mechanism and the information mixing domain. Although both CNN-based and transformer-based have made efforts in these two principles and obtained favorable classification results, there is still room for improvement in terms of accuracy and efficiency. To further enhance the accuracy and efficiency under the two principles, fast Fourier transform (FFT) is introduced to HSI classification and a fast Fourier filter is designed to mix information efficiently in the frequency domain by means of FFT. The parametric-free characteristic and fast computation of FFT can assist us in efficiently learning interactions among features in the frequency domain. Furthermore, a fast Fourier filter block is built upon the fast Fourier filter for repeatedly using as a basic block. In addition, we propose a spectral-spatial convolution tokenizer (SSCT) to extract shallow features and prepare spectral-spatial tokens for fast Fourier filter blocks. Finally, by employing SSCT and fast Fourier filter blocks, a novel deep neural network architecture—fast Fourier filter network (F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> Net) is proposed for HSI classification. F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> Net-P as a pyramidal variant of F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> Net is also investigated. Experimental results on four datasets comprehensively evaluate our models and indicate that they are competitive with several current state-of-the-art methods, especially when the training samples are extremely limited. Specifically, F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> Net-P achieves the highest accuracy of 97.25%, 98.08%, 97.49% and 97.95% on the four datasets, respectively, outperforming second best compared model by 1.49%, 2.03%, 2.14% and 1.94%.

Avoiding the bit-reversed ordering in parallel multi-digit multiplication based on FFT

The paper for the parallel model of computation, a modification of the method of implementing the multiplication of multi-digit integers based on the fast Fourier transform (FFT) avoiding the bit-reversed ordering is proposed. The paper researches the calculation of FFT according to the “butterfly” scheme based on decimation-in- frequency and decimation-in-time methods, an input signal with elements in direct and bit-reversed order, with an increase and decrease in the number Fourier series coefficients at each step of the "butterfly", the use of a list of Fourier series coefficients in direct and bit-reversed order. The standard FFT-based multiplication algorithm uses the same “butterfly” operation to compute the forward and inverse Fourier transforms. The paper analyzes two combinations of the FFTFDN–FFTTBN and FFTFBN–FFTTDN “butterfly” calculation schemes for calculating forward and inverse discrete Fourier transforms (DFT) in the case of implementing the multi-digit operation in parallel computational model to exclude bit-reversed permutation. A scheme for distributing calculations among four processors is proposed, in which forward and inverse Fourier transform calculations are localized within one parallel processor. The proposed modification does not reduce the computational complexity in terms of the number of complex operations, but due to the exclusion of bit-reversed permutation, the number of synchronization commands between processors and data is reduced, which reduces the algorithm execution time. The scheme can be adapted to distribute the computations among a larger number of processors. Four algorithms for implementing FFT based on decimation-in-frequency and decimation-in-time methods, an input vector with elements in direct and bit-reversed orders are presented. To check the result of the calculation, the algorithm of multiplication avoiding the steps of bit-reversed ordering was implemented in the APL programming language. An example of calculation is given in the form of a table.

An ultra-precise fast fourier transform

<h2>Abstract</h2> The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, is often used to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy' from spectral peaks may ‘leak' into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT, like many other DSP algorithms, is a discrete time approximation of continuous time mathematics. This paper describes a new FFT calculation which uses two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained from each windowing function applied to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase. This technique addresses FFT limitations as follows: (1) spectral peak parameters are calculated directly, unrestricted by FFT frequency step discretization; (2) the windowing functions have narrowband characteristics which attenuate and localize spectral leakage; (3) the windowing functions incorporate a Romberg Integration mechanism to overcome the discrete/continuous time approximation.

One-Step Calculation Circuit of FFT and Its Application

Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are core components in the field of signal processing. However, in the existing research, there is no fully analog circuit that can realize the one-step calculation of FFT. Therefore, in this paper, an analog circuit that can calculate FFT and its inverse transform IFFT in one-step is proposed. First, a circuit that can realize complex number operations is designed. On the basis of this structure, a fully analog circuit that can realize fast and efficient computing of FFT and IFFT in one-step is proposed. In addition, different coefficient matching can be obtained to achieve arbitrary points of FFT and IFFT by adjusting the resistance value of the memristor, which has good programmability. Specific examples are given in the paper to evaluate the proposed method. The PSPICE simulation results show that the average accuracy is above 99.98%. More importantly, the calculation speed has been greatly improved compared with MATLAB simulation. Finally, the proposed circuit can be used to quickly solve convolution operation, and the average accuracy can reach 99.95%.

Polycrystalline simulations of in-reactor deformation of recrystallized Zircaloy-4 tubes: Fast Fourier Transform computations and mean-field self-consistent model

Fuel cladding and structural components made of zirconium alloys, used in light and heavy water nuclear reactors, exhibit, during normal operation, significant in-reactor deformation. Fast Fourier Transform (FFT) simulations have been conducted on large grain aggregates to simulate the in-reactor behavior of recrystallized Zircaloy-4. Original constitutive equations have been proposed to account, at the microscopic scale, for thermal creep, irradiation creep and irradiation induced growth. The evolution of irradiation defects with irradiation is taken into account, especially to deduce the local growth strain. A good description of the in-reactor behavior is obtained with irradiation defects evolution consistent with Transmission Electron Microscopy observations. The FFT simulations are compared to a self-consistent model. A good agreement is obtained when the behavior is linear (irradiation creep and growth) while the nonlinear response (thermal creep) is underestimated by the self-consistent model. The FFT simulations are also compared to the lower-bound model which neglects the interactions between grains. The lower-bound model underestimates the growth strain proving the importance of using an accurate polycrystalline model to predict the growth strain from the knowledge of the irradiation defect evolution.

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.

Design and Implementation of AGU based FFT Pipeline Architecture

Present it is most needful task to get various applications with parallel computations by using a Fast Fourier Transform (FFT) and the derived outputs should be in regular format. This can be achieved by using an advanced technique called Multipath delay commutator (MDC) Pipelining FFT processor and this processor will be capable to perform the computation of a different data streams at a time. In this paper the design and implementation of AGU based Pipelined FFT architecture is done Caluclation of a butterfly is done within 2 cycles by the instructions proposed. A Data Processing Unit (DPU) is employed in this pipeline architecture and supports the instructions & an FFT Adress Generation Unit (FAGU) caluclates butterfly input & output data adresses automatically. The DPU proposed sysyem requires less area compared to commericial DSP chips. Futhermore, the proposed FAGU reduces the number of FFT computation cycles. The FFT design architecture will have real data paths. With various FFT sizes, different radix & various parallesim levels, the FFT can be mapped to the pipeline architecture. The most attractive feature of the pipelined FFT architecture is it consists of bit reversal operation so it requires little number of registers and better throughput.

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.

Customizing FFT with FMA for China Accelerator

Recently, Fast Fourier Transform (FFT) was introduced to study pattern characterization in textiles. Accelerators are a promising platform to accelerate large-scale FFT computation. However, current accelerating FFT only uses the accelerator to compute, but uses a CPU as a mere task controller. Additionally, a specified interface for FFT is built into the China accelerator (CA), which severely restricts FFT parallelization and performance. Hence, we transform four multiplications and six additions into six Fused Multiply Add (FMA) operations, then reduce total float operations by 40%, assisted by FMAs equipped with a Vector Processing Unit (VPE). Moreover, we propose an Interface Adapter (IA) to cater to a specified interface and a Fused Algorithm for Interface Adapter (FAIA) to fully use both the CA and CPU to compute large-scale FFT with coordination. Experimental results validated successful performance.

Fast calculation of computer generated hologram based on single Fourier transform for holographic three-dimensional display

We present an efficient method for the fast calculation of computer generated hologram (CGH). The 3D object is split into sub-layers according to its depth information. A 2D all-in-focus image is generated by sequential tiling all the layers in one plane. A Fourier hologram that contains all the information of 3D object is calculated from the fast Fourier transform (FFT) of the reassembled 2D image. By multiplying a pre-calculated multifocal off-axis digital phase mask (DPM) to the Fourier hologram, the content of each layer is axially relocated to different depth in the Fourier transform optical system to reconstruct the 3D object. The computation speed of the proposed method is greatly improved with only single FFT calculation process. Both of simulation and experimental results proves the validation of the proposed method.

A novel fast time jamming analysis transmission selection technique for radar systems

The jamming analysis transmission selection (JATS) sub-system is used in radar systems to detect and avoid the jammed frequencies in the available operating bandwidth during signal transmission and reception. The available time to measure the desired frequency spectrum and select the non-jammed frequency for transmission is very limited. A novel fast time (FAT) technique that measures the channel spectrum, detects the jamming sub-band and selects the non-jammed frequency for radar system transmission in real time is proposed. A JATS sub-system has been designed, simulated, fabricated and implemented based on FAT technique to verify the idea. The novel FAT technique utilizes time-domain analysis instead of the well-known fast Fourier transform (FFT) used in conventional JATS sub-systems. Therefore, the proposed fast time jamming analysis transmission selection (FAT-JATS) sub-system outperforms other reported JATS sub-systems as it uses less FPGA resources, avoids time-delay occurred due to complex FFT calculations and enhances the real time operation. This makes the proposed technique an excellent candidate for JATS sub-systems.

Comparison of Discrete Fourier Transform and Fast Fourier Transform with Reduced Number of Multiplication and Addition Operations

Fast Fourier Transform is an advanced algorithm for computing Discrete Fourier Transform efficiently. Although the results available from the operation of Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are same, but exploiting the periodicity and symmetry property of phase factor Fast Fourier Transform computes the Discrete Fourier Transform using reduced number of multiplication and addition operations. The basic structure used in the operations of Fast Fourier Transform is the Butterfly structure. For the implementation of Fast Fourier Transform the two methods are used such as decimation in time (DIT) and decimation in frequency (DIF). Both the methods give same result but for decimation in time of Fast Fourier Transform bit reversed inputs are applied and for decimation in frequency of Fast Fourier Transform normal order inputs are applied, and the result is reversed again. In this paper, operations for DFT and FFT have been discussed and shown with examples. It is found that generalized formula for FFT have been described same in the books, but the expressions in the intermediate computations for the first decimation and second decimation are different in the various books of Digital Signal Processing. The expressions in the intermediate computation of FFT described in different books are broadly compared in this paper

Parameter Estimation of Polynomial-Phase Signals

Introduction . Polynomial phase signals frequently appear in radar, sonar, communication and technical applications. Therefore, estimation of polynomial phase coefficients of such signals is an urgent problem in signal theory. Currently, a large number of estimation algorithms have been proposed. The best way is the maximum likelihood (ML) method. However, its implementation is associated with a multidimensional retrieval, which makes the method unsuitable for practical implementation. A number of alternative strategies have been developed to circumvent the ML difficulties. These strategies are very close to optimal. Among them one can single out the HAF-algorithm based on the computation of the High order Ambiguity Function and the CPF algorithm, which uses the computation of the Cubic Phase Function and produces very accurate estimates for signals with the quadratic frequency modulation. However, both algorithms have obvious drawbacks. The HAF algorithm pro-duces a large number of combinatorial noise components. The CPF algorithm is limited in its implementation to the third order polynomial signals and does not use fast algorithms, such as the Fast Fourier Transform. Aim. Synthesis of an estimation algorithm that produces a small number of noise combinatorial components and uses the Fast Fourier Transform computation algorithms to find coefficient estimates of an arbitrary order phase polynomial. Materials and methods. In the paper a concept of a decisive function was introduced. It was calculated so that its phase contained only a first-order monomial with a coefficient equal to the highest coefficient of the signal phase polynomial. Results. A new estimation algorithm was proposed able to use Fast Fourier Transform computation algorithms to find estimates. Each polynomial coefficient was estimated on the basis of a unified procedure, which reduced the number of combinatorial noise components in an estimate search. Conclusions. The synthesized algorithm gives asymptotically efficient estimates for lower signal-to-noise ratios in comparison with the HAF-algorithm.

2-D Systolic Array architecture of CBNS based Discrete Hilbert Transform Processor

This paper proposes an optimized design of Discrete Hilbert Transform (DHT) processor using Complex Binary Number System (CBNS). The conventional implementation of DHT based on the “divide and conquer” approach involves two separate computational units for the real and imaginary parts, which requires a large silicon area and increases the path delay. In contrast, incorporation of CBNS in transformation techniques facilitates complex-valued signal processing through a single computational unit.The CBNS-DHT processor has been designed using the standard computational method of Fast Fourier Transform (FFT). The 2-D Systolic Array architecture along with a novel processing element has been proposed for CBNS based Complex-valued FFT (CFFT) and Inverse FFT (CIFFT) computations. The architecture of CBNS-CFFT/CIFFT has been extended to develop the CBNS-DHT processor on the Zynq-7000 family, XC7Z020-CLG484 FPGA platform. A comparative performance analysis of CBNS-DHT and Normal Binary Number System (NBNS)-DHT highlights the efficiency of CBNS-DHT in terms of VLSI parameters — silicon area, path-delay and memory utilization. CBNS-CFFT shows significant improvement in path delay and area consumption as compared to NBNS-CFFT for both Twiddle Factors and FFT size, which proves that CBNS based CFFT and DHT processor design is more efficient in terms of speed and area requirements.

A Signal Reconstruction Method Based on Quadratic Spline Interpolation Applied in Power Quality Analysis for SCM-TTU

Aiming at the accurate and quick analysis of power quality especially of harmonic problem in power system, interpolation approaches should be applied if the samples collected by hardware are not matched with Fast Fourier Transform (FFT) calculation. A quadratic spline interpolation algorithm is proposed on Single Chip Micyoco-Transformer Terminal Unit (SCM-TTU) in this paper. This algorithm considers the continuous of interpolation function and also the first derivative in order to improve the accuracy. It could be applied before FFT calculation to avoid the mismatch of sampling rates. A simulation with mathematic example and also an application with SCM-TTU contains the harmonics from 2nd to 50th orders are experimented, results are presented to show the effectiveness.

A tensorial fundamental measure density functional theory for the description of adsorption in substrates of arbitrary three-dimensional geometry

Fundamental measure theory (FMT) is commonly considered within classical density functional theory (DFT) to describe inhomogeneous hard-sphere (HS) fluids. As opposed to the original FMT of Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)], the dimensional interpolation FMT (DI-FMT) is a specific version of FMT which is well adapted to accurately describe the freezing of HSs and adsorption in extreme confinements by including tensorial weighted densities. The computation of these weighted densities is generally performed analytically for specific simple scenarios (e.g., planar, cylindrical, or spherical geometries), and this method is challenging to apply to pores of generic geometry. On the other hand, numerical approaches, using fast Fourier transform (FFT) techniques, can be adapted to deal with arbitrary 3D geometries. Computations with tensorial weights are, however, generally not considered with these approaches. In our current work, the FFT computation of weighted densities is detailed for tensorial quantities. We present a DI-FMT in general 3D computational space, for an arbitrary pore geometry, to obtain density profiles of pure HS fluids or mixtures. The other thermodynamic quantities, such as surface tension or excess adsorption, can then be determined by using the standard DFT framework. As an example of the implementation of the method, we present the results for the adsorption on a hard-wall model, representative of the solid structure of an anisotropic zeolite cavity.