PURPOSE: To reduce a circuit scale and to improve arithmetic precision by replacing the coefficient of a data conversion arithmetic means with an integer ratio and permitting a quantizing means to adjust gain change generated by means of changing into an integer ratio.

CONSTITUTION: An operation by the two coefficients being COS(2/16)π and COS(6/16)π is required in order to obtain the arithmetic output F6' of a butterfly arithmetic part 131. These values are indicated as two infinit decimals being 0.923... and 0.3826.... The ratio of COS(2/16)π with COS(6/16)π is approximated by the ratio 5:2 and the operation is executed by the value obtained by replacing the arithmetic coefficient with the integer ratio. Then, gain change generated by replacing the arithmetic coefficient with the integer ratio is absorbed by the quantizing part. Thus, the arithmetic bit width of a data converting part is drastically reduced, therefore, the circuit scale is sharply reduced.