# Discrete Cosine Transform

@article{Ahmed1974DiscreteCT, title={Discrete Cosine Transform}, author={Nasir Ahmed and T. Raj Natarajan and K. R. Rao}, journal={IEEE Transactions on Computers}, year={1974}, volume={C-23}, pages={90-93} }

A discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed. It is shown that the discrete cosine transform can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering. Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Loève transform, which is known to be optimal. The performances of the Karhunen-Loève and…

## 2,884 Citations

### Recursive algorithms for discrete cosine transform

- Computer ScienceProceedings of Third International Conference on Signal Processing (ICSP'96)
- 1996

A recursive algorithm with a regular structure is first presented for computing the discrete cosine transform (DCT-II), it requires no data shifts, the multiplication coefficients can be generated by a simple recursion.

### Generalized Discrete Cosine Transform

- Computer Science2009 Pacific-Asia Conference on Circuits, Communications and Systems
- 2009

In simulating the discrete cosine transform, a generalized discrete Cosine transform with three parameters is proposed, and its orthogonality for some new cases is proved.

### A new look at DCT-type transforms

- Computer ScienceIEEE Trans. Acoust. Speech Signal Process.
- 1989

The proposed transform offers a higher computational efficiency than the traditional even discrete cosine transform and yields a mean-squared error close to that of the DCT.

### Discrete cosine transform filtering

- EngineeringInternational Conference on Acoustics, Speech, and Signal Processing
- 1990

Circular convolution-multiplication relationships for the discrete cosine transform (DCT) that are similar to those forThe discrete Fourier transform (DFT) are developed and can be used to filter an image in the frequency domain as an approximation of circular convolution in the spatial domain.

### Frequency cosine transform: A bridge between gradient based frequency transform and discrete cosine transform

- Computer Science, Engineering2008 International Conference on Neural Networks and Signal Processing
- 2008

It is shown that the FCT can be regarded as a special case of FRT or DCT and it is as sophisticated as the FRT and as fast as the DCT.

### Image coding using weighted cosine transform

- Computer ScienceIEEE TENCON'90: 1990 IEEE Region 10 Conference on Computer and Communication Systems. Conference Proceedings
- 1990

A new orthogonal transform, called weighted cosine transform (WCT), is developed for digital image coding applications and the transform matrix is the weighted version of that in the discrete cosinetransform (DCT).

### On the Discrete Cosine Transform of Weakly Stationary Signals

- Computer Science, Engineering
- 2012

The transformed autocorrelation matrix has half of its elements equal to zero, which means that it is possible to improve current DCT signal processing systems by means of more efficient implementation and algorithms.

### A new algorithm to compute the DCT and its inverse

- Computer Science, EngineeringIEEE Trans. Signal Process.
- 1991

A novel algorithm to convert the discrete cosine transform (DCT) to skew-circular convolutions is presented and it is shown that the inverse DCT (IDCT) can be computed using the same building blocks which are used for computing the DCT.

### Fast algorithms for the discrete cosine transform

- Computer ScienceIEEE Trans. Signal Process.
- 1992

Algorithms for computing scaled DCTs and their inverses have applications in compression of continuous tone image data, where the DCT is generally followed by scaling and quantization.

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The classical signal processing technique known as Wiener filtering has been extended to the processing of one-and two-dimensional discrete data by digital operations with emphasis on reduction of…

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A new unitary transform called the slant transform, specifically designed for image coding, has been developed. The transformation possesses a discrete sawtoothlike basis vector which efficiently…

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The transform-coding concept has been applied to the coding of color images represented by three primary color planes of data and it is shown that, by transform coding, the chrominance content of a color image can be coded with an average of 1.0 bits per element or less without serious degradation.

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This paper develops performance criteria for evaluating transform data coding schemes under computational constraints characterized by a rate-distortion relation R(D) similar in form to the theoretical rate- Distortion function.

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### External link This page was last modified 17:12, 7 Apr 2005. All text is available under the terms of the GNU Free Documentation License (see Copyrights for details)

- External link This page was last modified 17:12, 7 Apr 2005. All text is available under the terms of the GNU Free Documentation License (see Copyrights for details)

### Retrieved from "http://en.wikipedia.org/wiki/Discrete_cosine_transform" Categories: Digital signal processing | Fourier analysis

- Retrieved from "http://en.wikipedia.org/wiki/Discrete_cosine_transform" Categories: Digital signal processing | Fourier analysis

### discrete cosine transform (http://planetmath.org/?op=getobj&from=objects&id=1469) on PlanetMath

- discrete cosine transform (http://planetmath.org/?op=getobj&from=objects&id=1469) on PlanetMath