Nasir Ahmed (engineer)

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Nasir Ahmed
Nasir Ahmed.png
EducationBishop Cotton Boys' School,
University Visvesvaraya College of Engineering (BSc),
University of New Mexico (MSc, PhD)
Known forDiscrete cosine transform (DCT)
Inverse DCT (IDCT)
DCT lossy compression
DCT image compression
Lossless DCT (LDCT)
Discrete sine transform (DST)

Nasir Ahmed (born 1940 in Bangalore, India) is an Indian-American electrical engineer and computer scientist. He is Professor Emeritus of Electrical and Computer Engineering at University of New Mexico (UNM). He is best known for inventing the discrete cosine transform (DCT) in the early 1970s. The DCT is the most widely used data compression transformation, the basis for most digital media standards (image, video and audio) and commonly used in digital signal processing. He also described the discrete sine transform (DST), which is related to the DCT.

Discrete cosine transform (DCT)[edit]

The discrete cosine transform (DCT) is a lossy compression algorithm that was first conceived by Ahmed while working at the Kansas State University, and he proposed the technique to the National Science Foundation in 1972. He originally intended the DCT for image compression.[1][2] Ahmed developed a working DCT algorithm with his PhD student T. Natarajan and friend K. R. Rao in 1973,[1] and they presented their results in a January 1974 paper.[3][4][5] It described what is now called the type-II DCT (DCT-II),[6] as well as the type-III inverse DCT (IDCT).[3]

Ahmed was the leading author of the benchmark publication,[7][8] Discrete Cosine Transform (with T. Natarajan and K. R. Rao),[9] which has been cited as a fundamental development in many works[10] since its publication. The basic research work and events that led to the development of the DCT were summarized in a later publication by N. Ahmed, "How I came up with the Discrete Cosine Transform".[1]

The DCT is widely used for digital image compression.[11][12][13] It is a core component of the 1992 JPEG image compression technology developed by the JPEG Experts Group[14] working group and standardized jointly by the ITU,[15] ISO and IEC. A tutorial discussion of how it is used to achieve digital video compression in various international standards defined by ITU and MPEG (Moving Picture Experts Group) is available in a paper by K. R. Rao and J. J. Hwang[16] which was published in 1996, and an overview was presented in two 2006 publications by Yao Wang.[17][18] The image and video compression properties of the DCT resulted in its being an integral component of the following widely used international standard technologies:

Standard Technologies
JPEG Storage and transmission of photographic images on the World Wide Web (JPEG/JFIF); and widely used in digital cameras and other photographic image capture devices (JPEG/Exif).
MPEG-1 Video Video distribution on CD or via the World Wide Web.
MPEG-2 Video (or H.262) Storage and handling of digital images in broadcast applications: digital TV, HDTV, cable, satellite, high speed internet; video distribution on DVD.
H.261 First of a family of video coding standards (1988). Used primarily in older video conferencing and video telephone products.
H.263 Video telephony over Public Switched Telephone Network (PSTN)

The form of DCT used in signal compression applications is sometimes referred to as "DCT-2" in the context of a family of discrete cosine transforms,[19] or as "DCT-II".[20]

More recent standards have used integer-based transforms that have similar properties to the DCT but are explicitly based on integer processing rather than being defined by trigonometric functions.[21] As a result of these transforms having similar symmetry properties to the DCT and being, to some degree, approximations of the DCT, they have sometimes been called "integer DCT" transforms. Such transforms are used for video compression in the following technologies pertaining to more recent standards:

Standard Technologies
VC-1 Windows media, Blu-ray Discs.
H.264/MPEG-4 AVC The most commonly used format for recording, compression and distribution of high definition video; streaming internet video; Blu-ray Discs; HDTV broadcasts (terrestrial, cable and satellite).
HEVC The emerging successor to the H.264/MPEG-4 AVC standard, having substantially improved compression capability.
WebP Images A graphic format that support the lossy compression of digital images. Developed by Google.
WebM Video A multimedia open source format developed by Google intended to be used with HTML5.

The "integer DCT" design is conceptually similar to the conventional DCT; however, it is simplified and made to provide exactly specified decoding.

The DCT has been widely cited in patents that have been awarded since 1976.

A DCT variant, the modified discrete cosine transform (MDCT), is used in modern audio compression formats such as MP3,[22] Advanced Audio Coding (AAC), and Vorbis (OGG).

The discrete sine transform (DST) is derived from the DCT, by replacing the Neumann condition at x=0 with a Dirichlet condition.[23] The DST was described in the 1974 DCT paper by Ahmed, Natarajan and Rao.[3]

Ahmed later was involved in the development a DCT lossless compression algorithm with Giridhar Mandyam and Neeraj Magotra at the University of New Mexico in 1995. This allows the DCT technique to be used for lossless compression of images. It is a modification of the original DCT algorithm, and incorporates elements of inverse DCT and delta modulation. It is a more effective lossless compression algorithm than entropy coding.[24]



Have been translated into Russian, Chinese and Japanese:

  • Leading author of Orthogonal Transforms for Digital Signal Processing, Springer-Verlag (Berlin – Heidelberg – New York), 1975, with K.R. Rao; translated into Russian (1980) and Chinese (1979). It is the first text book that included the DCT, and one of the first to present a unified approach to using sinusoidal and non-sinusoidal orthogonal transforms for signal processing. To quote one reviewer, "the authors have treaded where others have feared to venture. In doing so, they have developed a useful book as a first effort in the exciting area of digital signal processing and general orthogonal transforms;"
  • Leading author of Discrete-Time Signals and Systems, Reston Publishing Company, Inc. (A Prentice-Hall Company), Reston, Virginia, 1983, with T. Natarajan; translated into Japanese (1990).

In popular culture[edit]

In season 5, episode 8 of NBC's This Is Us, Ahmed's story was told to highlight the importance of image and video transmission over the Internet in modern society, particularly during the COVID-19 pandemic. The episode ends with a picture of Ahmed and his wife, along with captions explaining the importance of his work, and that producers spoke to the couple over video chat to understand their story and incorporate it into the episode.


  1. ^ a b c Ahmed, Nasir (January 1991). "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing. 1 (1): 4–5. doi:10.1016/1051-2004(91)90086-Z.
  2. ^ Stanković, Radomir S.; Astola, Jaakko T. (2012). "Reminiscences of the Early Work in DCT: Interview with K.R. Rao" (PDF). Reprints from the Early Days of Information Sciences. 60. Retrieved 13 October 2019.
  3. ^ a b c Ahmed, Nasir; Natarajan, T.; Rao, K. R. (January 1974), "Discrete Cosine Transform" (PDF), IEEE Transactions on Computers, C-23 (1): 90–93, doi:10.1109/T-C.1974.223784
  4. ^ Rao, K. R.; Yip, P. (1990), Discrete Cosine Transform: Algorithms, Advantages, Applications, Boston: Academic Press, ISBN 978-0-12-580203-1
  6. ^ Britanak, Vladimir; Yip, Patrick C.; Rao, K. R. (2010). Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations. Elsevier. p. 51. ISBN 9780080464640.
  7. ^ Selected Papers on Visual Communication: Technology and Applications, (SPIE Press Book), Editors T. Russell Hsing and Andrew G. Tescher, April 1990, pp. 145-149 [1].
  8. ^ Selected Papers and Tutorial in Digital Image Processing and Analysis, Volume 1, Digital Image Processing and Analysis, (IEEE Computer Society Press), Editors R. Chellappa and A. A. Sawchuk, June 1985, p. 47.
  9. ^ Ahmed, N.; Natarajan, T.; Rao, K. R. (January 1974), "Discrete Cosine Transform", IEEE Transactions on Computers, C-23 (1): 90–93, doi:10.1109/T-C.1974.223784
  10. ^ DCT citations via Google Scholar [2].
  11. ^ Andrew B. Watson (1994). "Image Compression Using the Discrete Cosine Transform" (PDF). Mathematica Journal. 4 (1): 81–88.
  12. ^ image compression.
  13. ^ Transform coding.
  14. ^ G. K. Wallace, JPEG 1992 [3].
  15. ^ CCITT 1992 [4].
  16. ^ K. R. Rao and J. J. Hwang, Techniques and Standards for Image, Video, and Audio Coding, Prentice Hall, 1996; JPEG: Chapter 8; H.261: Chapter 9; MPEG-1: Chapter 10; MPEG-2: Chapter 11.
  17. ^ Yao Wang, Video Coding Standards: Part I, 2006
  18. ^ Yao Wang, Video Coding Standards: Part II, 2006
  19. ^ Gilbert Strang (1999). "The Discrete Cosine Transform" (PDF). SIAM Review. 41 (1): 135–147. Bibcode:1999SIAMR..41..135S. doi:10.1137/S0036144598336745.
  20. ^ Discrete cosine transform.
  21. ^ Jae-Beom Lee and Hari Kalva, The VC-1 and H.264 Video Compression Standards for Broadband Video Services, Springer Science+Business Media, LLC., 2008, pp. 217-245; for more on this book, see [5]
  22. ^ Guckert, John (Spring 2012). "The Use of FFT and MDCT in MP3 Audio Compression" (PDF). University of Utah. Retrieved 14 July 2019.
  23. ^ Britanak, Vladimir; Yip, Patrick C.; Rao, K. R. (2010). Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations. Elsevier. pp. 35–6. ISBN 9780080464640.
  24. ^ Mandyam, Giridhar D.; Ahmed, Nasir; Magotra, Neeraj (17 April 1995). "DCT-based scheme for lossless image compression". Digital Video Compression: Algorithms and Technologies 1995. International Society for Optics and Photonics. 2419: 474–478. Bibcode:1995SPIE.2419..474M. doi:10.1117/12.206386. S2CID 13894279.

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