Spectrum Analysis of Signal in Wolfram Mathematica System

The purpose of this paper is a spectrum analysis of signals of various nature, construction of the signal scalogram using Morlet wavelet, modification of the scalogram to obtain a more informative graphic representation of the signal. Spectral analysis of the signal is constructed by means of the Fourier transform. A modification of the graphical representation of the result of the wavelet transform has been developed with the help of  the Mathematica system. For this, a wavelet scalogram has been used as a two-dimensional representation of the original signal. A scale has been introduced on it for the value of the signal amplitude depending on the time and period of its constituent components. This graphical representation allows us to obtain additional information about the dynamic properties of the original signal.  A modification of the representation of the original signal scalogram has been developed for a more complete spectrum analysis (determination of the period of the constituent components). The paper contains an example using a modified scalogram for the analysis of a signal containing two pulses, an audio signal and white noise. The basic wavelet in this case is the Morlet wavelet. A comparison of the scalogram, obtained using the built-in function, and the modified scalogram has been made in the paper. The disadvantage of the first scalogram is the impossibility of assessing the frequency of the signal; its advantage is the ability to assess the localization of the pulse. For a modified scalogram, the advantage is the estimation of the signal periodicity, and the disadvantage is the inaccuracy in determining the range of pulse localization. For spectrum analysis in Mathematica, it is recommended to use a combination of two approaches (using a standard built-in function to determine the localization of the pulse) and a modified scalogram (to determine the periods of the constituent components).

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