PURPOSE: To provide a two-dimensional 4×4 discrete cosine transformation circuit(two- dimensional 4×4 DCT circuit in which the number of times of multiplication can be reduced, and a computing precision can not be lowered

CONSTITUTION: The expression of a factor resolution between original input matrix data [X] and output matrix data [Y] can be expressed by [Y]=1/4.[W] [V] [R] [Q] [R] [Q] [X]. The matrix [R], [Q], and [V] is a constant matrix including 0, 1, and -1, and the matrix is the matrix including an irrational number normalized by the two-dimensional 4×4 DCT. The arithmetic operation of the constant matrix [R] [Q] and [v] can be realized by an addition and subtraction, and only the arithmetic operation of the matrix [W] is realized by a multiplication. A first adding and subtracting circuit performs the first arithmetic operation of [X] with [RQ], and the first arithmetic operation of the result with [RQ] by a time division, a second adding and subtracting circuit 4 performs the second arithmetic operation of [RQ] with [S] and the third arithmetic operation of the result with [V] by the time division, and a multiplying and adding circuit 6 performs the arithmetic operation of [U] with [W]. Intermediate value holding circuits 3 and 5 hold intermediate calculated values in the time-division arithmetic operation.