Showing papers on "Split-radix FFT algorithm published in 2008"

Measuring power system harmonics and interharmonics by an improved fast Fourier transform-based algorithm

Abstract: The fast Fourier transform (FFT) has been widely used for the signal processing because of its computational efficiency. Because of the spectral leakage and picket-fence effects associated with the system fundamental frequency variation and improperly selected sampling time window, a direct application of the FFT algorithm with a constant sampling rate may lead to inaccurate results for continuously measuring power system harmonics and interharmonics. An improved FFT-based algorithm to measure harmonics and interharmonics accurately is proposed. In the proposed algorithm, a frequency-domain interpolation approach is adopted to determine the system fundamental frequency, and the interpolatory polynomial method is applied to reconstruct the sampled time-domain signal; it is followed by using the FFT to calculate the actual harmonic components. Then, the frequency-domain interpolation is again applied to find the interharmonic components. The performance of the proposed algorithm is validated by testing the actual measured waveforms. Results are compared with those obtained by directly applying a typical FFT algorithm and by the IEC grouping method. It shows that the solutions determined by the proposed algorithm are more accurate, and a reasonable computational efficiency is maintained.

Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for DCTs and DSTs

Abstract: In this paper, we systematically derive a large class of fast general-radix algorithms for various types of real discrete Fourier transforms (real DFTs) including the discrete Hartley transform (DHT) based on the algebraic signal processing theory. This means that instead of manipulating the transform definition, we derive algorithms by manipulating the polynomial algebras underlying the transforms using one general method. The same method yields the well-known Cooley-Tukey fast Fourier transform (FFT) as well as general radix discrete cosine and sine transform algorithms. The algebraic approach makes the derivation concise, unifies and classifies many existing algorithms, yields new variants, enables structural optimization, and naturally produces a human-readable structural algorithm representation based on the Kronecker product formalism. We show, for the first time, that the general-radix Cooley-Tukey and the lesser known Bruun algorithms are instances of the same generic algorithm. Further, we show that this generic algorithm can be instantiated for all four types of the real DFT and the DHT.

A Tutorial on Fast Fourier Sampling

Abstract: This article describes a computational method, called the Fourier sampling algorithm. The algorithm takes a small number of (correlated) random samples from a signal and processes them efficiently to produce an approximation of the DFT of the signal. The algorithm offers provable guarantees on the number of samples, the running time, and the amount of storage. As we will see, these requirements are exponentially better than the FFT for some cases of interest.

On the Fixed-Point Accuracy Analysis of FFT Algorithms

Abstract: In this paper, we investigate the effect of fixed-point arithmetics with limited precision for different fast Fourier transform (FFT) algorithms. A matrix representation of error propagation model is proposed to analyze the rounding effect. An analytic expression of overall quantization loss due to the arithmetic quantization errors is derived to compare the performance with decimation-in-time (DIT) and decimation-in-frequency (DIF) configurations. From the simulation results, the radix-2 DIT FFT algorithm has better accuracy in term of signal-to-quantization-noise ratio (SQNR). Based on the results, a simple criterion of wordlength optimization is proposed to yield comparable accuracy with fewer bit budget.

An Efficient VLSI Architecture for Normal I/O Order Pipeline FFT Design

Abstract: In this paper, an efficient VLSI architecture of a pipeline fast Fourier transform (FFT) processor capable of producing the normal output order sequence is presented. A new FFT design based on the decimated dual-path delay feed-forward data commutator unit by splitting the input stream into two half-word streams is first proposed. The resulting architecture can achieve full hardware efficiency such that the required number of adders can be reduced by half. Next, in order to generate the normal output order sequence, this paper also presents a sequence conversion method by integrating the conversion function into the last-stage data commutator module.

Inter-Harmonic Identification Using Group-Harmonic Weighting Approach Based on the FFT

Abstract: The fast Fourier transform (FFT) is still a widely-used tool for analyzing and measuring both stationary and transient signals with power system harmonics in power systems. However, the misapplications of FFT can lead to incorrect results caused by some problems such as aliasing effect, spectral leakage and picket-fence effect. A strategy of group-harmonic weighting distribution is proposed for system-wide inter-harmonic evaluation in power systems. The proposed algorithm can restore the dispersing spectral leakage energy caused by the FFT, and calculate the power distribution proportion around the adjacent frequencies at each harmonic to determine the inter-harmonic frequency. Therefore, not only high-precision in integer harmonic measurement by the FFT can be retained, but also the inter-harmonics can be identified accurately, particularly under system frequency drift. The numerical examples are presented to verify the performance of the proposed algorithm.

An Efficient FFT Engine With Reduced Addressing Logic

Abstract: In this study, an improved butterfly structure and an address generation method for fast Fourier transform (FFT) are presented. The proposed method uses reduced logic to generate the addresses, avoiding the parity check and barrel shifters commonly used in FFT implementations. A general methodology for radix-2 N-point transforms is derived and the signal flow graph for a 16-point FFT is presented. Furthermore, as a case study, a 16-point FFT with 32-bit complex numbers is synthesized using a CMOS 0.18 mum technology. The circuit gate count analysis indicates that significant logic reduction can be achieved with improved throughput compared to the conventional implementations.

Cost-Effective Triple-Mode Reconfigurable Pipeline FFT/IFFT/2-D DCT Processor

Abstract: This investigation proposes a novel radix-42 algorithm with the low computational complexity of a radix-16 algorithm but the lower hardware requirement of a radix-4 algorithm. The proposed pipeline radix-42 single delay feedback path (R42SDF) architecture adopts a multiplierless radix-4 butterfly structure, based on the specific linear mapping of common factor algorithm (CFA), to support both 256-point fast Fourier transform/inverse fast Fourier transform (FFT/IFFT) and 8times8 2D discrete cosine transform (DCT) modes following with the high efficient feedback shift registers architecture. The segment shift register (SSR) and overturn shift register (OSR) structure are adopted to minimize the register cost for the input re-ordering and post computation operations in the 8times8 2D DCT mode, respectively. Moreover, the retrenched constant multiplier and eight-folded complex multiplier structures are adopted to decrease the multiplier cost and the coefficient ROM size with the complex conjugate symmetry rule and subexpression elimination technology. To further decrease the chip cost, a finite wordlength analysis is provided to indicate that the proposed architecture only requires a 13-bit internal wordlength to achieve 40-dB signal-to-noise ratio (SNR) performance in 256-point FFT/IFFT modes and high digital video (DV) compression quality in 8 times 8 2D DCT mode. The comprehensive comparison results indicate that the proposed cost effective reconfigurable design has the smallest hardware requirement and largest hardware utilization among the tested architectures for the FFT/IFFT computation, and thus has the highest cost efficiency. The derivation and chip implementation results show that the proposed pipeline 256-point FFT/IFFT/2D DCT triple-mode chip consumes 22.37 mW at 100 MHz at 1.2-V supply voltage in TSMC 0.13-mum CMOS process, which is very appropriate for the RSoCs IP of next-generation handheld devices.

A Novel Algorithm for Accurate Frequency Measurement Using Transformed Consecutive Points of DFT

Abstract: A novel algorithm based on discrete Fourier transform (DFT) to estimate the frequency of power system is proposed. The algorithm that we called transformed discrete Fourier transform (TDFT) involves transforming consecutive points of DFT of voltage signals to reduce the leakage components. The algorithm has the following merits: It is immune to inter-harmonics as well as harmonics; it has simple and easy implementation; and it has good performance both in steady and dynamic states. What is more, it can keep high precision in a very wide frequency deviation range, for example, 40-60 Hz. Simulation experiments validate this algorithm can track power system frequency precisely.

Parallel Implementations of the Split-Step Fourier Method for Solving Nonlinear Schrodinger Systems

Abstract: We present a parallel version of the well-known Split-Step Fourier method (SSF) for solving the Nonlinear Schrodinger equation, a mathematical model describing wave packet propagation in fiber optic lines. The algorithm is implemented un- der both distributed and shared memory programming paradigms on the Silicon Graphics/Cray Research Origin 200. The 1D Fast-Fourier Transform (FFT) is par- allelized by writing the 1D FFT as a 2D matrix and performing independent 1D sequential FFTs on the rows and columns of this matrix. We can attain almost perfect speedup in SSF for small numbers of processors depending on both problem size and communication contention. The parallel algorithm is applicable to other computational problems constrained by the speed of the 1D FFT.

Fast computation of general fourier transforms on graphics processing units

Abstract: Described is a technology for use with general discrete Fourier transforms (DFTs) performed on a graphics processing unit (GPU). The technology is implemented in a general library accessed through GPU-independent APIs. The library handles complex and real data of any size, including for non-power-of-two data sizes. In one implementation, the radix-2 Stockham formulation of the fast Fourier transform (FFT) is used to avoid computationally expensive bit reversals. For non-power of two data sizes, a Bluestein z-chirp algorithm may be used.

Multifunctional signal transform engine

Abstract: A technique involves using a fast Fourier transform (FFT) module to transform multiple different types of signals. This may be accomplished using one or more of three techniques: logic within the FFT module can enable different processing depending upon a processing state, the FFT module can be called iteratively to transform a signal that is larger than the FFT implemented in the FFT module, the FFT module can be used for parallel transformation of multiple signals that are smaller than the FFT implemented in the FFT module. Thus, a single FFT module can be used to transform a first type of signal (e.g., WIFI) and a second type of signal (e.g., GPS) if configured according to the technique.

A family of scalable FFT architectures and an implementation of 1024-point radix-2 FFT for real-time communications

Abstract: The paper presents a family of architectures for FFT implementation based on the decomposition of the perfect shuffle permutation, which can be designed with variable number of processing elements. This provides designers with a trade-off choice of speed vs. complexity (cost and area.). A detailed case study is provided on the implementation of 1024-point FFT with 2 processing elements using 45 nm process technology, including area, timing, power and place-and-route results.

Convolution-Based Trigonometric Interpolation of Band-Limited Signals

Abstract: This paper presents a method to obtain a trigonometric polynomial that accurately interpolates a given band-limited signal from a finite sequence of samples. The polynomial delivers accurate approximations in the range covered by the sequence, except for a short frame close to the range limits. Besides, its accuracy increases exponentially with the frame width. The method is based on using a band-limited window in order to reduce the truncation error of a convolution series. It is shown that the polynomial can be efficiently constructed and evaluated using algorithms designed for the discrete Fourier transform (DFT). Specifically, two basic procedures are presented, one based on the fast Fourier transform (FFT), and another based on a recursive update algorithm for the short-time FFT. The paper contains three applications. The first is a variable fractional delay (VFD) filter, which consists of a short-time FFT combined with the evaluation of a trigonometric polynomial. This filter has low complexity and can be implemented using CORDIC rotations. The second is the interpolation of nonuniform Fourier summations, where the proposed method eliminates the need to interpolate any kernel sample. Finally, the third can be viewed as a generalization of the FFT convolution algorithm and makes it possible to interpolate the output of an finite-impulse-response (FIR) filter efficiently.

Real FFT based on graphic processing unit for image processing

Abstract: By analysis of general real Fast Fourier Transform(FFT)algorithm,an improved real FFT algorithm is presented based on Graphic Processing Unit(GPU).A general real FFT can reduce the computation consumption of the conventional complex FFT algorithm by about 40%,and the presented real FFT algorithm improves the reduction to 50%.On the basis of the specific configuration of data storage,the presented real FFT algorithm can be applied in two directions continuously to generate the 2D Fourier spectrum,also the parallel real FFT transform can be implemented by using the 1D complex FFT function from the CUFFT library.The precision and the efficiency of the presented real FFT are inspected by Wiener filter's application,image processing results demonstrate that the presented real FFT algorithm shows operating properly and working well.With the help of the presented real FFT,Wiener filter can restore a 2 048×2 048 8-bit image by motion speed of 19.26 ms,which is 2.34 times as compared with that of the Wiener filter based on complex FFT on GPU,and is 37.46 times that of the Wiener filter based on real FFT on CPU.The experiment results show that the presented algorithm is practical for image processing.

Comparison of different FFT implementations in the encrypted domain

Abstract: Signal processing modules working directly on the encrypted data could provide an elegant solution to application scenarios where valuable signals should be protected from a malicious processing device. In this paper, we compare different implementations of the discrete Fourier transform (DFT) in the encrypted domain. Both radix-2 and radix-4 fast Fourier transforms (FFTs) will be defined using the homomorphic properties of the underlying cryptosystem. We derive the maximum size of the sequence that can be transformed by using the different implementations and we provide computational complexity analyses and comparisons. The results show that the radix-4 FFT is best suited for an encrypted domain implementation.

A Pipelined Memory-efficient Architecture for Ultra-long Variable-size FFT Processors

Abstract: A scheme of ultra-long variable-size pipelined FFT processor is presented and a prototype is implemented with one FPGA, which may compute various 4n (n = 1 ~ 10) points FFT at a speed as high as 150 MHz. The solutions are to transform the one-dimension FFT to two-dimension repeatedly, and propose an efficient twiddle-factor memory compression method. Based on two techniques storage resource of FFT processor can be reduced largely.

Improved Algorithm for Non-integer Harmonics Analysis Based on FFT Algorithm and Neural Network

Abstract: By using an artificial neural network(ANN) model,high measurement accuracy of integer harmonics can be obtained.Combining the windowed fast Fourier transform(FFT) algorithm with the improved ANN model,the paper provides an improved algorithm for analysis of non-integer harmonics in electric power systems.Firstly,the Hanning-windowed FFT algorithm processes the sampled signal.By this time,the number of harmonics and the orders of harmonics are obtained.Secondly,choose the number of neural nodes according to the number of harmonics.Thirdly,choose the initial values of orders of harmonics according to the result obtained from the Hanning-windowed FFT algorithm.Moreover,an adaptive algorithm for the adjusting step of the order of harmonic is presented.Finally,by using the improved linear ANN model obtained in the paper,non-integer harmonics can be detected precisely.Through such processing,the time of iterations is shortened and the convergence rate of neural network is raised thereby.The simulation results show that close non-integer harmonics can be separated from a signal with higher accuracy and better real-time by using the improved algorithm presented.

A New Method for Phase Difference Measurement Based on FFT with Negative Frequency Contribution

Abstract: While measuring the phase difference between two sine signals with a low frequency using the FFT method,the precision declines evidently and the method even becomes ineffective,for the contribution of negative frequency is neglected in the model.A new method for phase difference measurement that contains the contribution of negative frequency is proposed.New formulas for phase difference calculation are presented in the case of rectangular window and Hanning window respectively.Simulation results show that the precision of the new method,especially in the case of Hanning window,is so high that it almost approaches the lower limit of double precision arithmetic.Under noise background,the precision of the new method is also higher than that of the FFT method.The new method has the virtue of simplicity and practicability,and is proved to be applicable especially for signals with a quite low frequency or with a frequency close to the Nyquist frequency.

Memory-based FFT/IFFT processor and design method for general sized memory-based FFT processor

Abstract: For a large size FFT computation, this invention decomposes it into several smaller sizes FFT by decomposition equation and then transform the original index from one dimension into multi-dimension vector. By controlling the index vector, this invention could distribute the input data into different memory banks such that both the in-place policy for computation and the multi-bank memory for high-radix structure could be supported simultaneously without memory conflict. Besides, in order to keep memory conflict-free when the in-place policy is also adopted for I/O data, this invention reverses the decompose order of FFT to satisfy the vector reverse behavior. This invention can minimize the area and reduce the necessary clock rate effectively for general sized memory-based FFT processor design.

A revisited and stable Fourier transform method for affine jump diffusion models

Abstract: In the last decade, fast Fourier transform methods (i.e. FFT) have become the standard tool for pricing and hedging with affine jump diffusion models (i.e. AJD), despite the FFT theoretical framework is still in development and it is known that the early solutions have serious problems in terms of stability and accuracy. This fact depends from the relevant computational gain that the FFT approach offers with respect to the standard Fourier transform methods that make use of a canonical inverse Levy formula. In this work we revisit a classic FT method and find that changing the quadrature algorithm and using alternative, less flawed, representation for the pricing formulas can improve the computational performance up to levels that are only three time slower than FFT can achieve. This allows to have at the same time a reasonable computational speed and the well known stability and accuracy of canonical FT methods.

Note on the FFT Based Computational Code and Its Application

Abstract: The discrete convolution based Fast Fourier Transform algorithm (DC-FFT) has been successfully applied in numerical simulation of contact problems. The algorithm is revisited from a mathematical point of view, equivalent to a Toeplitz matrix multiplied by a vector. The nature of the convolution property permits one to implement the algorithm with fewer constraints in choosing the computational domains. This advantageous feature is explored in the present work, and is expected to be beneficial to many tribological studies.Copyright © 2008 by ASME

Methods and systems using fft window tracking algorithm

Abstract: Techniques for the adjustment of a position of Fast Fourier Transform (FFT) window are provided. The adjustment may be based on the condition that the length of channel impulse response is larger than the length of cyclic prefix. The technique may determine a position of the FFT window that attempts to maximize carrier-to-noise (C/N) ratio value measured at the receiver.

Finding Significant Fourier Transform Coefficients Deterministically and Locally

Abstract: Computing the Fourier transform is a basic building block used in numerous applications. For data intensive applications, even the O(N log N) running time of the Fast Fourier Transform (FFT) algorithm may be too slow, and sub-linear running time is necessary. Clearly, outputting the entire F ourier transform in sub-linear time is infeasible, nevertheless, in many applications it suffices to find only the τ-significant Fourier transform coefficients, that is, the Fourier coefficients whose magnitude is at leas t τ-fraction (say, 1%) of the energy (i.e., the sum of squared Fourier coefficients). We call algorithm s achieving the latter SFT algorithms. In this paper we present a deterministic algorithm that finds the τ-significant Fourier coefficients of functions f over any finite abelian group G in time polynomial in log|G|, 1/τ and L1(b) (for L1(b) denoting the sum of absolute values of the Fourier coefficien ts of f ). Our algorithm is robust to random noise. Our algorithm is the first deterministic and efficient ( i.e., polynomial in log|G|) SFT algorithm to handle functions over any finite abelian groups, as well as th e first such algorithm to handle functions over ZN that are neither compressible nor Fourier-sparse. Our analysis is the first to show robustness to noise in the context of deterministic SFT algorithms. Using our SFT algorithm we obtain (1) deterministic (universal and explicit) algorithms for sparse Fourier approximation, compressed sensing and sketching; (2) an algorithm solving the Hidden Number Problem with advice, with cryptographic bit security implications; and (3) an efficient decoding algorithm in the random noise model for polynomial rate variants of Homomorphism codes and any other concentrated & recoverable codes.

Modified algorithm for real time sar signal processing

Abstract: The generation of the picture out of the SAR raw data is a computational intensive task. Both range compression and azimuth compression utilized Fast Fourier Transform (FFT) algorithms and Inverse Fast Fourier Transform (IFFT) in order to perform convolution with respective reference signal. Thus FFT and IFFT occupied about 70% of the total computation operation in SAR image formation. In this paper a modified algorithm based on conventional FFT is proposed to optimize the computation performance. It is shown that the proposed algorithm can essentially achieve better performance with minimum computational burden compare to conventional FFT.

A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

Abstract: The discrete Fourier transform (DFT) is the base of modern signal processing 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N2 log N) respectively Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm DFT has two properties One property is that DFT is energy conservation transform The other property is that many DFT coefficients are close to zero The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper The quantum algorithm for convolution estimation is also presented in this paper Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible

Efficient computation of the DFT of a 2N - point real sequence using FFT with CORDIC based butterflies

Abstract: In this paper, an efficient method for computation of the DFT of a 2N - point real sequence by using DIT FFT with CORDIC based butterflies is presented. Most of the real world applications use long real valued sequences. By using FFT with CORDIC based butterflies, the space required on ROM and also the time required to perform the operation can be reduced. Further, to calculate the 2N - point DFT, by using one N-point DFT involving complex valued data, efficiency is almost doubled.