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.

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 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.

scholarly journals A Study of Parameters Setting of the STADZT

10.14311/1654 ◽  
2012 ◽  
Vol 52 (5) ◽  
Author(s):  
Václav Turoň
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Stationary Signals ◽  
Zolotarev Polynomials ◽  
Non Stationary Signal ◽  
Short Time ◽  
Main Influence

This paper deals with the new time-frequency Short-Time Approximated Discrete Zolotarev Transform (STADZT), which is based on symmetrical Zolotarev polynomials. Due to the special properties of these polynomials, STADZT can be used for spectral analysis of stationary and non-stationary signals with the better time and frequency resolution than the widely used Short-Time Fourier Transform (STFT). This paper describes the parameters of STADZT that have the main influence on its properties and behaviour. The selected parameters include the shape and length of the segmentation window, and the segmentation overlap. Because STADZT is very similar to STFT, the paper includes a comparison of the spectral analysis of a non-stationary signal created by STADZT and by STFT with various settings of the parameters.

scholarly journals How can the Fourier Transform be Used in Radio Astronomy to Perform Spectral Analysis of Pulsars

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Pranesh Kumar ◽  
Arthur Western
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Low Frequency ◽  
Radio Frequency Interference ◽  
Radio Waves ◽  
Folding Algorithm ◽  
Radio Signals ◽  
Multiple Characteristics ◽  
The Fourier Transform

The analysis of pulsars is a complicated procedure due to the influence of background radio waves. Special radio telescopes designed to detect pulsar signals have to employ many techniques to reconstruct interstellar signals and determine if they originated from a pulsating radio source. The Discrete Fourier Transform on its own has allowed astronomers to perform basic spectral analysis of potential pulsar signals. However, Radio Frequency Interference (RFI) makes the process of detecting and analyzing pulsars extremely difficult. This has forced astronomers to be creative in identifying and determining the specific characteristics of these unique rotating neutron stars. Astrophysicists have utilized algorithms such as the Fast Fourier Transform (FFT) to predict the spin period and harmonic frequencies of pulsars. However, FFT-based searches cannot be utilized alone because low-frequency pulsar signals go undetected in the presence of background radio noise. Astrophysicists must stack up pulses using the Fast Folding Algorithm (FFA) and utilize the coherent dedispersion technique to improve FFT sensitivity. The following research paper will discuss how the Discrete Fourier Transform is a useful technique for detecting radio signals and determining the pulsar frequency. It will also discuss how dedispersion and the pulsar frequency are critical for predicting multiple characteristics of pulsars and correcting the influence of the Interstellar Medium (ISM).

Wavelet-based Segmentation and Feature Extraction of Heart Sounds for Intelligent PDA-based Phonocardiography

2007 ◽  
Vol 46 (02) ◽  
pp. 135-141 ◽  
Author(s):  
H. Nazeran
Keyword(s):  
Feature Extraction ◽  
Spectral Analysis ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Digital Signal ◽  
Heart Sounds ◽  
Segmentation Algorithm ◽  
Frequency Resolution ◽  
Time Frequency ◽  
Frequency Information

Summary Objectives : Many pathological conditions of the cardiovascular system cause murmurs and aberrations in heart sounds. Phonocardiography provides the clinician with a complementary tool to record the heart sounds heard during auscultation. The advancement of intracardiac phonocardiography combined with modern digital signal processing techniques has strongly renewed researchers' interest in studying heart sounds and murmurs.The aim of this work is to investigate the applicability of different spectral analysis methods to heart sound signals and explore their suitability for PDA-based implementation. Methods : Fourier transform (FT), short-time Fourier transform (STFT) and wavelet transform (WT) are used to perform spectral analysis on heart sounds. A segmentation algorithm based on Shannon energy is used to differentiate between first and second heartsounds. Then wavelet transform is deployed again to extract 64 features of heart sounds. Results : The FT provides valuable frequency information but the timing information is lost during the transformation process. The STFT or spectrogram provides valuable time-frequency information but there is a trade-off between time and frequency resolution. Waveletanalysis, however, does not suffer from limitations of the STFT and provides adequate time and frequency resolution to accurately characterize the normal and pathological heartsounds. Conclusions : The results show that the wavelet-based segmentation algorithm is quite effective in localizing the important components of both normal and abnormal heart sounds. They also demonstrate that wavelet-based feature extraction provides suitable feature vectors which are clearly differentiable and useful for automatic classification of heart sounds.

Improvement of frequency resolution using sub-binstructure in discrete Fourier transform

2021 ◽  
Author(s):  
Manabu Sato ◽  
Yuuki Kimura ◽  
Junpei Masuta ◽  
Tetsuo Kosaka ◽  
Izumi Nishidate
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Resolution
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