scholarly journals Parametric Decomposition of Pulsed Lidar Signals with Noise Corruption Using FRFT Spectrum Analysis

2021 ◽  
Vol 13 (16) ◽  
pp. 3296
Author(s):  
Fan Xu ◽  
Jun Chen ◽  
Ya Liu ◽  
Qihui Wu ◽  
Xiaofei Zhang ◽  
...  
Keyword(s):  
Spectrum Analysis ◽  
Fractional Fourier Transform ◽  
Signal To Noise Ratio ◽  
Mean Deviation ◽  
Lidar Signal ◽  
Noise Interference ◽  
Time Frequency ◽  
Parametric Decomposition ◽  
Time Offset ◽  
Waveform Lidar

The parametric decomposition of full-waveform Lidar data is challenging when faced with heavy noise scenarios. In this paper, we report a fractional Fourier transform (FRFT)-based approach for accurate parametric decomposition of pulsed Lidar signals with noise corruption. In comparison with other joint time-frequency analysis (JTFA) techniques, FRFT is found to present a one-dimensional Lidar signal by a particular two-dimensional spectrum, which can exhibit the mathematical distribution of the multiple components in Lidar signals even with a heavy noise interference. A FRFT spectrum-processing solution with histogram clustering and moving LSM fitting is designed to extract the amplitude, time offset, and pulse width contained in the mathematical distribution. Extensive experimental results demonstrate that the proposed FRFT spectrum analysis method can remarkably outperform the conventional Levenberg–Marquardt-based method. In particular, it can accurately decompose the amplitudes, time offsets, and pulse widths of the pulsed Lidar signal with a −10-dB signal-to-noise-ratio by mean deviation ratios of 4.885%, 0.531%, and 7.802%, respectively.

FRFT Based Method to Estimate DOA for Wideband Signal

2013 ◽  
Vol 712-715 ◽  
pp. 2716-2720 ◽  
Author(s):  
Wei Yang ◽  
Yao Wu Shi
Keyword(s):  
Fractional Fourier Transform ◽  
Signal To Noise Ratio ◽  
Doa Estimation ◽  
New Method ◽  
New Technique ◽  
Signal Frequency ◽  
Signal To Noise ◽  
One Dimensional ◽  
Time Frequency ◽  
Better Than

This paper presents a new direction-of-arrival (DOA) estimation for wideband sources, using fractional Fourier transform with fitting angle (F3A). Unlike other coherent wideband methods, the new method does not require any preprocessing for initial values and decomposing into narrowband components. This new technique estimates DOA by rotating the time frequency plate with the fitting angle to fit the time frequency distribution approximately. The algorithm can be applied to arbitrary shaped one dimensional or two dimensional arrays. The signal frequency can be higher than the frequencies in many wideband algorithms. The performance of this wideband technique is compared with that of the new method through simulations. The simulations show that this new technique performs better than others, while this algorithm does not apparently vary with signal-to-noise ratio (SNR).

scholarly journals Noise and Interference Suppression in Sonar Echoes Using the Fractional Fourier Transform

2017 ◽  
Vol 2 (7) ◽  
pp. 40
Author(s):  
Seema Sud
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Signal To Noise Ratio ◽  
Frequency Domain Method ◽  
Time Axis ◽  
Rotational Parameter ◽  
Frequency Space ◽  
Time Frequency ◽  
Cluttered Background ◽  
Sonar Echoes

The Fractional Fourier Transform (FrFT) enables separation of signals from noise and interference by utilizing the entire time-frequency space. Signals are filtered by rotating to a new time axis ‘ta’, with rotational parameter ‘a’, selected using some metric such as mean-square error (MSE) between a desired signal-of-interest (SOI) and its estimate. The FrFT has been applied to numerous problems, but it is most suited for applications such as sonar and radar, when the time-frequency distribution of the SOI and the undesired environment are different. It can greatly outperform the conventional fast Fourier Transform (FFT), which is solely a frequency domain method (a=1), as well as conventional time-based MMSE adaptive filtering (a=0). In this paper, we present a simple FrFT-based algorithm that separates sonar echoes of a desired SOI, e.g. a chirp, from the cluttered background, which could be noise or interference (i.e. another signal). We exploit the fact that we can find the best time axis ‘ta’ in which the SOI becomes a tone, or close to it, with the FrFT, enabling easy notching (zeroing) of the clutter. By searching for the tone peak and notching everywhere except the peak, we can successfully and easily remove the clutter. This algorithm is robust because clutter typically does not correlate with the signal in the FrFT domain, and thus does not impair our ability to estimate the peaks and notch the clutter. We compute the MSE between the true transmitted signal and the received echo with and without this algorithm as a function of signal-to-noise ratio (SNR) and show that 5 dB reduction in MSE is possible with the FrFT.

scholarly journals Robust Image Compression Algorithm using Discrete Fractional Cosine Transform

2022 ◽  
Vol 17 ◽  
pp. 25-33
Author(s):  
Vivek Arya
Keyword(s):  
Image Compression ◽  
Compression Ratio ◽  
Fractional Fourier Transform ◽  
Signal To Noise Ratio ◽  
Quality Parameters ◽  
Cosine Transform ◽  
Time Frequency ◽  
Compressed Images ◽  
Discrete Fractional Fourier Transform ◽  
Image Compression Algorithm

The discrete fractional Fourier transform become paradigm in signal processing. This transform process the signal in joint time-frequency domain. The attractive and very important feature of DFrCT is an availability of extra degree of one free parameter that is provided by fractional orders and due to which optimization is possible. Less execution time and easy implementation are main advantages of proposed algorithm. The merit of effectiveness of proposed technique over existing technique is superior due to application of discrete fractional cosine transform by which higher compression ratio and PSNR are obtained without any artifacts in compressed images. The novelty of the proposed algorithm is no artifacts in compressed image along with good CR and PSNR. Compression ratio (CR) and peak signal to noise ratio (PSNR) are quality parameters for image compression with optimum fractional order.

scholarly journals A fractional Fourier transform analysis of the scattering of ultrasonic waves

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140958 ◽  
Author(s):  
Katherine M.M. Tant ◽  
Anthony J. Mulholland ◽  
Matthias Langer ◽  
Anthony Gachagan
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Fractional Fourier Transform ◽  
Signal To Noise Ratio ◽  
Homogeneous Solution ◽  
Ultrasonic Waves ◽  
Destructive Testing ◽  
Time Frequency ◽  
Forcing Function ◽  
Linear Chirp

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification.

Image encryption based on Fractional wavelet transform, Arnold transform with the double random phases in HSV color domain

2020 ◽  
Vol 13 ◽  
Author(s):  
Aarushi Shrivastava ◽  
Janki Ballabh Sharma ◽  
Sunil Dutt Purohit
Keyword(s):  
Wavelet Transform ◽  
Image Encryption ◽  
Fractional Fourier Transform ◽  
Color Image ◽  
Random Phase ◽  
Arnold Transform ◽  
Time Frequency ◽  
Key Space ◽  
Secret Keys ◽  
Fractional Wavelet Transform

Objective: In the recent multimedia technology images play an integral role in communication. Here in this paper, we propose a new color image encryption method using FWT (Fractional Wavelet transform), double random phases and Arnold transform in HSV color domain. Methods: Firstly the image is changed into the HSV domain and the encoding is done using the FWT which is the combination of the fractional Fourier transform with wavelet transform and the two random phase masks are used in the double random phase encoding. In this one inverse DWT is taken at the end in order to obtain the encrypted image. To scramble the matrices the Arnold transform is used with different iterative values. The fractional order of FRFT, the wavelet family and the iterative numbers of Arnold transform are used as various secret keys in order to enhance the level of security of the proposed method. Results: The performance of the scheme is analyzed through its PSNR and SSIM values, key space, entropy, statistical analysis which demonstrates its effectiveness and feasibility of the proposed technique. Stimulation result verifies its robustness in comparison to nearby schemes. Conclusion: This method develops the better security, enlarged and sensitive key space with improved PSNR and SSIM. FWT reflecting time frequency information adds on to its flexibility with additional variables and making it more suitable for secure transmission.

scholarly journals A Local Search Maximum Likelihood Parameter Estimator of Chirp Signal

2021 ◽  
Vol 11 (2) ◽  
pp. 673
Author(s):  
Guangli Ben ◽  
Xifeng Zheng ◽  
Yongcheng Wang ◽  
Ning Zhang ◽  
Xin Zhang
Keyword(s):  
Maximum Likelihood ◽  
Local Search ◽  
Signal To Noise Ratio ◽  
Estimation Accuracy ◽  
Chirp Signal ◽  
Estimation Of Parameters ◽  
Parameter Estimator ◽  
Denoising Method ◽  
Time Frequency ◽  
Approximate Estimation

A local search Maximum Likelihood (ML) parameter estimator for mono-component chirp signal in low Signal-to-Noise Ratio (SNR) conditions is proposed in this paper. The approach combines a deep learning denoising method with a two-step parameter estimator. The denoiser utilizes residual learning assisted Denoising Convolutional Neural Network (DnCNN) to recover the structured signal component, which is used to denoise the original observations. Following the denoising step, we employ a coarse parameter estimator, which is based on the Time-Frequency (TF) distribution, to the denoised signal for approximate estimation of parameters. Then around the coarse results, we do a local search by using the ML technique to achieve fine estimation. Numerical results show that the proposed approach outperforms several methods in terms of parameter estimation accuracy and efficiency.

Dispersive noise removal in t-x space: Application to Arctic data

Geophysics ◽  
1988 ◽  
Vol 53 (3) ◽  
pp. 346-358 ◽  
Author(s):  
Greg Beresford‐Smith ◽  
Rolf N. Rango
Keyword(s):  
Signal To Noise Ratio ◽  
Noise Analysis ◽  
Noise Removal ◽  
North Slope ◽  
Frequency Bandwidth ◽  
The North ◽  
North Slope Of Alaska ◽  
Seismic Records ◽  
Time Offset ◽  
Undersampled Data

Strongly dispersive noise from surface waves can be attenuated on seismic records by Flexfil, a new prestack process which uses wavelet spreading rather than velocity as the criterion for noise discrimination. The process comprises three steps: trace‐by‐trace compression to collapse the noise to a narrow fan in time‐offset (t-x) space; muting of the noise in this narrow fan; and inverse compression to recompress the reflection signals. The process will work on spatially undersampled data. The compression is accomplished by a frequency‐domain, linear operator which is independent of trace offset. This operator is the basis of a robust method of dispersion estimation. A flexural ice wave occurs on data recorded on floating ice in the near offshore of the North Slope of Alaska. It is both highly dispersed and of broad frequency bandwidth. Application of Flexfil to these data can increase the signal‐to‐noise ratio up to 20 dB. A noise analysis obtained from a microspread record is ideal to use for dispersion estimation. Production seismic records can also be used for dispersion estimation, with less accurate results. The method applied to field data examples from Alaska demonstrates significant improvement in data quality, especially in the shallow section.

LFM Signal Detection Method Based on Fractional Fourier Transform

2014 ◽  
Vol 989-994 ◽  
pp. 4001-4004 ◽  
Author(s):  
Yan Jun Wu ◽  
Gang Fu ◽  
Yu Ming Zhu
Keyword(s):  
Fourier Transform ◽  
Signal Detection ◽  
Frequency Analysis ◽  
Experimental Analysis ◽  
Fractional Fourier Transform ◽  
Detection Method ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Frequency Information ◽  
Strong Impulse

As a generalization of Fourier transform, the fractional Fourier Transform (FRFT) contains simultaneity the time-frequency information of the signal, and it is considered a new tool for time-frequency analysis. This paper discusses some steps of FRFT in signal detection based on the decomposition of FRFT. With the help of the property that a LFM signal can produce a strong impulse in the FRFT domain, the signal can be detected conveniently. Experimental analysis shows that the proposed method is effective in detecting LFM signals.

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