The continuity of the mapping which associates a spectral factor to a spectral density is investigated. This mapping can be defined on several classes of spectral densities and spectral factors. For the usual largest class of spectral densities, i.e., essential bounded functions on the imaginary axis that are bounded away from zero, it is known that this mapping is not continuous. It is shown here that for slightly smaller, but still generic class the mapping becomes continuous.
- Spectral density
- Spectral factor
- Approximate spectral factorization