With Richard Duffin at Carnegie Mellon, Bott studied existence of electronic filters corresponding to given positive-real functions. In 1949 they proved a fundamental theorem of filter synthesis. Duffin and Bott extended earlier work by Otto Brune that requisite functions of complex frequency "s" could be realized by a passive network of inductors and capacitors. The proof, relying on induction on the sum of the degrees of the polynomials in the numerator and denominator of the rational function, was published in Journal of Applied Physics, volume 20, page 816.