scholarly journals Iterative FFT-algorithms with high frequency resolution

2021 ◽  
pp. 121-134
Author(s):  
О.В. Осипов
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Spectral Characteristic ◽  
High Frequency ◽  
Iterative Algorithms ◽  
Digital Signal ◽  
Frequency Resolution ◽  
Training Process ◽  
Source Signal ◽  
Fft Algorithms

В работе представлены три итерационных алгоритма быстрого преобразования Фурье с прореживанием по времени, имеющие алгоритмическую сложность O (N·R·log2N), где R — частотное разрешение спектральной характеристики (отношение длины набора частот к длине N набора отсчетов исходного сигнала). Алгоритмы отличаются способами организации вычислений: некоторые используют обратную перестановку битов, другие — дополнительные массивы. Приведены подробные вычислительные графы, а также блок-схемы разработанных алгоритмов. Полученные результаты можно использовать для улучшения отечественной электроники и программного обеспечения, а также включать в учебный процесс при подготовке инженеров в области цифровой обработки сигналов. This paper presents three iterative algorithms for fast Fourier transform with decimation in time; these algorithms have the algorithmic complexity O (N·R·log2N), where R is the frequency resolution of the spectral characteristic (the ratio of the length of the frequency set to the length of the N set of samples of the source signal). The algorithms differ in the way they organize calculations: some use reverse bit permutation, while the others use additional arrays. Detailed computational graphs and flowcharts of the developed algorithms are provided. The results obtained can be used to improve domestic electronics and software as well as may be included in the training process for engineers in the field of digital signal processing.

The fast Fourier transform

2020 ◽  
pp. 134-189
Author(s):  
Rob H. Bisseling
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Weather Forecasting ◽  
Data Access ◽  
Regular Pattern ◽  
Matrix Products ◽  
Data Redistribution ◽  
Fft Algorithms ◽  
Matrix Vector

This chapter demonstrates the use of different data distributions in different phases of a parallel fast Fourier transform (FFT), which is a regular computation with a predictable but challenging data access pattern. Both the block and cyclic distributions are used and also intermediates between them. Each required data redistribution is a permutation that involves communication. By making careful choices, the number of such redistributions can be kept to a minimum. FFT algorithms can be concisely expressed using matrix/vector notation and Kronecker matrix products. This notation is also used here. The chapter then shows how permutations with a regular pattern can be implemented more efficiently by packing the data. The parallelization techniques discussed for the specific case of the FFT are also applicable to other related computations, for instance in signal processing and weather forecasting.

Digital Signal Processing for Step-Scan Fourier Transform Infrared Photoacoustic Spectroscopy

1997 ◽  
Vol 51 (4) ◽  
pp. 453-460 ◽  
Author(s):  
David L. Drapcho ◽  
Raul Curbelo ◽  
Eric Y. Jiang ◽  
Richard A. Crocombe ◽  
William J. McCarthy
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Digital Signal Processing ◽  
Phase Modulation ◽  
Modulation Frequency ◽  
Digital Signal ◽  
Sampling Depth ◽  
Ft Ir ◽  
Infrared Photoacoustic Spectroscopy ◽  
Additional Hardware

A software-based digital signal processing (DSP) method using the data system processor has been developed to demodulate the photoacoustic responses of a sample to the fundamental phase modulation frequency and its harmonic frequencies (up to the ninth harmonic) in step-scan FT-IR photoacoustic measurements, without the use of any additional hardware. The DSP algorithm and its sampling depth multiplexing advantages are compared to conventional hardware demodulation. Comparison of results from the DSP method to those from hardware demodulators are shown at both the phase modulation frequency and the harmonics, and application of the DSP method to step-scan photoacoustic measurements with phase modulation is discussed as it applies to obtaining depth profile information in heterogeneous materials.

scholarly journals Digital signal processing in telecommunications based on parametric discrete Fourier transform

2019 ◽  
Vol 30 ◽  
pp. 04010 ◽  
Author(s):  
Olga Ponomareva ◽  
Alexey Ponomarev ◽  
Natalya Smirnova
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Digital Signal Processing ◽  
Discrete Fourier Transform ◽  
Digital Signal ◽  
Discrete Transformation ◽  
Stochastic Properties

A generalization of the discrete Fourier transform in the form of a parametric discrete Fourier transform is proposed. The analytical and stochastic properties of the introduced discrete transformation are investigated. An example of the application of the parametric discrete Fourier transform in telecommunications is given - a generalization of the well-known Herzel algorithm

Classification of Women's Voices Using Fast Fourier Transform (FFT) Method

2021 ◽  
Vol 10 (1) ◽  
pp. 59
Author(s):  
Made Sri Ayu Apsari ◽  
I Made Widiartha
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Digital Signal Processing ◽  
Fast Fourier Transform ◽  
Digital Signal ◽  
Women's Voices ◽  
Mezzo Soprano

Everyone has a different kind of voice. Based on gender, voice type is divided into six parts, namely soprano, mezzo soprano, and alto for women; and tenor, baritone, and bass in men. Each type of sound has a different range and with different frequencies. This study classified the type of voice in women using the Fast Fourier Transform (FFT) method by recording the voices of each user which would then be processed using the FFT method to obtain the appropriate sound range. This research got results with an accuracy of up to 80%.The results obtained from this study are quite appropriate and it is proven that the FFT method can be used in digital signal processing.

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.

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