Response Functions for Arbitrary Weight Functions and Data Distributions. Part I: Framework for Interpreting the Response Function

The response function is a commonly used measure of analysis scheme properties. Its use in the interpretation of analyses of real-valued data, however, is unnecessarily complicated by the structure of the standard form of the Fourier transform. Specifically, interpretation using this form of the Fourier transform requires knowledge of the relationship between Fourier transform values that are symmetric about the origin. Here, these relationships are used to simplify the application of the response function to the interpretation of analysis scheme properties. In doing so, Fourier transforms are used because they can be applied to studying effects that both data sampling and weight functions have upon analyses. A complication arises, however, in the treatment of constant and sinusoidal input since they do not have Fourier transforms in the traditional sense. To handle these highly useful forms, distribution theory is used to generalize Fourier transform theory. This extension enables Fourier transf...