Comparison of the continuous wavelet transform (CWT) versus the discrete wavelet transform (DWT), in this example applied to the ordinary beam (upper panel) and extraordinary beam (lower panel) of one spectrum of AT 2021blz. The original spectra (binned by 25 Å) are shown in grey, and the grey shaded region marks the location of one telluric absorption line. We compare the reconstructed spectra de-noised via a CWT (blue) with a Mexican Hat wavelet, where the detail coefficients of the first ten levels were removed, to the reconstructed spectra de-noised via DWT (green) with the sixth-order Symlet wavelet, where the coefficients of the first six levels were removed. The inset in the upper panel illustrates the shapes of these wavelets, with the Mexican Hat wavelet on the left in blue, and the Symlet wavelet on the right in green.