scholarly journals Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Rui Li ◽  
Yong Huang ◽  
Jia-Bao Liu
Keyword(s):  
Fourier Transform ◽  
Computational Complexity ◽  
Linear Equation ◽  
Discrete Fourier Transform ◽  
Delta Function ◽  
Gabor Transform ◽  
Gabor Analysis ◽  
Analysis Window ◽  
Orthogonality Constraint ◽  
Infinite Sequences

The long-periodic/infinite discrete Gabor transform (DGT) is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of delta function, the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform (FFT). The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms.

Research on the Existence of Genuine Inter-Harmonic Components Based on the Component Appearance Rate

2014 ◽  
Vol 875-877 ◽  
pp. 1847-1851
Author(s):  
Xiao Dong Yuan ◽  
Qun Li ◽  
Jin Hui ◽  
Bin Chen
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Theoretical Perspective ◽  
Harmonic Spectrum ◽  
Measured Signal ◽  
Time Frequency ◽  
Appearance Rate ◽  
The Matrix ◽  
Analysis Window ◽  
Harmonic Components

The inter-harmonic spectrum of an electrical voltage or current from discrete Fourier transform can not only be caused by genuine inter-harmonic components, but can also be caused by other system disturbances. Therefore, the existence determination of genuine inter-harmonic s from the spectrum becomes the premise for further calculation of inter-harmonic parameters. From the theoretical perspective, this paper firstly analyzes and points out that the waveform difference among each cycle in the analysis window is the cause of the existence of inter-harmonic spectrum, and then presents a method to determine the existence of genuine inter-harmonic components, which is based on inter-harmonic time-frequency contour chart and the component appearance rate. The presented method firstly performs continuous discrete Fourier transform on the captured signal with certain duration and obtains the corresponding absolute time-frequency matrix, and then the genuine inter-harmonics can be distinguished based on the component appearance rate of the matrix and the criterion threshold. The method is easy to implement with clear principle, it can distinguish the genuine inter-harmonic s from the measured signal. The analysis on several data groups from real measurements verifies the effectiveness and the practicability of the method.

scholarly journals Determining the Weights of A Fourier Series Neural Network on the Basis of the Multidimensional Discrete Fourier Transform

2008 ◽  
Vol 18 (3) ◽  
pp. 369-375 ◽  
Author(s):  
Krzysztof Halawa
Keyword(s):  
Neural Network ◽  
Fourier Transform ◽  
Fourier Series ◽  
Computational Complexity ◽  
Discrete Fourier Transform ◽  
Dynamic Systems ◽  
Low Computational Complexity

Determining the Weights of A Fourier Series Neural Network on the Basis of the Multidimensional Discrete Fourier TransformThis paper presents a method for training a Fourier series neural network on the basis of the multidimensional discrete Fourier transform. The proposed method is characterized by low computational complexity. The article shows how the method can be used for modelling dynamic systems.

scholarly journals Peak-to-Average Power Ratio Reduction Method Based on Partial Transmit Sequence and Discrete Fourier Transform Spreading

Electronics ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 642
Author(s):  
Nahla Al Harthi ◽  
Zhongfeng Zhang ◽  
Daejin Kim ◽  
Seungwon Choi
Keyword(s):  
Fourier Transform ◽  
Computational Complexity ◽  
Discrete Fourier Transform ◽  
Computer Simulations ◽  
Orthogonal Frequency Division Multiplexing ◽  
Complexity Analysis ◽  
Average Power ◽  
Power Ratio ◽  
Partial Transmit Sequence ◽  
Ber Performance

Recently, filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) has received increasing attention from researchers, owing to its merits and superior spectral efficiency. High peak-to-average power ratio (PAPR) occurs in approximately all multicarrier systems, including FBMC/OQAM, and may cause bit-error-rate (BER) degradation if not appropriately handled. Conventional PAPR reduction methods for orthogonal frequency division multiplexing (OFDM), such as partial transmit sequence (PTS), selective mapping (SLM), and discrete Fourier transform (DFT) spreading, are ineffective in FBMC/OQAM because of the different structure of the symbols. This study proposes a novel method combining DFT spreading and PTS methods to reduce the PAPR of FBMC/OQAM systems with reasonable computational complexity. Numerical results obtained from various computer simulations show that the proposed method achieves a noticeable enhancement in the PAPR performance of the FBMC/OQAM signal compared to other existing methods without affecting the BER performance. Further, the computational complexity analysis and BER performance of the proposed method are presented in comparison to typical existing methods. From our computer simulations, the proposed method reduces the PAPR by approximately 32.8% compared to that of the conventional methods, and the BER performance is improved by 25% with a high-power amplifier effect.

High-resolution spectral analysis (HSA) vs. discrete fourier transform (DFT)

2021 ◽  
Vol 263 (4) ◽  
pp. 2555-2566
Author(s):  
Roland Sottek ◽  
Thiago Lobato
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
High Resolution ◽  
Discrete Fourier Transform ◽  
Human Perception ◽  
Standard Technique ◽  
Frequency Resolution ◽  
Time Bandwidth Product ◽  
Analysis Window ◽  
Almost All

The Discrete Fourier Transform (DFT) is the standard technique for performing spectral analysis. It is used in the form of the well-known fast implementation (FFT) in almost all areas that deal with signal processing. However, the DFT algorithm has some limitations in terms of its resolution in time and frequency: the higher the time resolution, the lower the frequency resolution, and vice versa. The product of time (analysis duration) and analysis bandwidth (frequency resolution) is a constant. DFT results depend on the analysis window used (type and duration), although the physical signal properties do not change. The High-Resolution Spectral Analysis (HSA) method, published at the ASST '90, considers the window influence through spectral deconvolution and thus leads to a much lower time-bandwidth product, correlating better with human perception. Recently, variants of the HSA have been used for a psychoacoustic standard (roughness). Additionally, HSA is planned for a new model of fluctuation strength. This paper describes the improvements made to the HSA algorithm as well as its robustness against noise, and compares application results for both methods: HSA and DFT.

Multirate and DFT Based Fast Parallel Algorithm for 2-D Inverse Discrete Gabor Transform

2013 ◽  
Vol 411-414 ◽  
pp. 1377-1380
Author(s):  
Juan Juan Gu ◽  
Liang Tao
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Computational Complexity ◽  
Parallel Algorithm ◽  
Gabor Transform ◽  
Parallel Channel ◽  
Inverse Discrete Fourier Transform ◽  
Real Time Image ◽  
Parallel Channels ◽  
Time Image

Multirate and DFT based fast parallel algorithm for the 2-D inverse discrete Gabor transform (IDGT) is presented. A 2-D synthesis filterbank is designed for the 2-D IDGT. The parallel channels in the filterbank have a unified structure and can apply the 2-D fast inverse discrete Fourier transform (IFFT) algorithm to reduce the computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate. Thus, the proposed parallel algorithm is attractive for real time image processing.

Filterbank and DFT Based Fast Parallel Discrete Gabor Transform for Image Representation

2012 ◽  
Vol 461 ◽  
pp. 444-447 ◽  
Author(s):  
Juan Juan Gu ◽  
Liang Tao
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Computational Complexity ◽  
Parallel Algorithm ◽  
Image Representation ◽  
Gabor Transform ◽  
Parallel Channel ◽  
Real Time Image ◽  
Parallel Channels ◽  
Time Image

Fast parallel algorithm for the 2-D discrete Gabor transform (DGT) is presented based on 2-D filterbank. A 2-D analysis filterbank is designed for the 2-D DGT. The parallel channels in the filterbank have a unified structure and can apply the 2-D inverse fast discrete Fourier transform (IFFT) algorithm to reduce the computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate. Thus, the proposed parallel algorithm is attractive for real time image processing.

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