Orthogonal transform apparatus, orthogonal transform method, orthogonal transform computer program, and audio decoding apparatus

An orthogonal transform apparatus for transforming a plurality of modified discrete cosine transform coefficients contained in a prescribed interval into a coefficient sequence containing a plurality of quadrature mirror filter coefficients, comprising:nan inverse exponential transform unit which computes either one of the real and imaginary components of the quadrature mirror filter coefficient contained in a first subinterval of a plurality subintervals among which the coefficient sequence is divided so that the values of basis functions used to compute the coefficient sequence 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 first subinterval, and 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 of the plurality of subintervals by performing a butterfly operation using a computed value produced as a result of the sum of products; anda coefficient adjusting unit which computes the quadrature mirror filter coefficients by combining the real component and the imaginary component for each of the plurality of quadrature mirror filter coefficients.

An orthogonal transform method for transforming a plurality of modified discrete cosine transform coefficients contained in a prescribed interval into a coefficient sequence containing a plurality of quadrature mirror filter coefficients, comprising:ncomputing either one of the real and imaginary components of the quadrature mirror filter coefficient contained in a first subinterval of a plurality subintervals among which the coefficient sequence is divided so that the values of basis functions used to compute the coefficient sequence 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 first subinterval;computing 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 of the plurality of subintervals by performing a butterfly operation using a computed value produced as a result of the sum of products; andcomputing the quadrature mirror filter coefficients by combining the real component and the imaginary component for each of the plurality of quadrature mirror filter coefficients.

A non-transitory computer-readable recording medium having recorded thereon an orthogonal transform computer program that causes a computer to execute a process of transforming a plurality of modified discrete cosine transform coefficients contained in a prescribed interval into a coefficient sequence containing a plurality of quadrature mirror filter coefficients, the process comprising:ncomputing either one of the real and imaginary components of the quadrature mirror filter coefficient contained in a first subinterval of a plurality subintervals among which the coefficient sequence is divided so that the values of basis functions used to compute the coefficient sequence 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 first subinterval;computing 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 of the plurality of subintervals by performing a butterfly operation using a computed value produced as a result of the sum of products; andcomputing the quadrature mirror filter coefficients by combining the real component and the imaginary component for each of the plurality of quadrature mirror filter coefficients.

An audio decoding apparatus for decoding a multichannel audio signal from a data stream containing a main signal code into which a main signal representing a main component of each channel obtained by downmixing each channel signal of the multichannel audio signal is encoded, a residual signal code into which coefficients obtained by performing a modified discrete cosine transform on a residual signal orthogonal to the main signal are encoded, and a spatial information code into which spatial information representing the degree of interchannel similarity and interchannel intensity difference is encoded, the audio decoding apparatus comprising:na demultiplexing unit which demultiplexes the main signal code, the residual signal code, and the spatial information code from the data stream;a main signal decoding unit which reconstructs the main signal in a time domain by decoding the main signal code;a quadrature mirror filtering unit which transforms the main signal in the time domain into quadrature mirror filter coefficients in a time-frequency domain by applying quadrature mirror filtering to the main signal;a spatial information decoding unit which reconstructs the spatial information by decoding the spatial information code;a residual signal decoding unit which reconstructs the modified discrete cosine transform coefficients of the residual signal by decoding the residual signal code;an orthogonal transform unit which, for each of a plurality of prescribed intervals generated so as to overlap each other by one half by dividing an entire frequency band, transforms the modified discrete cosine transform coefficients of the residual signal contained in the prescribed interval into a coefficient sequence containing a plurality of quadrature mirror filter coefficients in the time-frequency domain;an upmixing unit which computes quadrature mirror filter coefficients for each channel of the audio signal by upmixing the quadrature mirror filter coefficients of the main signal and the quadrature mirror filter coefficients of the residual signal by using the spatial information; andan inverse quadrature mirror filtering unit which reconstructs each channel signal of the audio signal by applying inverse quadrature mirror filtering to the quadrature mirror filter coefficients of each channel, and whereinthe orthogonal transform unit comprises:an inverse exponential transform unit which computes either one of the real and imaginary components of the quadrature mirror filter coefficient of the residual signal contained in a first subinterval of a plurality subintervals among which the coefficient sequence is divided so that the values of basis functions used to compute the coefficient sequence 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 first subinterval, and computes the other one of the real and imaginary components of the quadrature mirror filter coefficient of the residual signal contained in the first subinterval and the real and imaginary components of the quadrature mirror filter coefficient of the residual signal contained in another subintervals of the plurality of subintervals by performing a butterfly operation using a computed value produced as a result of the sum of products; anda coefficient adjusting unit which computes the quadrature mirror filter coefficients by combining the real component and the imaginary component for each of the plurality of quadrature mirror filter coefficients of the residual signal.