A method includes defining a transition band for a signal having a spectrum within a first frequency band, where the transition band is defined as a portion of the first frequency band, and is located near an adjacent frequency band that is adjacent to the first frequency band. The method analyzes the transition band to obtain a transition band spectral envelope and a transition band excitation spectrum; estimates an adjacent frequency band spectral envelope; generates an adjacent frequency band excitation spectrum by periodic repetition of at least a part of the transition band excitation spectrum with a repetition period determined by a pitch frequency of the signal; and combines the adjacent frequency band spectral envelope and the adjacent frequency band excitation spectrum to obtain an adjacent frequency band signal spectrum. A signal processing logic for performing the method is also disclosed.