This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. We develop the notion of a separable approximation to the Continuous Wavelet Transform (CWT) and use it to define a power signature. We present a simple technique which uses the Singular Value Decomposition (SVD) to compute such an approximation, and demonstrate through an example how it is used to perform the classification process. This example serves to show both the effectiveness and limitations of the approach. Our main result is an alternate approach which develops the idea of using orthogonal projections to refine the approximation process, thus allowing for the definition of better signatures.