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Nasir Ahmed: The Transform Inside Every Codec

By Infinite Creation · Profile

1940-

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At a Glance

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.

Born 1940, India, worked in the United States
Anchor year: 1974, the DCT paper
Strand: overlooked, standards absorbed the credit

Career

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.

Known For

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

The DCT sits inside JPEG and MPEG, the compression step covered in A History of Broadcast Technology.

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.

Sources

The paper was checked against its publication record. Checked 20 August 2026.

N. Ahmed, T. Natarajan and K. R. Rao, Discrete Cosine Transform. IEEE Transactions on Computers, volume C-23, issue 1, pages 90 to 93, January 1974. The record confirms the author order given above, Ahmed then Natarajan then Rao, on the paper every image and video codec descends from.