Optimized scale factor for frequency band extension in an audio frequency signal decoder

A method for determining an optimized scale factor to be applied to an excitation signal or to a filter in a method of extending a frequency band of an audio frequency signal,

• the method comprising steps of:
• computing of a frequency response, R, of a linear prediction filter of a frequency band,
• smoothing of the value of R, so as to obtain Rsmoothed, the smoothing method being selected, from a group of smoothing methods including at least two smoothing methods, in function of a set of parameters comprising a plurality of parameters including the value of spectral slope, tilt,
• the method further comprising further comprising the step of determining the optimized scale factor, said step of determining the optimized scale factor comprising the computation of
• max(min(Rsmoothed,Q),P)/P,
• where P is the frequency response of linear prediction filter over a second frequency band, the second frequency band being higher than the first frequency band, Q is the frequency response of an additional filter obtained by truncating the linear prediction filter polynom.