Optimization of the representation of sampled data signals on orthonormal bases

Some classes of sampled-data signals can be divided into epochs of equal duration. Each epoch or segment can be represented by a small discrete set of values on an orthogonalized basis. This paper investigates an iterative method for finding a suitable orthogonalized basis by using the digital computer for the case in which a complete description of the sampled-data signal is available. The signal is divided into equal segments. For each segment the iterative method defines at each iteration a "trial basis" which then provides an approximate discrete representation for the epoch in the succeeding iterations. A suitable basis can thus be generated for the entire signal by starting with an initial trial basis which may provide only a poor representation. The process is terminated when no further improvement is obtained. An example is presented to demonstrate various features of the method.