This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. This independence is a requirement in common classification problems like stratigraphic analysis, which was a motivation for this research. We achieve this objective by developing the notion of an approximation to the Continuous Wavelet Transform (CWT), which is separable in the time and scale parameters, and using it to define power signatures, which essentially characterize the scale energy density, independent of time. 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. The proposed classification approach has potential applications in areas like moving target detection, object recognition, oil exploration, and speech processing.