Asynchronous Filters and Mobile Radio Communication Based on Walsh Functions

It is well known that the usual frequency filters based on sine-cosine functions do not require synchronization. Furthermore, sinusoidal electromagnetic waves of different frequency can be separated in mobile communication without any synchronization between the various transmitters and receivers, It is widely believed that this is a result of certain shift invariant features of sinusoidal functions that do not exist for other functions, The purpose of this paper is to show by means of simple examples that there are infinitely many systems of functions on which one may base asynchronous filters and mobile radio commnuication. The difference in the usefulness of these systems of functions depends only on the state of technology, no system is inherently better than others.