An orthogonal transform apparatus computes either one of the real and imaginary components of the quadrature mirror filter coefficient contained in a first subinterval of a plurality of subintervals among which a coefficient sequence containing a plurality of quadrature mirror filter coefficients is divided so that the values of basis functions are symmetrically placed, by computing a sum of products of the plurality of modified discrete cosine transform coefficients and the basis functions corresponding to the subinterval, computes the other one of the real and imaginary components of the quadrature mirror filter coefficient contained in the first subinterval and the real and imaginary components of the quadrature mirror filter coefficient contained in another subintervals by performing a butterfly operation using a computed value produced as a result of the sum of products and computes each quadrature mirror filter coefficient by combining the real component and imaginary component thereof.