To provide a synthesis filter for an MPEG audio decoder, and a decoding method thereof with which a computation time for speedy decoding can be shortened.

The synthesis filter for the MPEG audio decoder includes a butterfly computation part which performs a butterfly computation with respect to an input MPEG audio subband sample by a prescribed unit; a matrix computation part which performs a matrix computation using a result of the butterfly computation; a first buffer which stores a result of the matrix computation according to a prescribed address; a window computation address generation part which generates first and second addresses with respect to the first buffer to use for each cycle of the window computation; a window computation part which outputs the matrix computation result stored in the first and second addresses to perform the window computation; and an output part which outputs a result of the window computation.