Wavelet Theory and Application in Communication and Signal Processing

Abstract

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.

Analysis of Electroencephalograms Based on the Phase Plane Method

“…It can be seen that, with the help of the PP, it is possible to obtain the statistical characteristics of the EEG, which can be used in diagnostics. Recently, the wavelet transform (WT) has been widely used in the study of biomedical signals, given their nonstationarity, and, in particular, in EEG processing [30][31][32][33][34]. This method makes it possible to numerically characterize the duration and change of the basic physiological rhythms, as well as to trace the change in frequency in time within each rhythm.…”

“…To realize this possibility, there are series of orthogonal wavelets. They are created based on the representation of the signal space as a system of nested subspaces, which differ from each other only by changing the scale of the independent variable [31,35].…”

Filtered-orthogonal wavelet division multiplexing (F-OWDM) technique for 5G and beyond communication systems

“…Wavelets are effective for investigating aperiodic, noisy signals in both time and frequency domains simultaneously. These are small waveforms which are time limited or exist only for a short period of time 34 . The wavelet analysis constitute two general operations such as decomposition (DWT) and reconstruction (IDWT).…”

“…This process is called wavelet transform (WT). The method of transforming the decomposed signal to original wave is called inverse wavelet transform (IWT) 34 .…”

A Competent Hybrid Digital Image Watermarking Technique Based on Daubechies Wavelet and Block Bitmap Modification

“…It possesses a highly convenient position to break down images with characteristics of multiple determination [7]. Furthermore, DWT superiorly detects isotropic merit of the system of human vision more than other transformation techniques [8]. This merit helps to include watermarks in less sensitive positions in accordance with the system of human vision.…”