We present a signal processing algorithm to convert speech signals with “standard telephone” quality into 7 kHz wideband speech. A statistical approach based on a hidden Markov model (HMM) is used, which takes into account several features of the band-limited speech. The narrowband input signal is classified into a limited number of speech sounds (HMM states) for which the wideband spectral envelope is estimated using the pre-trained model. The enhanced speech exhibits a signicantly improved quality without objectionable artifacts.