Fast algorithms for computation of 5-point dct-ii, dct-iv, and dst-iv, and architectures
AssigneeQUALCOMM Incorporated
InventorsYuriy Reznik, Ravi Kiran Chivukula
Life of this patent
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Abstract
A more efficient encoder/decoder is provided in which an N-point MDCT transform is mapped into smaller sized N/2-point DCT-IV, DST-IV and/or DCT-II transforms. The MDCT may be systematically decimated by factor of 2 by utilizing a uniformly scaled 5-point DCT-II core function as opposed to the DCT-IV or FFT cores used in many existing MDCT designs in audio codecs. Various transform factorizations of the 5-point transforms may be implemented to more efficiently implement a transform.
Claims52
A method of computing transform values, comprising:
- receiving time-domain input values representing an audio signal;
- and
- transforming the input values into spectral coefficients using a Modified Discrete Cosine Transform (MDCT) that is recursively decimated into a plurality of 5-point transforms.
A scalable speech and audio encoder device, comprising:
- a Discrete Cosine Transform (DCT)-type transform layer module adapted to obtain time-domain input values representing an audio signal;
- and
- transform the input values into spectral coefficients using a Modified Discrete Cosine Transform (MDCT) that is recursively decimated into a plurality of 5-point transforms.
A scalable speech and audio encoder device, comprising:
- means for obtaining time-domain input values representing an audio signal;
- and
- means for transforming the input values into spectral coefficients using a Modified Discrete Cosine Transform (MDCT) that is recursively decimated into a plurality of 5-point transforms.
A processor including a scalable speech and audio encoding circuit adapted to:
- obtain time-domain input values representing an audio signal;
- and
- transform the input values into spectral coefficients using a Modified Discrete Cosine Transform (MDCT) that is recursively decimated into a plurality of 5-point transforms, wherein at least one of the plurality of 5-point transforms includes at least one Discrete Cosine Transform type II (DCT-II) (802) that takes an input vector [x0, x1, x2, x3, x4] to produce an output vector [X0, X1, X2, X3, X4] and is characterized by at least a plurality of the intermediate results:
- w1=x0+x4;
- w2=x4−x0;
- w3=x3−x1;
- w4=x3+x1;
- w5=w1+w4;
- w6=w4−w1;
- u1=x2−αw5;
- u2=x2+w5;
- u3=βw2+γw3;
- u4=βw3−γw2;
- u5=5w6;
- such that
- X0=u2;
- X1=u4;
- X2=u4−u1;
- X3=u3;
- X4=u1+u5;
- where
-
-
- α
- =
- 1
- 4
- ;
- β
- =
- cos
-
- (
- 3
-
- π
- 10
- )
- ;
- γ
- =
- -
- cos
-
- (
- π
- 10
- )
- ;
- and
-
-
- δ
- =
- -
- 5
- 4
- .
A machine-readable medium comprising instructions operational for scalable speech and audio encoding, which when executed by one or more processors causes the processors to:
- obtain time-domain input values representing an audio signal;
- and
- transform the input values into spectral coefficients using a Modified Discrete Cosine Transform (MDCT) that is recursively decimated into a plurality of 5-point transforms, wherein at least one of the plurality of 5-point transforms includes at least one Discrete Cosine Transform type II (DCT-II) (802) that takes an input vector [x0, x1, x2, x3, x4] to produce an output vector [X0, X1, X2, X3, X4] and is characterized by at least a plurality of the intermediate results:
- w1=x0+x4;
- w2=x4−x0;
- w3=x3−x1;
- w4=x3+x1;
- w5=w1+w4;
- w6=w4−w1;
- u1=x2−αw5;
- u2=x2+w5;
- u3=βw2+γw3;
- u4=βw3−γw2;
- u5=δw6;
- such that
- X0=u2;
- X1=u4;
- X2=u4−u1;
- X3=u3;
- X4=u1+u5;
- where
-
-
- α
- =
- 1
- 4
- ;
- β
- =
- cos
-
- (
- 3
-
- π
- 10
- )
- ;
- γ
- =
- -
- cos
-
- (
- π
- 10
- )
- ;
- and
-
-
- δ
- =
- -
- 5
- 4
- .
A method of computing inverse transform values, comprising:
- receiving spectral coefficient input values representing an audio signal;
- and
- transforming the spectral coefficient input values into time-domain output values using an Inverse Modified Discrete Cosine Transform (IMDCT) that is recursively decimated into a plurality of 5-point inverse transforms.
A scalable speech and audio decoder device, comprising:
- an Inverse Discrete Cosine Transform (DCT)-type transform layer module adapted to receive spectral coefficient input values representing an audio signal;
- and
- transform the spectral coefficient input values into time-domain output values using an Inverse Modified Discrete Cosine Transform (IMDCT) that is recursively decimated into a plurality of 5-point inverse transforms.
A scalable speech and audio decoder device, comprising:
- means for receiving spectral coefficient input values representing an audio signal;
- and
- means transforming the spectral coefficient input values into time-domain output values using an Inverse Modified Discrete Cosine Transform (IMDCT) that is recursively decimated into a plurality of 5-point inverse transforms.
A processor including a scalable speech and audio decoding circuit adapted to:
- receive spectral coefficient input values representing an audio signal;
- and
- transform the spectral coefficient input values into time-domain output values using an Inverse Modified Discrete Cosine Transform (IMDCT) that is recursively decimated into a plurality of 5-point inverse transforms,
- wherein at least one of the plurality of 5-point inverse transforms includes at least one Inverse Discrete Cosine Transform type II (IDCT-II) (3202) that takes an input vector [X0, X1, X2, X3, X4] to produce an output vector [x0, x1, x2, x3, x4] and is characterized by at least a plurality of the intermediate results:
- u1=X4−X2;
- u5=X4+X2;
- w0=X0+u1;
- w5=X0−αu1;
- w2=βX3−βX1;
- w3=γX3−βX1;
- w6=δu5;
- w1=w5−w6;
- w4=w5+w6;
- such that
- x0=w1−w2;
- x1=w4+w3;
- x2=w0.
- x3=w4−w3;
- x4=w1+w2;
- where
-
-
- α
- =
- 1
- 4
- ;
- β
- =
- cos
-
- (
- 3
-
- π
- 10
- )
- ;
- γ
- =
- -
- cos
-
- (
- π
- 10
- )
- ;
- δ
- =
- -
- 5
- 4
- .
A machine-readable medium comprising instructions operational for scalable speech and audio decoding, which when executed by one or more processors causes the processors to:
- receive spectral coefficient input values representing an audio signal;
- and
- transform the spectral coefficient input values into time-domain output values using an Inverse Modified Discrete Cosine Transform (IMDCT) that is recursively decimated into a plurality of 5-point inverse transforms,
- wherein at least one of the plurality of 5-point inverse transforms includes at least one Inverse Discrete Cosine Transform type II (IDCT-II) (3202) that takes an input vector [X0, X1, X2, X3, X4] to produce an output vector [x0, x1, x2, x3, x4] and is characterized by at least a plurality of the intermediate results:
- u1=X4−X2;
- u5=X4+X2;
- w0=X0+u1;
- w5=X0−αu1;
- w2=βX3−γX1;
- w3=γX3−γX1;
- w6=5u5;
- w1=w5−w6;
- w4=w5+w6;
- such that
- x0=w1−w2;
- x1=w4+w3;
- x2=w0.
- x3=w4−w3;
- x4=w1+w2;
- where
-
-
- α
- =
- 1
- 4
- ;
- β
- =
- cos
-
- (
- 3
-
- π
- 10
- )
- ;
- γ
- =
- -
- cos
-
- (
- π
- 10
- )
- ;
- δ
- =
- -
- 5
- 4
- .
Dependencies are inferred from the claim text.