  We present an algorithm using transformation groups and their irreducible
representations to generate an orthogonal basis for a signal in the vector
space of the signal. It is shown that multiresolution analysis can be done with
amplitudes using a transformation group. G-lets is thus not a single transform,
but a group of linear transformations related by group theory. The algorithm
also specifies that a multiresolution and multiscale analysis for each
resolution is possible in terms of frequencies. Separation of low and high
frequency components of each amplitude resolution is facilitated by G-lets.
Using conjugacy classes of the transformation group, more than one set of basis
may be generated, giving a different perspective of the signal through each
basis. Applications for this algorithm include edge detection, feature
extraction, denoising, face recognition, compression, and more. We analyze this
algorithm using dihedral groups as an example. We demonstrate the results with
an ECG signal and the standard `Lena' image.
