The W-Transform

The classical z-transform is not adequate for calculations on time-varying systems, as it assumes that the system under consideration is linear time-invariant. The most successful attempt at extension of the z-transform to linear time-varying systems has been called the 'W-transform'. It is a straight generalization of the z-transform and is remarkably effective in providing a framework in which most of the classical linear time-invariant synthesis techniques also extend to the time-varying case. This paper defines the W-transformation and discusses one typical application of it: interpolation.