Textbook in PDF format

Wavelet analysis is a new branch of mathematics widely applied in signal analysis, image processing, numerical analysis, etc. The name wavelets means small waves, and in short, a wavelet is an oscillation that decays quickly. Wavelet analysis has become a significant computational tool in signal processing and image processing applications. The wavelet analysis is renowned for its successful approach to the problem of analyzing a signal in both time domain and frequency domain. Analyzing non stationary signal had been a big challenge for various transform techniques. The transform techniques such as Fourier Transform (FT), short time Fourier Transform (STFT) are failed in analyzing non-stationary signals. But wavelet transform (WT) techniques can be able to analyze both stationary and non-stationary signals in an effective manner. WT is capable to analyze one dimensional signal like audio signals and two dimensional signals like images. This book deals with wavelet transform techniques and its applications. Many real-world sources of data display suggestively periodic behavior, but with time-varying period, amplitude, or mean. This variation can lead to inaccurate results when the data is analyzed with standard Fourier techniques, as Fourier analysis assumes stationary of the signal and its basis functions are unbounded in time. Wavelets, in contrast, are localized in both time and frequency. This in turn localizes the analysis, allowing the changes in signal properties to be tracked over time. A major disadvantage of the Fourier Transform is it captures global frequency information, meaning frequencies that persist over an entire signal. This kind of signal decomposition may not serve all applications well, for example Electrocardiography (ECG) where signals have short intervals of characteristic oscillation. An alternative approach is the Wavelet Transform, which decomposes a function into a set of wavelets. Wavelet analysis has proven to be invaluable in many problem domains, including ecological cycles, sunspot cycles, circadian cycles, in radian cycles associated with gene transcripts, blood-flow dynamics, and ECG signals. The wavelet transform (WT) can be used to analyze signals in time–frequency space and reduce noise, while retaining the important components in the original signals. In the past 20 years, WT has become a very effective tool in signal processing