scholarly journals Generalized Orthogonal Discrete W Transform and Its Fast Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jichao Sun ◽  
Zhengping Zhang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fast Algorithm ◽  
Basis Functions ◽  
Real Sequence ◽  
Communication Signal ◽  
Numerical Computing ◽  
Orthogonal Transform ◽  
Generalized Orthogonal ◽  
And Storage

Based on the generalized discrete Fourier transform, the generalized orthogonal discrete W transform and its fast algorithm are proposed and derived in this paper. The orthogonal discrete W transform proposed by Zhongde Wang has only four types. However, the generalized orthogonal discrete W transform proposed by us has infinite types and subsumes a family of symmetric transforms. The generalized orthogonal discrete W transform is a real-valued orthogonal transform, and the real-valued orthogonal transform of a real sequence has the advantages of simple operation and facilitated transmission and storage. The generalized orthogonal discrete W transforms provide more basis functions with new frequencies and phases and hence lead to more powerful analysis and processing tools for communication, signal processing, and numerical computing.

scholarly journals Expansions of Functions Based on Rational Orthogonal Basis with Nonnegative Instantaneous Frequencies

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaona Cui ◽  
Suxia Yao
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Fast Algorithm ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Almost Everywhere ◽  
Integrable Functions ◽  
Instantaneous Frequencies ◽  
Square Integrable Functions

We consider in this paper expansions of functions based on the rational orthogonal basis for the space of square integrable functions. The basis functions have nonnegative instantaneous frequencies so that the expansions make physical sense. We discuss the almost everywhere convergence of the expansions and develop a fast algorithm for computing the coefficients arising in the expansions by combining the characterization of the coefficients with the fast Fourier transform.

scholarly journals Fast Jacket-Haar Transform with Any Size

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Guibo Liu ◽  
Dazu Huang ◽  
Dayong Luo ◽  
Wang Lei ◽  
Ying Guo ◽  
...  
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Fast Algorithm ◽  
Ecg Signal ◽  
Arbitrary Length ◽  
Haar Transform ◽  
Ecg Signal Processing ◽  
Simulation Results ◽  
Electrocardiogram Ecg

Jacket-Haar transform has been recently generalized from Haar transform and Jacket transform, but, unfortunately, it is not available in a case where the lengthNis not a power of 2. In this paper, we have proposed an arbitrary-length Jacket-Haar transform which can be conveniently constructed from the 2-point generalized Haar transforms with the fast algorithm, and thus it can be constructed with any sizes. Moreover, it can be further extended with elegant structures, which result in the fast algorithms for decomposing. We show that this approach can be practically applied for the electrocardiogram (ECG) signal processing. Simulation results show that it is more efficient than the conventional fast Fourier transform (FFT) in signal processing.

A Fast Algorithm of Linear Canonical Transformation for Radar Signal Processing System

2014 ◽  
Vol 1049-1050 ◽  
pp. 1245-1248
Author(s):  
Yan Xin Yu ◽  
Chun Yang Wang ◽  
Yu Chen ◽  
Hong Yan Sun
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Canonical Transformation ◽  
Fast Algorithm ◽  
Processing System ◽  
Practical Significance ◽  
Radar Signal ◽  
Radar Signal Processing ◽  
Linear Canonical Transformation ◽  
Non Stationary Signal

Linear canonical transformation is a new signal processing tools developing in recent years. As a unified multi-parameter linear integral transform, linear canonical transformation has its unique advantages when dealing with non-stationary signal. However, from the existing literatures, the basic theoretical system is not perfect, some of the theories associated with signal processing needs to be further established or strengthened, the research of linear canonical transformation has important theoretical significance and practical significance, but linear canonical transformation needs a lot of calculation, it is not like Fourier transform, fractional Fourier transform, Fresnel transform and scale operator, they have already been widely used in various fields of expertise, in order to reduce the amount of calculation, this paper puts forward a fast algorithm which uses duality theorem of linear canonical transformation to reduce the amount of calculation, it can quickly complete the operation when we use linear canonical transformation to process the signal during radar signal processing, the time for normal algorithm is 5s, the fast algorithm needs only 0.2s.

scholarly journals Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Irena Orović ◽  
Vladan Papić ◽  
Cornel Ioana ◽  
Xiumei Li ◽  
Srdjan Stanković
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Signal Acquisition ◽  
Transform Domain ◽  
Hermite Transform ◽  
Time Frequency ◽  
Reconstruction Methods ◽  
Fourier Transform Domain

Compressive sensing has emerged as an area that opens new perspectives in signal acquisition and processing. It appears as an alternative to the traditional sampling theory, endeavoring to reduce the required number of samples for successful signal reconstruction. In practice, compressive sensing aims to provide saving in sensing resources, transmission, and storage capacities and to facilitate signal processing in the circumstances when certain data are unavailable. To that end, compressive sensing relies on the mathematical algorithms solving the problem of data reconstruction from a greatly reduced number of measurements by exploring the properties of sparsity and incoherence. Therefore, this concept includes the optimization procedures aiming to provide the sparsest solution in a suitable representation domain. This work, therefore, offers a survey of the compressive sensing idea and prerequisites, together with the commonly used reconstruction methods. Moreover, the compressive sensing problem formulation is considered in signal processing applications assuming some of the commonly used transformation domains, namely, the Fourier transform domain, the polynomial Fourier transform domain, Hermite transform domain, and combined time-frequency domain.

The whole can be very much less than the sum of its parts

2019 ◽  
Vol 103 (556) ◽  
pp. 117-127
Author(s):  
Peter Shiu
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Mr Imaging ◽  
Fast Fourier Transform ◽  
Data Compression ◽  
Mobile Phones ◽  
Processing Data ◽  
Speed Up ◽  
Indispensable Tool ◽  
Computing Machines

This Article is on the discrete Fourier transform (DFT) and the fast Fourier transform (FFT). As we shall see, FFT is a slight misnomer, causing confusion to beginners. The idiosyncratic title will be clarified in §4.Computing machines are highly efficient nowadays, and much of the efficiency is based on the use of the FFT to speed up calculations in ultrahigh precision arithmetic. The algorithm is now an indispensable tool for solving problems that involve a large amount of computation, resulting in many useful and important applications: for example, in signal processing, data compression and photo-images in general, and WiFi, mobile phones, CT scanners and MR imaging in particular.

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