There is provided a method or a device for extending a bandwidth of a first band speech signal to generate a second band speech signal wider than the first band speech signal and including the first band speech signal. The method comprises receiving a segment of the first band speech signal having a low cut off frequency and a high cut off frequency; determining the high cut off frequency of the segment; determining whether the segment is voiced or unvoiced; if the segment is voiced, applying a first bandwidth extension function to the segment to generate a first bandwidth extension in high frequencies; if the segment is unvoiced, applying a second bandwidth extension function to the segment to generate a second bandwidth extension in the high frequencies; using the first bandwidth extension and the second bandwidth extension to extend the first band speech signal beyond the high cut off frequency.