The ISO/ITC stipulates the sub-band synthesis for decoding a signal coded in accordance with the MPEG audio signal coding method as follows: The sub-bandsynthesis includes orthogonal transform given by .SIGMA.(N.times.S) where N is a cosine coefficient and S is a sub-band sample, window multiplication given by D.times.U where D is a window coefficient and U is an orthogonally transformed value, an