Representation of Frequency and Time Information by Using Wavelets Transform; The Method and Applications

Ali Naji Shaker

Abstract


The Fourier Transform (FT) is the well-known classical representation of signals components by providing the frequency analysis representations of the signals. The Fourier transformation is found with some determinant such as signal dependent transforming, in another word, [15] the FT is helpful with only particular types of signals such as the pseudo-stationary signals and stationary signals, whereas the FT is not fulfilling the expectations while its being used with non-periodic signals such as noise, and non-stationary signals. As an alternative technique, a Wavelets Transformation (WT) was proposed to perform the frequency analysis for such kind of signals. Since its a revolved theory and is not broadly famous as compared with FT and other techniques. In this paper, we are going to review the wavelets theory with analysis and demonstrate the applications of this technique.


Keywords


Wavelets Transformation; Fourier Transform; short time Fourier transformation; continues wavelets transform; Partial differential equations; Ordinary Differential Equations.

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References


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