N. Ahmed

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Nasir Ahmed (born 1940 in Bangalore, India) is a Professor Emeritus of Electrical and Computer and Engineering at University of New Mexico (UNM). He is best known for the development of the discrete cosine transform (DCT), which is a data compression transformation.

Nasir Ahmed

Fundamental contribution: Discrete Cosine Transform (DCT)

Ahmed was the leading author of the benchmark publication,[1][2] Discrete Cosine Transform (with T. Natarajan and K. R. Rao),[3] which has been cited as a fundamental development in many works[4] 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".[5]

The DCT is widely used for digital image compression.[6][7][8] It is a core component of the 1992 JPEG image compression technology developed by the JPEG Experts Group[9] working group and standardized jointly by the ITU,[10] 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[11] which was published in 1996, and an overview was presented in two 2006 publications by Yao Wang.[12][13] 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,[14] or as "DCT-II".[15]

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.[16] 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, as evident from the following results corresponding to various search scenarios:

  • U.S. Patents Quick Search: Title: DCT. Description/Specification: Video [6];
  • U. S. Patent Quick Search: Title: Image. Abstract: DCT [7];
  • U. S Patent Quick Search: Title: Video. Abstract: DCT [8];
  • U.S. Patent Quick Search: Title: Image. Description/Specification: DCT [9];
  • U.S. Patent Quick Search: Title: Video. Description/Speification: DCT [10].



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;" for details, see H. Andrews [11].

It continues to be cited with respect to a broad spectrum of signal processing applications—see Google-Scholar citations [12] . Available in approximately 230 libraries. A softcover reprint of this first edition is now available—e.g., see Springer-Verlag, Amazon, Barnes and Noble and Alibris.

  • 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). Available in approximately 215 libraries.


  1. 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].
  2. 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.
  3. 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<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  4. DCT citations via Google Scholar [2].
  5. N. Ahmed,. "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing, Vol. 1, Iss. 1, 1991, pp. 4-5. Italic or bold markup not allowed in: |publisher= (help)CS1 maint: extra punctuation (link)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  6. Andrew B. Watson,. "Image Compression Using the Discrete Cosine Transform" (PDF). Mathematical Journal, 4(1), 1994, pp. 81-88. Italic or bold markup not allowed in: |publisher= (help)CS1 maint: extra punctuation (link)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  7. image compression.
  8. Transform coding.
  9. G. K. Wallace, JPEG 1992 [3].
  10. CCITT 1992 [4].
  11. 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.
  12. Yao Wang, Video Coding Standards: Part I, 2006
  13. Yao Wang, Video Coding Standards: Part II, 2006
  14. Gilbert Strang,. "The Discrete Cosine Transform," (PDF). SIAM REVIEW, Vol. 41, No. 1, 1999, pp. 135-147. Italic or bold markup not allowed in: |publisher= (help)CS1 maint: extra punctuation (link)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  15. Discrete cosine transform.
  16. 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]

External links

  • Google Scholar citations [13].
  • IEEE Fellow in 1985, "for his contributions to engineering education and to digital signal processing" .[14].
  • Distinguished Engineering Alumnus Award, University of New Mexico,2001.[15].
  • Distinguished Graduate Faculty Member Award, Kansas State University, 1982-83.[16].
  • Summary of UNM's Annual Awards Reports for fiscal year (FY): 1999 [17]; 1998 [18].