scholarly journals Computation of Wavelet and Multiwavelet Transforms Using Fast Fourier Transform

2021 ◽  
Vol 4 (2) ◽  
pp. 102-108
Author(s):  
Walid Amin Mahmoud
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fast Fourier Transform ◽  
Haar Wavelet ◽  
Discrete Wavelet ◽  
Haar Wavelet Transform ◽  
Linear Convolution ◽  
Multiwavelet Transform ◽  
Discrete Multiwavelet Transform ◽  
Accuracy Tradeoff

A novel fast and efficient algorithm was proposed that uses the Fast Fourier Transform (FFT) as a tool to compute the Discrete Wavelet Transform (DWT) and Discrete Multiwavelet Transform. The Haar Wavelet Transform and the GHM system are shown to be a special case of the proposed algorithm, where the discrete linear convolution will adapt to achieve the desired approximation and detail coefficients. Assuming that no intermediate coefficients are canceled and no approximations are made, the algorithm will give the exact solution. Hence the proposed algorithm provides an efficient complexity verses accuracy tradeoff.   The main advantages of the proposed algorithm is that high band and the low band coefficients can be exploited for several classes of signals resulting in very low computation.

scholarly journals FPGA Implementation of Digital Images Watermarking System Based on Discrete Haar Wavelet Transform

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Mohamed Ali Hajjaji ◽  
Mohamed Gafsi ◽  
Abdessalem Ben Abdelali ◽  
Abdellatif Mtibaa
Keyword(s):  
Wavelet Transform ◽  
High Performance ◽  
Large Scale ◽  
Image Watermarking ◽  
Haar Wavelet ◽  
Discrete Wavelet ◽  
Haar Wavelet Transform ◽  
Integration Architecture ◽  
Field Programmable ◽  
Scale Integration

In this paper we propose a novel and efficient hardware implementation of an image watermarking system based on the Haar Discrete Wavelet Transform (DWT). DWT is used in image watermarking to hide secret pieces of information into a digital content with a good robustness. The main advantage of Haar DWT is the frequencies separation into four subbands (LL, LH, HL, and HH) which can be treated independently. This permits ensuring a better compromise between robustness and visibility factors. A Field Programmable Gate Array (FPGA) that is based on a very large scale integration architecture of the watermarking algorithm is developed to accelerate media authentication. A hardware cosimulation strategy using the Matlab-Xilinx system generator (XSG) was applied to prove the validity of the suggested implementation. The hardware cosimulation results show the effectiveness of the developed architecture in terms of visibility and robustness against several attacks. The proposed hardware system presents also a high performance in terms of the operating speed.

scholarly journals Ensemble Discrete Wavelet Transform and Gray-Level Co-Occurrence Matrix for Microcalcification Cluster Classification in Digital Mammography

2019 ◽  
Vol 9 (24) ◽  
pp. 5388 ◽  
Author(s):  
Annarita Fanizzi ◽  
Teresa Maria Basile ◽  
Liliana Losurdo ◽  
Roberto Bellotti ◽  
Ubaldo Bottigli ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Haar Wavelet ◽  
Discrete Wavelet ◽  
Textural Features ◽  
Gray Level ◽  
Haar Wavelet Transform ◽  
Auc Value ◽  
Automatic Tool ◽  
Microcalcification Clusters ◽  
Occurrence Matrix

The presence of clusters of microcalcifications is a primary sign of breast cancer. Their identification is still difficult today for radiologists, and the wrong evaluations involve unnecessary biopsies. In this paper, an automatic tool for characterizing and discriminating clusters of microcalcifications into benign/malignant in digital mammograms is proposed. A set of 104 digital mammograms including microcalcification clusters was randomly extracted from a public available database and manually labeled by our radiologists, obtaining 96 abnormal ROIs. For each so-identified ROI, a multi-scale image decomposition based on the Haar wavelet transform was performed. On the decomposition, a textural features extraction step was carried out both on each sub-image and on the corresponding gray-level co-occurrence matrix. Then, a random forest classifier was employed for classifying microcalcification clusters into benign and malignant. The study found that the most discriminant features extracted from the ROIs decomposition by Haar transform were variance and relative smoothness, whereas as regards the textural features calculated on the GLCMs corresponding to the Haar-decomposed ROI, it emerged that the relationship between the pixels of the sub-image in the diagonal direction had high discriminating power for the classification of microcalcification clusters into benign and malignant. The proposed method was evaluated in cross-validation and performed highly in the prediction of the benign/malignant ROIs, with a mean AUC value of 97.39 ± 0.01 % .

scholarly journals Fault location identification of double circuit transmission line using discrete wavelet transform

2019 ◽  
Vol 15 (3) ◽  
pp. 1356
Author(s):  
Abdul Hadi Bin Mustapha ◽  
R Hamdan ◽  
F. H. Mohd Noh ◽  
N. A. Zambri ◽  
M. H. A. Jalil ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Transmission Line ◽  
Fast Fourier Transform ◽  
Discrete Wavelet Transform ◽  
Fault Location ◽  
Detection Algorithm ◽  
Percentage Error ◽  
Discrete Wavelet ◽  
Fast Fourier Transform Algorithm

<span lang="EN-GB">The importance of supplying undisturbed electricity keep increasing due to modernization and lifestyle. Any disturbance in the power system may lead to discontinuation and degradation in the power quality. Therefore, detecting fault, fault type and fault location is a major issue in power transmission system in order to ensure reliable power delivery system. This paper will compare two prominent methods to estimate the fault location of double circuit transmission line. Those methods are Discrete Wavelet Transform algorithm and Fast Fourier Transform algorithm. Simulations has been carried out in MATLAB/Simulink and a variety of fault has been imposed in order to analyse the capability and accuracy of the fault location detection algorithm. Results obtained portrayed that both algorithms provide good performance in estimating the fault location. However, the maximum percentage error produced by the Discrete Wavelet Transform is only 0.25%, 0.6% lower than maximum error produces by Fast Fourier Transform algorithm. As a conclusion, Discrete Wavelet Transform possesses better capability to estimate fault location as compared to Fast Fourier Transform algorithm.</span>

scholarly journals An Approach on MCSA-Based Fault Detection Using Discrete Wavelet Transform and Fault Classification Based on Deep Neural Networks

2021 ◽  
Vol 10 (3) ◽  
pp. 2256-2259
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fast Fourier Transform ◽  
Discrete Wavelet Transform ◽  
Three Dimensional ◽  
Fault Classification ◽  
Signal Frequency ◽  
Discrete Wavelet ◽  
Novel Approach ◽  
Motor Current Signature Analysis

This paper presents a novel approach on motor current signature analysis (MCSA) forbroken Rotor Bar fault and High Contact Resistance fault using stator current signals as an input from the three phases of Induction motors. Discrete Wavelet Transform is preferred over the Fast Fourier Transform (FFT). Fast Fourier Transform (FFT) converts signals from time domain to frequency domain on the other hand Discrete Wavelet Transform (DWT) gives complete three-dimensional information of the signal, frequency, amplitude, and the time where the frequency components exist. In wavelet analysis, thesignal is converted into scaled and translated version of mother wavelet, which is very irregular so cannot be predicted. Hence, mother wavelets are more appropriate for predicting the local behavior of the signal including irregularities and spikes. In this research features are extracted using DWT and then features are trained in Deep NN sequential model for the purpose of classification of the faults. In this research, MATLAB software has been used for building the motor model in Simulink environment and PyCharm software is used to implement Deep NN for getting accuracy and classification results. This research helps in early detection of the faults that assists in prevention from unscheduled downtimes in industry, economy loss and production loss as well.

scholarly journals Separation of the Structure Signal by the Maximal Overlap Discrete Wavelet Transform and Fast Fourier Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Thanh Q. Nguyen
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fast Fourier Transform ◽  
Discrete Wavelet Transform ◽  
Power Spectra ◽  
Vibration Signal ◽  
Discrete Wavelet ◽  
Single Spectrum ◽  
Power Spectral ◽  
Vibration Process

Power spectral density (PSD) is used for evaluating a structure’s vibration process. Moreover, PSD not only shows a discrete form of vibration but also presents various components in a vibration structure. The superposition of multiple vibration patterns on the same spectrum poses difficulty in analyzing the spectral information in the way needed to find the structure’s discrete vibration. This paper proposes a method for separating the synthetic vibration signal into a structure’s discrete vibration and other extraneous vibrations using the maximal overlap discrete wavelet transform (MODWT) method combined with the method of fast Fourier transform (FFT). With the combination of these two algorithms, MODWT and FFT, the signals of the synthesized vibration have been separated into component signals with different frequency ranges. This means that PSD will be formed, which is based on the combination of the single power spectra of the component signals. Thus, the single spectrum of each of these constructed components can be used to evaluate the types of discrete vibrations coexisting in a structure’s vibration process. The survey results in this paper show the sensitivity and suitability of select types of discrete vibrations to be separated out during the assessment of the structural change, so as to achieve the best possible plan for eliminating the unwanted and unexpected noise and vibration components.

scholarly journals Location of Faults In Transmission Line Using Fast Fourier Transform And Discrete Wavelet Transform In Power Systems

2012 ◽  
pp. 84-86
Author(s):  
Roshni Uppala ◽  
V. Niranjan ◽  
Ch. Das Prakash ◽  
R. Srinivas Rao
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Power Systems ◽  
Transmission Line ◽  
Fast Fourier Transform ◽  
Transmission Lines ◽  
High Signal ◽  
Discrete Wavelet ◽  
Matlab Simulation ◽  
Proposed Model

This paper demonstrates the usage of fast fourier transform and wavelet transform in locating faults using a simple transmission line. Transmission lines connect the generating stations and load centers. Hence, the chances of fault occurring in transmission lines are very high. Signal processing is the most important part of the digital distance protection schemes. The proposed model effectively helps in locating the fault such as L-G,LL,LL-G,LLL using MATLAB/SIMULINK. In doing so it describes the method of analysis of above two transforms in SIMULINK environment using the above two transforms. MATLAB simulation results show the wavelet method of transforms is a good and powerful tool to estimate the disrupts location on the transmission line when fault occurs.

scholarly journals Comparison of Image Compressions: Analog Transformations

Proceedings ◽  
2020 ◽  
Vol 54 (1) ◽  
pp. 37
Author(s):  
Jose Balsa
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Discrete Fourier Transform ◽  
Additive Noise ◽  
Haar Wavelet ◽  
Hadamard Transform ◽  
Performance Tests ◽  
Haar Wavelet Transform ◽  
Walsh Hadamard Transform ◽  
Different Levels

A comparison between the four most used transforms, the discrete Fourier transform (DFT), discrete cosine transform (DCT), the Walsh–Hadamard transform (WHT) and the Haar-wavelet transform (DWT), for the transmission of analog images, varying their compression and comparing their quality, is presented. Additionally, performance tests are done for different levels of white Gaussian additive noise.

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