Overview
Nasir Ahmed (born 1940) conceived the discrete cosine transform in 1972 at Kansas State University and published it in 1974 with T. Natarajan and K. R. Rao. The DCT is the mathematical core of JPEG, MPEG, H.264, HEVC and effectively every image and video codec in use. His funding application was rejected.
What You Need
- Born 1940, India, worked in the United States
- Anchor year: 1974 — the DCT paper
- Strand: overlooked — standards absorbed the credit
Steps
The problem as it stood
Compressing images requires concentrating their information into as few numbers as possible. The Karhunen-Loève transform is optimal for that but depends on the statistics of each image and is far too expensive to compute. A fast, fixed, near-optimal substitute was needed.
What he actually did
Ahmed proposed using cosine basis functions, and with Natarajan and Rao showed the resulting transform approaches the optimum for the kind of correlated data natural images produce, while being computable quickly. His proposal to the National Science Foundation was rejected as too simple.
How it worked
Natural images vary smoothly, so neighbouring pixels are highly correlated. The DCT re-expresses a block as a sum of cosine patterns of increasing frequency, and for smooth content nearly all the energy lands in the few lowest-frequency coefficients. Quantise the rest coarsely or to zero and you have discarded little that the eye notices.
What it made possible
JPEG, MPEG-1 and 2, MP3's cousin the MDCT, H.264, HEVC, AV1 — essentially all image and video compression, and therefore digital television, DVD, streaming and every photograph on the web. It is among the most-executed algorithms ever written.
What happened to him
He became a professor at the University of New Mexico and continued in signal processing. He has been increasingly recognised in recent years, though the DCT's ubiquity still vastly exceeds his public profile.
Where the credit landed
Nasir Ahmed conceived the discrete cosine transform in 1972 and published it with Natarajan and Rao in 1974; it is the core of the standards that carry essentially all compressed images and video, and those standards credit no individual. Standards-body authorship is its own erasure mechanism: MPEG, JPEG, ITU and ISO documents are the invention, so there is no inventor to credit.
Pro Tips
- The DCT approximates the optimal transform while being fast enough to compute.
- Natural images are smooth, so energy concentrates in low-frequency coefficients.
- His funding application was rejected as too simple to be useful.
Knowledge Base
What You'll Learn
One transform, published in 1974, underlies almost every image you will see today.
Why cosines, and why blocks
Cosine basis functions have the useful property that a smooth signal is represented by very few of them, and — unlike a Fourier transform — they impose an even symmetry at the block edges, which avoids the artificial discontinuities that would otherwise create spurious high frequencies. Working in small blocks, usually 8×8, keeps computation manageable and allows different regions to be treated differently. It is also why heavily compressed JPEGs break into visible squares.
Where This Fits
This guide covers one specific part of the history of media technology. The wider picture — how each link in the chain from capture through transmission to display was actually built, who built it, and why the credit so often landed somewhere else — is in A History of Broadcast Technology: The Chain From Capture to Screen, which frames the discipline as a whole and links out to the detailed guides underneath it, including this one. If you are starting from scratch rather than solving a specific problem, read that first and come back here.
FAQ
Q: What is the discrete cosine transform?
A: A transform re-expressing a block of image data as a sum of cosine patterns of increasing frequency. For smooth natural images almost all the energy falls into a few low-frequency coefficients, so the rest can be discarded or coarsely quantised.
Q: Why are heavily compressed JPEGs blocky?
A: Because the DCT is applied to small blocks, usually 8×8 pixels. Quantising each block independently means their edges no longer match, and the block boundaries become visible.