What is recorded here?
Ahmed, Natarajan and Rao introduce a discrete cosine transform with an FFT-based computation and report close performance to the Karhunen-Loeve transform for specified correlated-signal models and filtering/rate-distortion comparisons. A signal can be described by a mixture of slowly and rapidly varying cosine patterns. For correlated samples, much of the variation can concentrate in a smaller set of these coefficients, making selected processing tasks economical. This paper defines the transform and its inverse, connects computation to the FFT, and tests the representation against other transforms for a stated signal model. Keeping every coefficient preserves the signal; dropping or quantizing coefficients can make a smaller but imperfect representation. Later image and video standards use related ideas, but their complete codecs and performance belong to separate contributions.
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Scientific scope
Exact 1974 IEEE Transactions on Computers C-23(1),90-93; the assessed article is on pages 90–93. Adjacent correlation/sequential-machine letters excluded. Finite cosine/Chebyshev basis and inverse, with a 2 M-point FFT computation; Comparisons use Toeplitz covariance rho^abs(i-j),0<rho<1: variance example M 16/rho 0.95; scalar diagonal Wiener filtering with white zero-mean uncorrelated noise, Table I rho 0.9/SNR 1/M 2-64; Gaussian-source rate-distortion example M 16/rho 0.9. Close-to-KLT reported within these settings, not exact eigenvectors/optimal compression for arbitrary covariances or all data. No general vector-filter/JPEG/video-codec validation. Full transform is reversible; loss requires subsequent selection/quantization. Standard tiny DCT-II matrix checks use own normalization, not certified reconstruction of original glyphs. No independent scientific/calibration certification.
Read the original work
- Ahmed, Natarajan and Rao, Discrete Cosine Transform, IEEE Trans.Computers C-23(1),90-93(1974), original correspondence
- IEEE-deposited Crossref identity for1974 DCT correspondence
- DBLP exact DCT paper byline and publication identity
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People and systems
Nasir Ahmed; T. Raj Natarajan; K. R. Rao
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English catalogue narrative
Ahmed, Natarajan and Rao: discrete cosine representation for correlated signals
Ahmed, Natarajan and Rao introduce a discrete cosine transform with an FFT-based computation and report close performance to the Karhunen-Loeve transform for specified correlated-signal models and filtering/rate-distortion comparisons.
A signal can be described by a mixture of slowly and rapidly varying cosine patterns. For correlated samples, much of the variation can concentrate in a smaller set of these coefficients, making selected processing tasks economical. This paper defines the transform and its inverse, connects computation to the FFT, and tests the representation against other transforms for a stated signal model. Keeping every coefficient preserves the signal; dropping or quantizing coefficients can make a smaller but imperfect representation. Later image and video standards use related ideas, but their complete codecs and performance belong to separate contributions.
Scientific scope
Exact 1974 IEEE Transactions on Computers C-23(1),90-93; the assessed article is on pages 90–93. Adjacent correlation/sequential-machine letters excluded. Finite cosine/Chebyshev basis and inverse, with a 2 M-point FFT computation; Comparisons use Toeplitz covariance rho^abs(i-j),0<rho<1: variance example M 16/rho 0.95; scalar diagonal Wiener filtering with white zero-mean uncorrelated noise, Table I rho 0.9/SNR 1/M 2-64; Gaussian-source rate-distortion example M 16/rho 0.9. Close-to-KLT reported within these settings, not exact eigenvectors/optimal compression for arbitrary covariances or all data. No general vector-filter/JPEG/video-codec validation. Full transform is reversible; loss requires subsequent selection/quantization. Standard tiny DCT-II matrix checks use own normalization, not certified reconstruction of original glyphs. No independent scientific/calibration certification.
People and systems
Nasir Ahmed; T. Raj Natarajan; K. R. Rao