Rational orthogonal bases satisfying the Bedrosian identity

We develop a necessary and sufficient condition for the Bedrosian identity in terms of the boundary values of functions in the Hardy spaces. This condition allows us to construct a family of functions such that each of which has non-negative instantaneous frequency and is the product of two functions satisfying the Bedrosian identity. We then provide an efficient way to construct orthogonal bases of L-2(R) directly from this family. Moreover, the linear span of the constructed basis is norm dense in L-p(R), 1 < p < infinity. Finally, a concrete example of the constructed basis is presented.