Spectrum Coding Apparatus and Decoding Apparatus That Respectively Encodes And Decodes A Spectrum Including A First Band And A Second Band

A coding apparatus capable of coding a spectrum at a low bit rate and with high quality without producing any disturbance in a harmonic structure of the spectrum. In this apparatus, internal state setting section sets an internal state of a filtering section using a first spectrum S1(k). A pitch coefficient setting section outputs a pitch coefficient T by gradually changing it. The filtering section calculates an estimated value S′2(k) of a second spectrum S2(k) based on a pitch coefficient T. A search section calculates the degree of similarity between S2(k) and S′2(k). At this time, pitch coefficient T′ corresponding to the maximum calculated degree of similarity is given to a filter coefficient calculation section. The filter coefficient calculation section determines a filter coefficient βi using this pitch coefficient T′.