# Professional Objectives

** Diversions—2**

Two things I have always placed high value on in my writing:

- Trying to help others, through my writings, to learn how to see through the superficial layer of mathematical definitions and rules for manipulation of mathematical quantities to the deeper concepts that are the essence of the discipline of statistical signal processing.
- To be as scholarly as I can in searching out the origins of ideas, which go back a century in some cases, and crediting all important contributors along the way. I know of no work in spectral analysis that is as thorough in this respect as my book Statistical Spectral Analysis

I’ve always tried to bridge the gap between mathematicians, too many of whom seem not to understand the essence of real-world problems to which mathematics can be applied, and engineers, too many of who seem not to understand very well the mathematics they attempt to use to solve their real-world problems. This continuing effort has often put me in the middle between two largely noncommunicating groups, often being misunderstood by both; that is, not succeeding at communicating with either group. Fortunately, I have had enough success over the long run to have gathered the support of enough reputable people to obtain some degree of satisfaction that the effort has been worthwhile.

Two examples of this effort are the books *Random Processes* and *Spectral Analysis* in which I tried to do something substantial about the fundamentally important duality between mathematical expectation and time averaging that, with extremely few exceptions, has simply not been written about or taught and has, therefore, not been understood by the great majority of those who would benefit. Furthermore, a solid understanding of time-average expectation seems to be a prerequisite for learning and effectively using the newer subject of cyclostationary signal processing theory and method.