A system for coding and decoding an audio signal by using an orthogonal and inverse orthogonal transformation of a block unit, includes a coding unit having a circuit for obtaining a power level of the audio signal of a segment unit having a predetermined time interval shorter than the block unit, a circuit for generating a gain control signal from the power level, a circuit for performing a predetermined adaptive gain control responsive to the gain control signal to generate and output the adaptive gain control signal to a decoding unit, thereby performing a pre-treatment, and a coding portion for coding the adaptive gain control signal by using the orthogonal transformation to generate and output a coded signal; and the decoding unit having a decoding portion for decoding the coded signal, dequantizing and inversely and orthogonally transforming a decoded audio signal, and a circuit for performing an inverse gain control for the decoded audio signal responsive to the adaptive gain control signal from the adaptive gain control circuit to reproduce and output an audio signal, thereby performing post-treatment.