discrete cosine transform


Also found in: Medical, Acronyms, Wikipedia.

discrete cosine transform

(mathematics)
(DCT) A technique for expressing a waveform as a weighted sum of cosines.

The DCT is central to many kinds of signal processing, especially video compression.

Given data A(i), where i is an integer in the range 0 to N-1, the forward DCT (which would be used e.g. by an encoder) is:

B(k) = sum A(i) cos((pi k/N) (2 i + 1)/2) i=0 to N-1

B(k) is defined for all values of the frequency-space variable k, but we only care about integer k in the range 0 to N-1. The inverse DCT (which would be used e.g. by a decoder) is:

AA(i)= sum B(k) (2-delta(k-0)) cos((pi k/N)(2 i + 1)/2) k=0 to N-1

where delta(k) is the Kronecker delta.

The main difference between this and a discrete Fourier transform (DFT) is that the DFT traditionally assumes that the data A(i) is periodically continued with a period of N, whereas the DCT assumes that the data is continued with its mirror image, then periodically continued with a period of 2N.

Mathematically, this transform pair is exact, i.e. AA(i) == A(i), resulting in lossless coding; only when some of the coefficients are approximated does compression occur.

There exist fast DCT algorithms in analogy to the Fast Fourier Transform.
References in periodicals archive ?
2-Dimensional Discrete Cosine Transform (2D-DCT) scanning the co-efficient as zigzag as shown in Fig 6.
Nitesh Kumar More and Sipi Dubey, JPEG Picture Compression Using Discrete Cosine Transform.
Lab 1- Inverse Discrete Cosine Transform (IDCT) Hardware Acceleration - utilizes the MicroBlaze soft processor core and the Fast Simplex Link (FSL) that demonstrates the advantages of using hardware functions to accelerate software.
Picture data is converted to frequency components by discrete cosine transform (DCT).
Available in targeted-netlist formats for rapid integration in SoC/ASIC technologies and low-cost programmable logic devices (eg, Altera Cyclone or Xilinx Spartan-IIE) the Amphion product line-up for hardware-based Motion-JPEG includes the CS6100 Decoder, CS6150 Encoder, CS6190 Codec and Discrete Cosine Transform functions.
NOTE TO EDITOR: MPEG is a standard of the International Standards Organization (ISO) and is based on Discrete Cosine Transform (DCT) technology.
GIF LZW and TIFF scheme 5), or discrete cosine transforms, also known as DCT (i.
Embedded radiation-tolerant DSP Mathblocks feature 18 bit x 18 bit multiply-accumulate functions, enabling efficient implementation of DSP building blocks such as finite impulse response (FIR) and infinite impulse response (IIR) digital filters, fast Fourier transforms (FFT) and inverse Fourier transforms (IFT) and discrete cosine transforms (DCT).
The embedded radiation-tolerant DSP mathblock supports simple signed 18x18 multiply, dual signed 9x9 multiply, multiply plus accumulate and cascaded multiply applications, enabling efficient implementation of DSP structures such as finite impulse response (FIR), infinite impulse response (IIR) digital filters, fast Fourier transforms (FFT) and inverse Fourier transforms (IFT), discrete cosine transforms (DCT), correlators, and digital IF up/down converters.
Combines traditional methods such as discrete Fourier transforms and discrete cosine transforms with more recent techniques such as filter banks and wavelets

Full browser ?