scholarly journals A New Integer-to-Integer Transform

2020 ◽  
Author(s):  
Rajesh Cherian Roy
Keyword(s):  
Number Theory ◽  
Fourier Transform ◽  
Closed Form ◽  
Detailed Analysis ◽  
Discrete Fourier Transform ◽  
Simple Form ◽  
Integer Transform ◽  
Signal Structure ◽  
Salient Features

This chapter presents a detailed analysis of an integer-to-integer transform that is closely related to the discrete Fourier transform, but that offers insights into signal structure that the DFT does not. The transform is analyzed for its underlying properties using concepts from number theory. Theorems are given along with proofs to help establish the salient features of the transform. Two kinds of redundancy exist in the transform. It is shown how redundancy implicit in the transform can be eliminated to obtain a simple form. Closed-form formulas for the forward and inverse transforms are presented.

scholarly journals Multi-Tone Frequency Estimation Based on the All-Phase Discrete Fourier Transform and Chinese Remainder Theorem

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5066
Author(s):  
Xiangdong Huang ◽  
Lu Cao ◽  
Wei Lu
Keyword(s):  
Fourier Transform ◽  
Closed Form ◽  
Discrete Fourier Transform ◽  
High Efficiency ◽  
Chinese Remainder Theorem ◽  
Frequency Estimation ◽  
High Accuracy ◽  
Single Frequency ◽  
Tone Frequency ◽  
Spectrum Correction

The closed-form robust Chinese Remainder Theorem (CRT) is a powerful approach to achieve single-frequency estimation from noisy undersampled waveforms. However, the difficulty of CRT-based methods’ extension into the multi-tone case lies in the fact it is complicated to explore the mapping relationship between an individual tone and its corresponding remainders. This work deals with this intractable issue by means of decomposing the desired multi-tone estimator into several single-tone estimators. Firstly, high-accuracy harmonic remainders are calculated by applying all-phase Discrete Fourier Transform (apDFT) and spectrum correction operations on the undersampled waveforms. Secondly, the aforementioned mapping relationship is built up by a novel frequency classifier which fully captures the amplitude and phase features of remainders. Finally, the frequencies are estimated one by one through directly applying the closed-form robust CRT into these remainder groups. Due to all the components (including closed-form CRT, the apDFT, the spectrum corrector and the remainder classifier) only involving slight computation complexity, the proposed scheme is of high efficiency and consumes low hardware cost. Moreover, numeral results also show that the proposed method possesses high accuracy.

Processor arrays for two-dimensional discrete Fourier transform

1993 ◽  
Vol 140 (2) ◽  
pp. 101
Author(s):  
D.V. Korchev ◽  
Ju.S. Kanevsky
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Two Dimensional ◽  
Processor Arrays

Digital Image Watermarking in Discrete Fourier Transform domain

2018 ◽  
Vol 6 (5) ◽  
pp. 16-22
Author(s):  
Ningombam Jimson ◽  
◽  
◽  
Kattamanchi Hemachandran
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Digital Image ◽  
Image Watermarking ◽  
Digital Image Watermarking ◽  
Transform Domain ◽  
Fourier Transform Domain

APPLICATION OF UNCONVENTIONAL METHODS FOR FREQUENCY ANALYSIS IN ACOUSTICS

Akustika ◽  
2020 ◽  
Vol 36 (36) ◽  
pp. 25-32
Author(s):  
Jaroslav Smutný ◽  
Dušan Janoštík ◽  
Viktor Nohál
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Analysis ◽  
Mathematical Analysis ◽  
Measured Data ◽  
Application Area ◽  
Acoustic Response ◽  
Recommendations For Practice ◽  
Unconventional Methods ◽  
Frequency Area

The goal of this study is to familiarize a wider professional public with not fully known procedures suitable for processing measured data in the frequency area. Described is the use of the so-called Multi-taper method to analyze the acoustic response. This transformation belongs to a group of nonparametric methods outgoing from discrete Fourier transform, and this study includes its mathematical analysis and description. In addition, the use of respective method in a specific application area and recommendations for practice are described.

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