On Frequency Transformations

Frequency transformations are fundamental in the design of analog and digital filters and have been in use for many years. In the lowpass-bandpass or bandstop transformation, there are two ways to carry out the design. The filters resulting from these two ways, however, may be quite different. This fact does not seem to be widely known and, to the best of our knowledge, has never been discussed in the literature. In this note, this and related problems will be discussed. We will also discuss a stability problem in frequency transformations.