An orthogonal transform apparatus for transforming modified discrete cosine transform coefficients for an audio signal contained in a prescribed interval set in a frequency domain into quadrature mirror filter coefficients for the audio signal, comprising: an interchanging unit (41, 51, 33) which interchanges the modified discrete cosine transform coefficients contained in a first half of the prescribed interval with the modified discrete cosine transform coefficients contained in a second half of the prescribed interval; an inverting unit (42, 52, 34) which inverts the sign of the modified discrete cosine transform coefficients contained in the second half of the prescribed interval after the interchange; an inverse cosine transform unit (43-1, 43-2) which computes real components of the quadrature mirror filter coefficients by applying an inverse modified discrete cosine transform using a fast Fourier transform to the modified discrete cosine transform coefficients contained in the first half of the prescribed interval after the interchange and the sign-inverted modified discrete cosine transform coefficients contained in the second half of the prescribed interval after the interchange; an inverse sine transform unit (53-1, 53-2) which computes imaginary components of the quadrature mirror filter coefficients by applying an inverse modified discrete sine transform using a fast Fourier transform to the modified discrete cosine transform coefficients contained in the first half of the prescribed interval after the interchange and the sign-inverted modified discrete cosine transform coefficients contained in the second half of the prescribed interval after the interchange; and a coefficient adjusting unit which computes the quadrature mirror filter coefficients by combining the real components of the quadrature mirror filter coefficients with the imaginary components of the quadrature mirror filter coefficients. an interchanging unit (41, 51, 33) which interchanges the modified discrete cosine transform coefficients contained in a first half of the prescribed interval with the modified discrete cosine transform coefficients contained in a second half of the prescribed interval; an inverting unit (42, 52, 34) which inverts the sign of the modified discrete cosine transform coefficients contained in the second half of the prescribed interval after the interchange; an inverse cosine transform unit (43-1, 43-2) which computes real components of the quadrature mirror filter coefficients by applying an inverse modified discrete cosine transform using a fast Fourier transform to the modified discrete cosine transform coefficients contained in the first half of the prescribed interval after the interchange and the sign-inverted modified discrete cosine transform coefficients contained in the second half of the prescribed interval after the interchange; an inverse sine transform unit (53-1, 53-2) which computes imaginary components of the quadrature mirror filter coefficients by applying an inverse modified discrete sine transform using a fast Fourier transform to the modified discrete cosine transform coefficients contained in the first half of the prescribed interval after the interchange and the sign-inverted modified discrete cosine transform coefficients contained in the second half of the prescribed interval after the interchange; and a coefficient adjusting unit which computes the quadrature mirror filter coefficients by combining the real components of the quadrature mirror filter coefficients with the imaginary components of the quadrature mirror filter coefficients.