Lapped transform

discrete cosine transform with overlapping blocks
In signal processing, a lapped transform is a type of linear discrete block transformation where the basis functions of the transformation overlap the block boundaries, yet the number of coefficients overall resulting from a series of overlapping block transforms remains the same as if a non-overlapping block transform had been used.wikipedia
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Modified discrete cosine transform

MDCTModulated Lapped Transformtime-domain aliasing cancellation
The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.
The modified discrete cosine transform (MDCT) is a lapped transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset,

Daala

More recently, a form of lapped transform has also been used in the development of the Daala video coding format.
As a basic technology Daala uses an unconventional discrete cosine transform with overlapping blocks.

Signal processing

signal analysissignalsignal processor
In signal processing, a lapped transform is a type of linear discrete block transformation where the basis functions of the transformation overlap the block boundaries, yet the number of coefficients overall resulting from a series of overlapping block transforms remains the same as if a non-overlapping block transform had been used.

Linear map

linear operatorlinear transformationlinear
In signal processing, a lapped transform is a type of linear discrete block transformation where the basis functions of the transformation overlap the block boundaries, yet the number of coefficients overall resulting from a series of overlapping block transforms remains the same as if a non-overlapping block transform had been used.

Discrete transform

discrete block transformation
In signal processing, a lapped transform is a type of linear discrete block transformation where the basis functions of the transformation overlap the block boundaries, yet the number of coefficients overall resulting from a series of overlapping block transforms remains the same as if a non-overlapping block transform had been used.

Basis function

basis functionsbasisbases
In signal processing, a lapped transform is a type of linear discrete block transformation where the basis functions of the transformation overlap the block boundaries, yet the number of coefficients overall resulting from a series of overlapping block transforms remains the same as if a non-overlapping block transform had been used.

Discrete cosine transform

DCTiDCTinverse discrete cosine transform
Lapped transforms substantially reduce the blocking artifacts that otherwise occur with block transform coding techniques, in particular those using the discrete cosine transform.

MP3

.mp3MP3 downloadMP3 files
The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.

Vorbis

Ogg VorbisOGGaoTuV
The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.

Advanced Audio Coding

AACAAC-LCMPEG-4 AAC
The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.

Opus (audio format)

OpusOpus audio format.opus
The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.

Audio codec

audio codecscodecaudio
The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.

Video compression picture types

B-frameP-frameB-frames
They are used in video coding for coding I-frames in VC-1 and for image coding in the JPEG XR format.

VC-1

SMPTE VC1VC-1/WMV3VC1
They are used in video coding for coding I-frames in VC-1 and for image coding in the JPEG XR format.

JPEG XR

HD PhotoJPEG XR / HD PhotoHD
They are used in video coding for coding I-frames in VC-1 and for image coding in the JPEG XR format.

Video coding format

video coding standardsvideo codingvideo coding standard
More recently, a form of lapped transform has also been used in the development of the Daala video coding format.

Modulated complex lapped transform

The modulated complex lapped transform (MCLT) is a lapped transform, similar to the modified discrete cosine transform, that explicitly represents the phase (complex values) of the signal.

G.722.1

G.722
The G.722.1 algorithm is based on lapped transform technology, using a Modulated Lapped Transform (MLT), a type of MDCT.

Thor (video codec)

ThorThor video codec
As part of the NETVC work, the Constrained Low-Pass Filter (CLPF) and motion compensation techniques used in Thor were tested in conjunction with the lapped transform coding techniques from the Daala codec.

Rico Malvar

Henrique MalvarHenrique S. MalvarHenrique Sarmento Malvar