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1

Asymmetric cryptosystem with random decomposition using fractional Fourier and Fourier transforms

Gaur Kapil Shankar, Singh Hukum, Thakran Seema

Optica Applicata

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2023

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Vol. 53, nr 4

591--602

EN

In this paper, an asymmetric cryptosystem based on random decomposition is proposed. The suggested scheme used three different decryption keys to get decrypted image, two of which are generated using phase truncation and one through random decomposition. The combination of these keys and fractional Fourier transform parameter increase the security of cryptosystem against various attacks. MATLAB simulations are used to validate the scheme’s conclusions. The effectiveness of a scheme is validated by the key sensitivity performance of the cryptosystem. This research also includes a 3D plot for both grayscale and binary images. Correlation coefficient (CC) values between the original and recovered images is also calculated to validate the cryptosystem.

2

Image encryption algorithm based on rear-mounted phase mask and random decomposition

Yadav Shivani, Singh Hukum

Optica Applicata

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2022

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Vol. 52, nr 2

195--212

EN

To escalate the image encryption a new method has been devised which includes double random phase encoding (DRPE) using rear phase masking and random decomposition (RD) technique stranded on fractional Fourier transform. Here, asymmetric cryptographic system is developed in fractional Fourier transform (FrFT) mode using two random phase masks (RPM) and a rear mounted phase mask. In the projected scheme a colored image is decomposed into R, G and B channels. The amplitude of each channel is normalized, phase encoded and modulated using RPM. The modulated R, G and B channels of the colored image are individually transformed using FrFT to produce corresponding encrypted image. The proposed scheme is authorized on grayscale image also. The norm behind the development of the suggested scheme has been elaborated by carrying out cryptanalysis on system based on the RD. The method helps in escalations of the protection of double random phase encoding by cumulating the key length and the parameter amount, so that it vigorously can be used against various attacks. The forte of the suggested cryptographic system was verified using simulations with MATLAB 7.9.0 (R2008a). The efficiency of the suggested scheme includes the analysis using singular value decomposition (SVD), histogram and correlation coefficient.

3

Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space

Verma Amit K., Gupta Bivek

Opuscula Mathematica

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2021

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Vol. 41, no. 5

701--723

EN

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.

4

Fetal heart rate estimation using fractional Fourier transform and wavelet analysis

Jaba Deva Krupa Abel, Dhanalakshmi Samiappan, Sanjana N.L., Manivannan Naveen, Kumar Ramamoorthy, Tripathy Saswati

Biocybernetics and Biomedical Engineering

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2021

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Vol. 41, no. 4

1533--1547

EN

Objective: Monitoring fetal cardiac activity during pregnancy is a critical part of assessing the fetus’s health. Non-invasive fetal electrocardiogram (NIFECG) is a safe emerging fetal cardiac monitoring approach receiving considerable interest. This paper proposes an effective way to separate the fetal ECG signal from the single-channel abdominal ECG signals. Methods: The paper proposes a novel algorithm based on time-frequency analysis combining fractional Fourier transform (FrFT) and wavelet analysis to extract fetal ECG from abdominal signals at higher accuracy. The abdominal signals acquired from pregnant women are preprocessed and subjected to suppressing maternal ECG using fractional Fourier transform and maximum likelihood estimate. The estimated maternal signal is removed from the abdominal ECG. The residue is processed using wavelet decomposition to obtain a clean fetal ECG and calculate fetal heart rate. Results: The proposed algorithm’s performance is validated using signals from the Daisy database and Physionet challenge 2013 set-a dataset. Real-time signals acquired using Powerlab data acquisition hardware are also included for validation. The obtained results show that the proposed algorithm can effectively extract the fetal ECG and accurately estimate the fetal heart rate. Conclusion: The proposed method is a promising and straightforward algorithm for FECG extraction. Fractional Fourier transform maps the time domain abdominal signal into the fractional frequency domain, distinguishing the fetal and maternal ECG. The Wavelet transform can efficiently denoise the residue abdominal signal and provides a clean fetal ECG. The proposed approach achieves 98.12% of accuracy, 98.85% of sensitivity, 99.16% of positive predictive value, and 99.42% of F1 measure.

5

The fractional Fourier transform as a biomedical signal and image processing tool: A review

Gómez-Echavarría Alejandro, Ugarte Juan P., Tobón Catalina

Biocybernetics and Biomedical Engineering

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2020

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Vol. 40, no. 3

1081--1093

EN

This work presents a literature review of the fractional Fourier transform (FrFT) investiga-tions and applications in the biomedical field. The FrFT is a time-frequency analysis tool that has been used for signal and image processing due to its capability in capturing the nonstationary characteristics of real signals. Most biomedical signals are an example of such non-stationarity. Thus, the FrFT-based solutions can be formulated, aiming to enhance the health technology. As the literature review indicates, common applications of the FrFT involves signal detection, filtering and features extraction. Establishing adequate solutions for these tasks requires a proper fractional order estimation and implementing the suitable numeric approach for the discrete FrFT calculation. Since most of the reports barely describe the methodology on this regard, it is important that future works include detailed information about the implementation criteria of the FrFT. Although the applications in biomedical sciences are not yet among the most frequent FrFT fields of action, the growing interest of the scientific community in the FrFT, supports its practical usefulness for developing new biomedical tools.

6

Identification of sonar detection signal based on fractional Fourier transform

Wang B., Tang J., Yu F., Zhu Z.

Polish Maritime Research

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2018

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S 2

125--131

EN

Aiming at the source of underwater acoustic emission, in order to identify the enemy emission sonar source accurately. Using the digital watermarking technology and combining with the good time-frequency characteristics of fractional Fourier transform (FRFT),this paper proposes a sonar watermarking method based on fractional Fourier transform. The digital watermark embedding in the fractional Fourier transform domain and combined with the coefficient properties of the sonar signal in the fractional Fourier transform to select the appropriate watermark position. Using the different characteristics of the signals before and after embedding, an adaptive threshold was set for the watermark detection to realize the discrimination of sonar signals. The simulation results show the feasibility and has better resolution and large watermark capacity of this method, while the robustness of the watermark is better, and the detection precision is further improved.

7

Construction of waveform library in cognitive radar

Guo Y., Wu Y., Liu H.

Polish Maritime Research

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2017

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S 2

22--29

EN

Based on the thoughts of cognitive radar, Fractional Fourier Transform (FrFT) is used to generate a rotatable waveform libraries of Frank coded/Barker coded waveform in this paper. Then, the ambiguity function is used to analyze the delay resolution, Doppler resolution, delay side-lobe level, and Doppler side-lobe level of the waveform libraries and orthogonality of them is also analyzed. Furthermore, we proved theoretically that there is a fixed coordinate transformation between the waveforms of library and its origin waveform. Therefore, the Cramér-Rao low bound (CRLB) of motion parameters can be computed easily using the waveforms of the libraries, which facilitate the subsequent waveform scheduled work. Simulation results show that the library waveforms can reduce delay resolution to satisfy the different situations and can bring significant benefits for delay resolution, orthogonality and reuse interval.

8

Hybrid Watermarking Algorithm using Finite Radon and Fractional Fourier Transform

Sharmaa J. B., Sharmaa K. K., Purohit S. D., Atangana A.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

523--543

EN

Watermarking is proposed as solution to authentication, copyright protection and security requirements of multimedia objects (speech, image and video). In this paper a watermarking scheme based on finite radon transform (FRAT), fractional Fourier Transform (FRFT) and singular value decomposition is proposed. In the proposed scheme, image to be watermarked is first transformed by finite radon transform, the radon transformed image is further transformed by FRFT, and singular values of FRFT transformed image are modified to embed the watermark. Inverse transformation is applied to obtain watermarked image. Simulations are performed under various test conditions with different FRFT transform angles for improved robustness and visual transparence of watermarked image. Results of the proposed scheme are better in comparison to the existing schemes for most of the attacks. Proposed scheme provide additional degree of freedom in security, robustness, payload capacity and visual transparence. Proposed scheme can also be used to communicate or store the watermarked image as erasure code, to reduce communication errors over a network, due to the use of FRAT.

9

Dynamics of Commodities Prices : Integer and Fractional Models

David S. A., Machado J. A. T., Trevisan L. R., Inácio Jr. C. M. C., Lopes A. M.

Fundamenta Informaticae

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2017

|

Vol. 151, nr 1/4

389--408

EN

This paper examines the time series of four important agricultural commodities, namely the soybean, corn, coffee and sugar prices. Time series can exhibit long-range dependence and persistence in their observation. The long memory feature of data is a documented fact and there has been an increasing interest in studying such concepts in the perspective of economics and finance. In this work, we start by analyzing the time series of the four commodities by means of the Fractional Fourier Transform (FrFT) to unveil time-frequency patterns in the data. In a second phase, we apply Auto Regressive Integrated Moving Average (ARIMA) and Auto Regressive Fractionally Integrated Moving Average (ARFIMA) models for obtaining the spot price composition and predict future price. The ARFIMA process is a known class of long memory model, representing a generalization of the ARIMA algorithm. We compare the performances of the ARIMA and the ARFIMA models and we show that the ARFIMA has a superior performance for future price forecasting.

10

Abnormal Breast Detection in Mammogram Images by Feed-forward Neural Network Trained by Jaya Algorithm

Wang S., Rao R. V., Chen P., Zhang Y., Liu A., Wei L.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

191--211

EN

(Aim) Abnormal breast can be diagnosed using the digital mammography. Traditional manual interpretation method cannot yield high accuracy. (Method) In this study, we proposed a novel computer-aided diagnosis system for detecting abnormal breasts in mammogram images. First, we segmented the region-of-interest. Next, the weighted-type fractional Fourier transform (WFRFT) was employed to obtain the unified time-frequency spectrum. Third, principal component analysis (PCA) was introduced and used to reduce the spectrum to only 18 principal components. Fourth, feed-forward neural network (FNN) was utilized to generate the classifier. Finally, a novel algorithm-specific parameter free approach, Jaya, was employed to train the classifier. (Results) Our proposed WFRFT + PCA + Jaya-FNN achieved sensitivity of 92.26% ± 3.44%, specificity of 92.28% ± 3.58%, and accuracy of 92.27% ± 3.49%. (Conclusions) The proposed CAD system is effective in detecting abnormal breasts and performs better than 5 state-of-the-art systems. Besides, Jaya is more effective in training FNN than BP, MBP, GA, SA, and PSO.

11

A Comprehensive Survey on Fractional Fourier Transform

Zhang Y., Wang S., Yang J.-F., Zhang Z., Phillips P., Sun P., Yan J.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

1--48

EN

The Fractional Fourier transform (FRFT) is a relatively novel linear transforms that is a generalization of conventional Fourier transform (FT). FRFT can transform a particular signal to a unified time-frequency domain. In this survey, we try to present a comprehensive investigation of FRFT. Firstly, we provided definition of FRFT and its three discrete versions (weighted-type, sampling-type, and eigendecomposition-type). Secondly, we offered a comprehensive theoretical research and technological studies that consisted of hardware implementation, software implementation, and optimal order selection. Thirdly, we presented a survey on applications of FRFT to following fields: communication, encryption, optimal engineering, radiology, remote sensing, fractional calculus, fractional wavelet transform, pseudo-differential operator, pattern recognition, and image processing. It is hoped that this survey would be beneficial for the researchers studying on FRFT.

12

Automatic Genre Classification Using Fractional Fourier Transform Based Mel Frequency Cepstral Coefficient and Timbral Features

Bhalke D. G., Rajesh B., Bormane D. S.

Archives of Acoustics

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2017

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Vol. 42, No. 2

213--222

EN

This paper presents the Automatic Genre Classification of Indian Tamil Music and Western Music using Timbral and Fractional Fourier Transform (FrFT) based Mel Frequency Cepstral Coefficient (MFCC) features. The classifier model for the proposed system has been built using K-NN (K-Nearest Neighbours) and Support Vector Machine (SVM). In this work, the performance of various features extracted from music excerpts has been analysed, to identify the appropriate feature descriptors for the two major genres of Indian Tamil music, namely Classical music (Carnatic based devotional hymn compositions) & Folk music and for western genres of Rock and Classical music from the GTZAN dataset. The results for Tamil music have shown that the feature combination of Spectral Roll off, Spectral Flux, Spectral Skewness and Spectral Kurtosis, combined with Fractional MFCC features, outperforms all other feature combinations, to yield a higher classification accuracy of 96.05%, as compared to the accuracy of 84.21% with conventional MFCC. It has also been observed that the FrFT based MFCC effieciently classifies the two western genres of Rock and Classical music from the GTZAN dataset with a higher classification accuracy of 96.25% as compared to the classification accuracy of 80% with MFCC.

13

Comparative analysis of variants of Gabor-Wigner Transform for crossterm reduction

Ajab M., Taj I. A., Khan N. A.

Metrology and Measurement Systems

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2012

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Vol. 19, nr 3

499-508

EN

Gabor Wigner Transform (GWT) is a composition of two time-frequency planes (Gabor Transform (GT) and Wigner Distribution (WD)), and hence GWT takes the advantages of both transforms (high resolution of WD and cross-terms free GT). In multi-component signal analysis where GWT fails to extract auto-components, the marriage of signal processing and image processing techniques proved their potential to extract autocomponents. The proposed algorithm maintained the resolution of auto-components. This work also shows that the Fractional Fourier Transform (FRFT) domain is a powerful tool for signal analysis. Performance analysis of modified fractional GWT reveals that it provides a solution of cross-terms of WD and blurring of GT.