In search for the best wavelet for denoising low SNR RF Signal for FMCW Radar Altimeter

This research project / thesis proposes the best wavelet for Denoising under low Signal to Noise Ratio (SNR) conditions and Discrete Wavelet Transform Architecture based design for RF signal denoising, targeting the real time applications like FMCW (Frequency Modulated Continuous Wave) Radar Altimeter used in Anti-Radiation Missiles, Smart Bombs, Fighter aircrafts, Helicopters etc., and other Defense and RF carrier based applications like Cellular communication. DWT (Discrete Wavelet Transform) & IDWT(Inverse DWT) Architecture Models designed in MATLAB for the wavelets under study like dmey, coif1, sym2, & debouches db1, db2, db3, db4, db6. The reconstructed signal results after denoising are compared in various aspects. The results show that db3 is the best wavelet for denoising application point of view. Finally the db3 based architecture design implemented in VHDL(VHSIC Hardware Description Language) and the simulation results compared, synthesis has been done using Xilinx ISE Design suite targeting an FPGA. This project involves study and implementation of De-noising algorithms using Discrete Wavelet Transform. In a system the signal to noise ratio (SNR) is important for reliable information retrieval. Analysis of signals with poor SNR may lead to wrong interpretation of results. Conventional techniques like filtering in time domain and frequency domain has its own limitations in estimating and characterizing noise. Wavelet transforms is a very useful tool in the analysis of non-stationary signals. Wavelet transform has been used in signal processing fields such as de noising or data compression. This method consists of decomposing the data recursively into a sum of details and approximations at different levels of resolution. The details represent the high frequency components while the approximations represent the low frequency components of the signal

On the energy leakage of discrete wavelet transform

The energy leakage is an inherent deficiency of discrete wavelet transform (DWT) which is often ignored by researchers and practitioners. In this paper, a systematic investigation into the energy leakage is reported. The DWT is briefly introduced first, and then the energy leakage phenomenon is described using a numerical example as an illustration and its effect on the DWT results is discussed. Focusing on the Daubechies wavelet functions, the band overlap between the quadrature mirror analysis filters was studied and the results reveal that there is an unavoidable tradeoff between the band overlap degree and the time resolution for the DWT. The dependency of the energy leakage to the wavelet function order was studied by using a criterion defined to evaluate the severity of the energy leakage. In addition, a method based on resampling technique was proposed to relieve the effects of the energy leakage. The effectiveness of the proposed method has been validated by numerical simulation study and experimental study

Improving the performance of translation wavelet transform using BMICA

Research has shown Wavelet Transform to be one of the best methods for denoising biosignals. Translation-Invariant form of this method has been found to be the best performance. In this paper however we utilize this method and merger with our newly created Independent Component Analysis method – BMICA. Different EEG signals are used to verify the method within the MATLAB environment. Results are then compared with those of the actual Translation-Invariant algorithm and evaluated using the performance measures Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Signal to Distortion Ratio (SDR), and Signal to Interference Ratio (SIR). Experiments revealed that the BMICA Translation-Invariant Wavelet Transform out performed in all four measures. This indicates that it performed superior to the basic Translation- Invariant Wavelet Transform algorithm producing cleaner EEG signals which can influence diagnosis as well as clinical studies of the brain

Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra

We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the discrete wavelet transform (DWT) to the input signal, 'shrinking' certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by 'trial and error', which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the 'Haar' wavelet basis, which we found to provide excellent filtering for 1D stellar spectra, at a low computational cost. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI

Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a combination of the curvelet transform and a whitening filter along with procedure for noise variance estimation. The whitening filter is added to get the best performance of the curvelet transform under coherent and incoherent correlated noise cases, and furthermore, it simplifies the noise estimation method and makes it easy to use the standard threshold methodology without digging into the curvelet domain. The proposed method is tested on pseudo-synthetic data by adding noise to real noise-less data set of the Netherlands offshore F3 block and on the field data set from east Texas, USA, containing ground roll noise. Our experimental results show that the proposed algorithm can achieve the best results under all types of noises (incoherent or uncorrelated or random, and coherent noise)