Multiresolution Analysis and the Wavelet Decomposition

In this lesson you will learn how the wavelet decomposition for a signal follows naturally from a multiresolution analysis viewpoint. Wavelets represent the details needed to increase the resolution of the representation to the next level. This leads to a relationship between the wavelet and scaling function. You will learn that the discrete wavelet transform expresses a signal using a base resolution plus successively finer details associated with wavelet bases of increasing scale. This lesson completes the multiresolution analysis introduced in the previous lesson and prepares you to understand how to compute the discrete wavelet transform for sampled signals.