Multiresolution Analysis and the Scaling Function

Wavelets provide a multiresolution analysis of signals. This means they simultaneously describe the low- and high-resolution features of the signal. In this lesson you will learn how multiresolution analysis is performed using a scaling function that defines the lowest resolution view of the signal. Higher resolution views are obtained from scaled versions of the scaling function. You will also learn how the natural nesting of low-resolution spaces within high-resolution spaces places a key constraint on valid scaling functions. This lesson builds an important foundation for understanding and applying wavelet methods.