Figure illustrates some consequential properties of orthogonal basis sets and related Fourier basis sets, discussed in more detail in Part 2 of this report. Panel A shows the orthonormalized basis functions. Higher index curves have increasing numbers of zero crossings. The weightings of intensities from the underlying distribution for these curves are shown in Panel B of Figure . Being functionals of the data with the indicated mappings to the rate distributions, orthogonal basis parameters give information about the positions of rates in the underlying distribution. The precision with which the underlying distribution can be specified is low because increasingly rapid oscillations in the rate domain basis functions create increasing amounts of intensity cancellation in the time domain basis functions. Panel C shows the singular values for these basis functions, which reflect the decreasing importance of the orthogonal basis functions in fitting to data. The solid line shows the singular values for a large (256) finely incremented basis. These values fall of very rapidly and approximately exponentially. By about 15 singular values, the importance drops below one part in 10,000. Small basis sets follow nearly the same curve but have somewhat less importance for the higher indices. This provides another indication of the low resolution available from multicomponent exponential analysis. Panel D of Figure shows consequences along the time axis of using Fourier weightings of the rate distribution (not shown). These time domain functions are not orthogonal though they have been normalized. The advantage of the Fourier basis, as described below, is that it facilitates regularization when pseudo-continuous representation of the information in the decay curve is desired. The Fourier basis is discussed further in Part 2 of this report. OBP is especially useful when used for comparisons among different samples thanks to the commensurate parameters it generates. To illustrate the need for commensurate parameters, consider the examples of on-flow measurements or large numbers of related measurements on patients. Results may be compared or used to train or exploit machine learning models. Assume that each measurement is performed using the same experimental protocol with comparable instruments, and that the same orthonormal basis set is used for analysis of each one. Under these conditions, each parameter is a functional that weighs, integrates, and combines precisely the same decay rate ranges of the underlying distribution. Each parameter also reveals unique (orthogonal) information about that underlying distribution. In contrast, a common approach of finding an appropriate number of components, and fitting rates and intensities for those components, may generate incommensurate parameterizations. For example, the approach might find different numbers of components for different samples, in which case it will not be clear how to handle missing components, and it will not be possible to know which components should be compared from sample-to-sample. Orthonormal basis parameterization has none of these ambiguities. provides an example of OBP-based classification using simulated data. This exercise was intended to mimic the permeation of water into a porous material. For these situations, free water typically has slow transverse relaxation rates, while absorbed water may sample different environments where it has faster relaxation rates. It could be important to distinguish among materials that differ in their pore properties.