scholarly journals A New Approach for Enhancing the Services of the 5G Mobile Network and IOT-Related Communication Devices Using Wavelet-OFDM and Its Applications in Healthcare

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Mordecai F. Raji ◽  
JianPing Li ◽  
Amin Ul Haq ◽  
Victor Ejianya ◽  
Jalaluddin Khan ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Communication Systems ◽  
Mobile Network ◽  
Performance Comparison ◽  
Support Network ◽  
Time Frequency ◽  
Communication Devices ◽  
The Fourier Transform

The heart of the current wireless communication systems (including 5G) is the Fourier transform-based orthogonal frequency division multiplex (OFDM). Over time, a lot of research has proposed the wavelet transform-based OFDM as a better replacement of Fourier in the physical layer solutions because of its performance and ability to support network-intensive applications such as the Internet of Things (IoT). In this paper, we weigh the wavelet transform performances against the future wireless application system requirements and propose guidelines and approaches for wavelet applications in 5G waveform design. This is followed by a detailed impact on healthcare. Using an image as the test data, a comprehensive performance comparison between Fourier transform and various wavelet transforms has been done considering the following 5G key performance indicators (KPIs): energy efficiency, modulation and demodulation complexity, reliability, latency, spectral efficiency, effect of transmission/reception under asynchronous transmission, and robustness to time-/frequency-selective channels. Finally, the guidelines for wavelet transform use are presented. The guidelines are sufficient to serve as approaches for tradeoffs and also as the guide for further developments.

scholarly journals Design and construction of a prototype for the analysis of vibrations in an induction motor for the detection of faults

2020 ◽  
pp. 27-33
Author(s):  
Javier Garrido ◽  
Beatris Escobedo-Trujillo ◽  
Guillermo Miguel Martínez-Rodríguez ◽  
Oscar Fernando Silva-Aguilar
Keyword(s):  
Fourier Transform ◽  
Induction Motor ◽  
Wavelet Transforms ◽  
Data Acquisition System ◽  
Time Frequency ◽  
Different Types ◽  
Control Devices ◽  
The Fourier Transform ◽  
And Control ◽  
Types Of Faults

The contribution of this work is to present the design of a prototype integrated by an induction motor, a data acquisition system, accelerometers and control devices for stop and start, to generate and identify different types of faults by means of vibration analysis. in the domain: time, frequency or frequency-time, through the use of the Fourier Transform, Fast Fourier Transform or Wavelet Transforms (wavelet transform). In this prototype, failures can be generated in the induction motor such as: unbalance, different types of misalignment, mechanical looseness, and electrical failures such as broken bars or short-circuited rings, an example of a misalignment failure is presented to show the process of analysis and detection.

COMPLEMENTARY ANALYSIS TO HEART SOUNDS WHILE USING THE SHORT TIME FOURIER AND THE CONTINUOUS WAVELET TRANSFORMS

2007 ◽  
Vol 19 (05) ◽  
pp. 331-339
Author(s):  
S. M. Debbal ◽  
F. Bereksi-Reguig
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Continuous Wavelet Transforms ◽  
Time Frequency ◽  
Quantitative Measurements ◽  
Short Time

This paper presents the analysis and comparisons of the short time Fourier transform (STFT) and the continuous wavelet transform techniques (CWT) to the four sounds analysis (S1, S2, S3 and S4). It is found that the spectrogram short-time Fourier transform (STFT), cannot perfectly detect the internals components of these sounds that the continuous wavelet transform. However, the short time Fourier transform can provide correctly the extent of time and frequency of these four sounds. Thus, the STFT and the CWT techniques provide more features and characteristics of the sounds that will hemp physicians to obtain qualitative and quantitative measurements of the time-frequency characteristics.

SECOND CARDIAC SOUND ANALYSIS TECHNIQUES AND PERFORMANCE COMPARISON

2005 ◽  
Vol 05 (03) ◽  
pp. 429-442 ◽  
Author(s):  
S. M. DEBBAL ◽  
F. BEREKSI-REGUIG
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Wigner Distribution ◽  
Performance Comparison ◽  
Frequency Characteristics ◽  
Second Sound ◽  
Time Frequency ◽  
Cardiac Sound ◽  
And Performance ◽  
Short Time

This paper presents the applications of the spectrogram, Wigner distribution and wavelet transform analysis methods to the second cardiac sound S2 of the phonocardiogram signal (PCG). A comparison between these methods has shown the resolution differences between them. It is found that the spectrogram Short-Time Fourier Transform (STFT) cannot detect the two internals components of the second sound S2 (A2 and P2, atrial and pulmonary components respectively). The Wigner Distribution (WD) can provide time-frequency characteristics of the sound S2, but with insufficient diagnostic information as the two components (A2 and P2) are not accurately detected, appearing to be one component only. It is found that the wavelet transform (WT) is capable of detecting the two components, the aortic valve component A2 and pulmonary valve component P2, of the second cardiac sound S2. However, the standard Fourier transform can display these components in frequency but not the time delay between them. Furthermore, the wavelet transform provides more features and characteristics of the second sound S2 that will hemp physicians to obtain qualitative and quantitative measurements of the time-frequency characteristics.

scholarly journals Wavelet Theory and Application in Communication and Signal Processing

2021 ◽  
Author(s):  
Nizar Al Bassam ◽  
Vidhyalavanya Ramachandran ◽  
Sumesh Eratt Parameswaran
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Communication Systems ◽  
Orthogonal Frequency Division Multiplexing ◽  
Applied Mathematics ◽  
Multimedia Systems ◽  
Biomedical Signal Processing ◽  
Discrete Wavelet

Wavelet analysis is the recent development in applied mathematics. For several applications, Fourier analysis fails to provide tangible results due to non-stationary behavior of signals. In such situation, wavelet transforms can be used as a potential alternative. The book chapter starts with the description about importance of frequency domain representation with the concept of Fourier series and Fourier transform for periodic, aperiodic signals in continuous and discrete domain followed by shortcoming of Fourier transform. Further, Short Time Fourier Transform (STFT) will be discussed to induce the concept of time frequency analysis. Explanation of Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT) will be provided with the help of theoretical approach involving mathematical equations. Decomposition of 1D and 2D signals will be discussed suitable examples, leading to application concept. Wavelet based communication systems are becoming popular due to growing multimedia applications. Wavelet based Orthogonal Frequency Division Multiplexing (OFDM) technique and its merit also presented. Biomedical signal processing is an emerging field where wavelet provides considerable improvement in performance ranging from extraction of abnormal areas and improved feature extraction scheme for further processing. Advancement in multimedia systems together with the developments in wireless technologies demands effective data compression schemes. Wavelet transform along with EZW, SPIHT algorithms are discussed. The chapter will be a useful guide to undergraduate and post graduate who would like to conduct a research study that include wavelet transform and its usage.

scholarly journals Time Frequency Analysis of Wavelet and Fourier Transform

2020 ◽  
Author(s):  
Karlton Wirsing
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Frequency Analysis ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Efficient Access ◽  
The Fourier Transform

Signal processing has long been dominated by the Fourier transform. However, there is an alternate transform that has gained popularity recently and that is the wavelet transform. The wavelet transform has a long history starting in 1910 when Alfred Haar created it as an alternative to the Fourier transform. In 1940 Norman Ricker created the first continuous wavelet and proposed the term wavelet. Work in the field has proceeded in fits and starts across many different disciplines, until the 1990’s when the discrete wavelet transform was developed by Ingrid Daubechies. While the Fourier transform creates a representation of the signal in the frequency domain, the wavelet transform creates a representation of the signal in both the time and frequency domain, thereby allowing efficient access of localized information about the signal.

Multiscale Terrain Characterization Using Fourier and Wavelet Transforms for Unmanned Ground Vehicles

2009 ◽  
Author(s):  
Jeremy J. Dawkins ◽  
David M. Bevly ◽  
Robert L. Jackson
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Ground Vehicles ◽  
Quarter Car Model ◽  
Power Spectral ◽  
Before And After ◽  
Frequency Components ◽  
The Fourier Transform ◽  
Density Methods

This paper investigates the use of the Fourier transform and Wavelet transform as methods to supplement the more common root mean squared elevation and power spectral density methods of terrain characterization. Two dimensional terrain profiles were generated using the Weierstrass-Mandelbrot fractal equation. The Fourier and Wavelet transforms were used to decompose these terrains into a parameter set. A two degree of freedom quarter car model was used to evaluate the vehicle response before and after the terrain characterization. It was determined that the Fourier transform can be used to reduce the profile into the key frequency components. The Wavelet transform can effectively detect discontinuities of the profile and changes in the roughness of the profile. These two techniques can be added to current methods to yield a more robust terrain characterization.

Special affine wavelet transform and the corresponding Poisson summation formula

2021 ◽  
pp. 2050086
Author(s):  
Firdous A. Shah ◽  
Aajaz A. Teali ◽  
Azhar Y. Tantary
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Inversion Formula ◽  
Summation Formula ◽  
Poisson Summation Formula ◽  
Time Frequency ◽  
Fundamental Properties ◽  
Stationary Signals ◽  
Poisson Summation

In the article, “Windowed special affine Fourier transform” in J. Pseudo-Differ. Oper. Appl. (2020), we introduced the notion of windowed special affine Fourier transform (WSAFT) as a ramification of the special affine Fourier transform. Keeping in view the fact that the WSAFT is not befitting for in the context of non-stationary signals, we continue our endeavor and introduce the notion of the special affine wavelet transform (SAWT) by combining the merits of the special affine Fourier and wavelet transforms. Besides studying the fundamental properties of the SAWT including orthogonality relation, inversion formula and range theorem, we also demonstrate that the SAWT admits the constant [Formula: see text]-property in the time–frequency domain. Moreover, we formulate an analog of the well-known Poisson summation formula for the proposed SAWT.

Ground‐roll suppression using the wavelet transform

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1896-1903 ◽  
Author(s):  
Andrew J. Deighan ◽  
Doyle R. Watts
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Low Frequency ◽  
Seismic Signal ◽  
High Amplitude ◽  
Computationally Efficient ◽  
Time Frequency ◽  
Ground Roll ◽  
The Fourier Transform ◽  
Processing Techniques

Low‐frequency, high‐amplitude ground roll is an old problem in land‐based seismic field records. Current processing techniques aimed at ground‐roll suppression, such as frequency filtering, f-k filtering, and f-k filtering with time‐offset windowing, use the Fourier transform, a technique that assumes that the basic seismic signal is stationary. A new alternative to the Fourier transform is the wavelet transform, which decomposes a function using basis functions that, unlike the Fourier transform, have finite extent in both frequency and time. Application of a filter based on the wavelet transform to land seismic shot records suppresses ground roll in a time‐frequency sense; unlike the Fourier filter, this filter does not assume that the signal is stationary. The wavelet transform technique also allows more effective time‐frequency analysis and filtering than current processing techniques and can be implemented using an algorithm as computationally efficient as the fast Fourier transform. This new filtering technique leads to the improvement of shot records and considerably improves the final stack quality.

scholarly journals Efficient Time-Frequency Localization of a Signal

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Satish Chand
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Time Axis ◽  
Time Intervals ◽  
Time Frequency ◽  
Time Frequency Localization ◽  
The Fourier Transform ◽  
Special Case ◽  
Two Parameter ◽  
Time Point

A new representation of the Fourier transform in terms of time and scale localization is discussed that uses a newly coinedA-wavelet transform (Grigoryan 2005). TheA-wavelet transform uses cosine- and sine-wavelet type functions, which employ, respectively, cosine and sine signals of length2π. For a given frequencyω, the cosine- and sine-wavelet type functions are evaluated at time points separated by2π/ωon the time-axis. This is a two-parameter representation of a signal in terms of time and scale (frequency), and can find out frequency contents present in the signal at any time point using less computation. In this paper, we extend this work to provide further signal information in a better way and name it asA*-wavelet transform. In our proposed work, we use cosine and sine signals defined over the time intervals, each of length2πm/(2nω),m≤2n,mandnare nonnegative integers, to develop cosine- and sine-type wavelets. Using smaller time intervals provides sharper frequency localization in the time-frequency plane as the frequency is inversely proportional to the time. It further reduces the computation for evaluating the Fourier transform at a given frequency. TheA-wavelet transform can be derived as a special case of theA*-wavelet transform.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

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