In today’s digital telephone networks the acoustic bandwidth of speech signals is still limited to the range of about 300 Hz to 3.4 kHz due to the evolution from analogue transmission systems. This is the reason for the limited quality and intelligibility of “telephone speech”. The objective of this thesis is the artificial bandwidth extension of speech signals. The aim is to improve the speech quality at the receiving point without transmitting any additional side information about the original wideband speech signal. Using information theoretic methods the feasibility and prospects are pointed out. Based on these results, a signal processing algorithm is developed. The concept of artificial bandwidth extension is based on a linear source-filter model of the speech production process. For short segments of the narrowband speech signal parameters of the (wideband) model are estimated which are subsequently utilized to estimate the missing components of the speech signal. By this technique a wideband counterpart of the bandlimited speech signal is produced, comprising frequency components between 50 Hz and 7 kHz. By artificial bandwidth extension a significant improvement of the subjective speech quality is achieved.