Lapped transform
In today's world, Lapped transform has become increasingly relevant in different areas of society. From its impact on the economy to its influence on everyday life, Lapped transform has become a topic of constant interest and debate. Its importance lies in its ability to impact the way people, companies and institutions address different challenges and opportunities. In this article we will explore the various aspects related to Lapped transform, from its origin and evolution to its potential consequences and benefits. Through detailed analysis, we will try to understand how Lapped transform is shaping the world today and how it can influence the future.
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.
Lapped transforms substantially reduce the blocking artifacts that otherwise occur with block transform coding techniques, in particular those using the discrete cosine transform. The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.
Although the best-known application of lapped transforms has been for audio coding, they have also been used for video and image coding and various other applications. They are used in video coding for coding I-frames in VC-1 and for image coding in the JPEG XR format. More recently, a form of lapped transform has also been used in the development of the Daala video coding format.
References
- ^ Malvar, H. S. (1992). "Signal Processing with Lapped Transforms" (Document). Artech House.
- ^ de Queiroz, Ricardo L. "On Lapped Transforms". CiteSeerX 10.1.1.91.7148. Retrieved August 20, 2023.
- ^ Malvar, H. S. (November 1992). "Extended Lapped Transforms: Properties, Applications, and Fast Algorithms" (PDF). IEEE Transactions on Signal Processing. 40 (11): 2703–2714. Bibcode:1992ITSP...40.2703M. doi:10.1109/78.165657.
- ^ Tran, Trac D.; Liang, Jie; Tu, Chengjie (June 2003). "Lapped Transform via Time-Domain Pre- and Post-Filtering" (PDF). IEEE Transactions on Signal Processing. 51 (6): 1557. Bibcode:2003ITSP...51.1557T. doi:10.1109/TSP.2003.811222. Archived from the original (PDF) on 2016-03-04. Retrieved 2013-06-22.
- ^ a b "Next generation video: Introducing Daala". xiph.org. June 20, 2013.
 | This linear algebra-related article is a stub. You can help Wikipedia by expanding it. |
 | This electronics-related article is a stub. You can help Wikipedia by expanding it. |