ABSTRACT
The basic operation involved in the Wavelet Transform is convolution – have the (flipped) wavelet slide over the data, computing a sequence of dot products. This way, the wavelet is basically looking for similarity. The topic of wavelets is very different from that of Fourier transforms in other respects, as well. Notably, there is a lot less standardization in terminology, use of symbols, and actual practices. One choice Vistnes made was to favor depth over breadth, and to focus on a single wavelet. While overall, the topic of wavelets is more multifaceted, and thus, may seem more enigmatic than Fourier analysis, the transform itself is easier to grasp. Chances are the people have been mentally comparing what they are doing not with the Fourier Transform per se, but with its windowed progeny, the spectrogram. Both methods tell the reader how frequency composition varies over time. Both involve trade-offs between resolution in frequency and in time.
