The Continuous Wavelet Transform (CWT) is a highly useful signal processing technique for which low power implementations are desirable, for example to allow the transform to be used in battery powered, portable devices. This paper describes a Low Power CWT (LPCWT) implementation that is based around the mathematical approximation of a mother wavelet and uses application specific information to guide the approximation process. Simulations comparing the LPCWT and CWT are carried out with the two giving equivalent signal processing performance. The LPCWT is suitable for realisation in any desired circuit topology.