Adaptive algorithm based on FFT for frequency estimation

To assess the insulation condition of capacitive apparatus, on-line monitoring of dielectric loss angle is an effective measure. Harmonic analysis algorithm is used to calculate dielectric loss angle traditionally, this method can effectively suppress the DC (Direct Current) offset and harmonic interference. However, when the power system frequency fluctuates, the synchronous sampling condition is difficult to meet, so, traditional harmonic analysis method can produce leakage of spectrum and picket-fence effect, which greatly affects the accuracy of dielectric loss angle measurement. In order to reduce this adverse effect, this paper proposes a method called hamming windowed interpolated DFT (Discrete Fourier Transform) algorithm based on modified ideal sampling frequency. Time series analysis based on modified ideal sampling frequency can be used to modify the time series in non-synchronous sampling condition to meet synchronous sampling condition. Hamming windowed interpolated DFT algorithm can inhibit leakage of spectrum and picket-fence effect. Firstly this paper analyzes the principle of traditional DFT algorithm and the reason that causes leakage of spectrum and picket-fence effect in non-synchronous sampling condition. Secondly, the principle of hamming windowed interpolated DFT algorithm based on modified ideal sampling frequency is elaborated. Finally this paper presents the simulation result which shows that the improved approach has higher accuracy.

The signal processing technique is one of the principal tools for diagnosing power quality (PQ) issues in electrical power systems. The Discrete Fourier Transform (DFT) is a frequency analysis technique used to process power system signals and identify PQ problems. However, the DFT algorithm may lead to spectral leakage and picket-fence effect problems for asynchronously sampled signals that contain harmonic, inter-harmonic, and flicker components. To resolve this shortcoming, a hybrid method for frequency estimation based on a second-level DFT approach and a frequency-domain interpolation algorithm to obtain the accurate fundamental frequency of a power system is proposed in this paper. This method uses a second-level DFT to compute the cosine and sine parts for the fundamental frequency components of the acquired signals. Then, a frequency-domain interpolation approach is adopted to determine the amplitude ratio for the cosine and sine parts of the system’s fundamental frequency. A set of mixed signals with harmonic, inter-harmonic, and flicker components with the fundamental frequency deviation is used. The evaluation results demonstrate the superiority of the new method over other approaches for assessing asynchronously sampled signals contaminated with noise, harmonic, inter-harmonic, and flicker components.

The design of both area-efficient and reliable VLSI arrays for computation of the complex N-point discrete Fourier transform (DFT) is considered. C.D. Thompson's VLSI model of computation (1979) is used to quantify the area required by wiring and the achievable period. Four architectures using the fast two-dimensional (2-D) algorithm for the DFT that achieve the maximum throughput per chip area are presented. The first two use N-element 2-D meshes requiring N+2N/sup 3/2/ multiplications and 1+2 square root N periods per DFT. The first uses in place data I/O and can be made systolic with Goertzel's algorithm. The second is systolic with row parallel I/O. The third and fourth architectures both use pipelined DFT blocks of length square root N connected by a pipelined matrix transposer. The third uses systolic 2-D meshes for the short DFTs with period square root N. The fourth uses pipelined butterfly networks implementing standard FFT algorithms for the short DFTs, but only N(1+log/sub 2/ N) multiplications per DFT, thus preserving maximum throughput per unit area. The technique of algorithm-based fault-tolerance applies directly to all four architectures with only fractional redundant overhead. >

This paper presents a method to derive efficient frequency estimators from the Discrete Fourier Transform (DFT) of the signal. These estimators are very similar to the phase-based Discrete Fourier Spectrum (DFS) interpolators but have the advantage to allow any type of analysis window (and especially non-rectangular windows). As a consequence, it leads to better estimations in the case of a complex tone (cisoid) perturbed by other cisoids. Overall, our best estimator leads to results similar to those of phase vocoder and reassignment estimators but at a lower complexity, since it is based on a single Fast Fourier Transform (FFT) computation.

In order to realize the FFT algorithm more flexibly and effectively, this paper analyzed four kinds of amplitude spectrum or power spectrum correction methods, that is, ratio correction method, energy centrobaric correction method, phase difference method and FFT + FT spectrum analysis method. On this basis, a double-window function spectrum estimation algorithm was introduced, which was a kind of conjoint analysis algorithm with rectangular window function and improved window function. The algorithm could improve the amplitude estimation accuracy in the case of not reducing the frequency resolution. The effectiveness of this algorithm was proved by using MATLAB software. The simulation results show that the double-window function spectrum estimation algorithm significantly decreases the amplitude estimation error brought by the picket fence effect, and realizes the optimization of FFT algorithm.

The Discrete Fourier Transform (DFT), which can be calculated efficiently by the Fast Fourier Transform (FFT), is one of the most commonly used tools for frequency estimation of a multi-frequency exponential signal. However, the performance of the FFT is inherently affected by spectral leakage when non-coherent sampling occurs. The Chirp-Z Transform (CZT), which can refine the spectrum to the narrowband range of the source signal accurately, can be generalized to a special form of DFT. This paper proposes a CZT based algorithm which can estimate frequencies of the multi-frequency exponential signal accurately. In our method, the CZT bin, as a nonlinear equation, is firstly used to describe the correspondence among the frequencies, amplitudes, phases and the observed spectrum. Then, the above nonlinear equation is rewritten as a linear equation with unknown frequencies. We further extend the proposed method to the Discrete-time Fourier Transform (DTFT), zero-padding FFT and DFT, which are the special cases of the CZT. We also give the derivation procedure of theoretical variance of our method. In our method, the spectrum leakage is fully considered as useful information to establish the linear equation set. Therefore, it can estimate the frequencies of multi-frequency exponential signal with high accuracy. Simulation results verify the performance of the proposed method.

Abstract. Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex). It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT) engines. However, in face of the Software Defined Radio (SDR) development, more general (parallel) processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.

Chapter 10 - Discrete and Fast Fourier Transforms (DFT, FFT)

The detection of tonal signals with unknown frequencies is an important area of study in underwater signal processing. A common approach to address this issue is to use the Discrete Fourier Transform (DFT) for observations. When a tone does not lie precisely at the discrete DFT frequency point, its energy will leak to adjacent frequency point. This phenomenon is known as scalloping loss or Picket Fence Effect (PFE). PFE leads to the degradation of detection performance based on DFT. This paper studies the problem of robust detection in the case of PFE. A coherently-averaged power processor utilizing the information of adjacent frequency bins is designed. The results of simulations and experiments show that the proposed method is robust against PFE, and is highly suitable for tone detection in practical circumstances.

In today’s era, it is important to analyze and utilize various signals in industrial or laboratory applications. Measured signals provide critical information about the controlled system, which can be contained precisely within a narrow frequency range. Many methods and algorithms exist to process such signals in both the time and frequency domains. In particular, signal processing in the frequency domain is primary in industrial practice because dominant components within a specific narrow frequency band are sought. The discrete Fourier transformation (DFT) algorithm is the tool used in practice to find these frequency components. The DFT algorithm provides the full frequency spectrum with a higher number of calculation steps, and its spectrum frequency resolution is low. Therefore, research has focused on finding a method to achieve high-frequency spectrum resolution. An important factor in selecting the technique was that such an algorithm should be implementable on a microprocessor-based system under harsh industrial conditions. Research results showed that the DFT ZOOM method meets these requirements. The frequency zoom has many advantages but requires some modification. It is implemented in high-performance analyzers, but a thorough and detailed description of the respective algorithm is lacking in technical articles and literature. This article mathematically and theoretically describes the modified frequency zoom algorithm in detail. The steps of the frequency zoom, from creating an analytical signal through frequency shifting and decimation to the frequency analysis of the signal, are realized. The algorithm allows for the analysis of a signal with high-frequency resolution in a limited frequency band. A significant modification of DFT ZOOM is that of using the Hilbert transform to create an analytic signal. This resolves the aliasing issue caused by the overlap between fundamental and sideband spectra. Results from processing deterministic and stochastic signals using the modified DFT ZOOM are presented. The presented experimental results contribute to a more detailed frequency analysis of the signal. As part of this scientific research, the issues of frequency zoom were thoroughly addressed, solving the partial problems of this algorithm, both in theory and in the context of signal theory.

Discrete Fractional Fourier Transform (DFRFT) has received lots of attention in last two decades because of its superior benefits and wide applications in various fields. In this study we present a comparative analysis of the most famous algorithms for the computation of DFRFT. Analysis is done on the parameters like time complexity, accuracy, consistency, basic mathematical properties and generalization of Discrete Fourier Transform (DFT) and approximation of continuous Fractional Fourier Transform (FRFT). Main objective of the research is to portray the major advantages and disadvantages of the previously proposed algorithms so that appropriate algorithm may be selected as per requirements. On the basis of study it has been observed that there exist several definitions and algorithm for computing the DFRFT. These algorithms are based on different techniques, such as eigenvectors, chirp convolution, spectral decomposition, non-Fresnel integral, or orthogonal projection. Each of these algorithms has its own advantages and disadvantages. Despite of these developments, we still feel that there has been dire need of a standard definition and computing method for accurate and efficient computation of DFRFT.

Fast Fourier Transform (FFT) is used to obtain the Fourier spectrum of a periodic signal, but it is well known that special care must be taken to avoid severe distortions introduced by the sampling process. The major errors associated with this algorithm are spectral leakage and picket fence effect. This paper discusses the advancement in FFT algorithms for harmonic analysis in power system by applying windowed interpolation techniques. It is observed that the application of different WIFFT algorithms has different effects on the measuring accuracy. The advanced minimized sidelobe window (MSW) algorithm has better performance characteristics when compared to the conventional hanning and hamming windows adopted for harmonic analysis. By considering the practical harmonic data the hanning, hamming and MSW algorithms are validated using matlab programming. The simulation results demonstrate the effectiveness of hanning, hamming and MSW by considering the magnitude and phase angle error variations with respect to the harmonic order.

Machine Learning Algorithms have found their application is all the domain of engineering. In this work, we try to compare the performance of traditional signal processing algorithms and neural networks for the calculation of Discrete Fourier Transform. The Discrete Fourier Transform (DFT) is of greater importance in all areas of digital signal processing. Calculating the frequency spectrum of a signal is the fundamental goal of DFT. The phase, frequency, and magnitude of a signal's component sinusoids are all contained in its frequency spectrum. Given the importance of DFT, it is necessary to evaluate which algorithm or method is efficient and takes very less time in computing the results. In this paper, two different methods, namely Fast Fourier Transform (FFT), which is a tradition signal processing algorithm and Deep Neural Networks (DNN) are used to compute DFT on a random discrete signal and are compared based on the time taken to execute the algorithms.

This paper describes an implementation of the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). We show how the computation of the DFT and IDFT may be performed in Java and show why such operations are typically considered slow. This is a multi-part paper, in part 2, we discuss a speed up of the DFT and IDFT using a class of algorithms known as the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). Part 3 demonstrates the computation of the PSD (Power Spectral Density) and applications of the DFT and IDFT. The applications include filtering, windowing, pitch shifting and the spectral analysis of re-sampling.

The Fast Fourier Transform (FFT) is an efficient algorithm to calculate the Discrete Fourier Transform (DFT), which is often employed in Digital Signal Processing (DSP) and communication. In FFT, complex multiplication and addition units in the butterfly module consume most of the hardware resources. Compared to the addition operation, multiplication is more complicated. In this paper, the multiplier in the complex multiplication unit of the FFT is approximated. Four Radix-4 Booth multipliers with different approximation levels are proposed to reduce the hardware complexity. The pipeline FFT and the parallel FFT based on the proposed approximate multipliers are implemented and extensively evaluated. Compared with the state-of-the-art FFT designs, the LUTs amount is reduced up to 20.3% and 29.1% for pipeline and parallel FFTs, respectively. The power is reduced up to 69.9% for pipeline FFT, and the delay is reduced up to 45.7%. Moreover, the PSNR is reduced by less than 1dB in both pipeline FFT and parallel FFT. Proved by experiment results, the overall performance of the proposed designs is better than FFT designs using other approximate multipliers.