A good introduction to wavelets is given here. Below we show how to use wavelets using the "jsci" package which is incorporated into the the core of the DataMelt package.
In this example, we will create a 1D vector of Gaussian numbers and transform using Fast Wavelet Transform (daubechies 2). We convert the input array into a histogram for visualization. Then we extract coefficients and convert the signal back. Then we compare the original data with the converted ones.
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You will see 2 identical histograms. Please refer the package jsci.maths.wavelet.