Comparison of spectrograms of audio in an uncompressed format and several lossy formats. The lossy spectrograms show bandlimiting of higher frequencies, a common technique associated with lossy audio compression.
Nasir Ahmed, the inventor of the discrete cosine transform (DCT), which he first proposed in 1972.
Solidyne 922: The world's first commercial audio bit compression sound card for PC, 1990
Illustration of the implicit even/odd extensions of DCT input data, for N=11 data points (red dots), for the four most common types of DCT (types I-IV).
Processing stages of a typical video encoder
336x336px
An example showing eight different filters applied to a test image (top left) by multiplying its DCT spectrum (top right) with each filter.
Original size, scaled 10x (nearest neighbor), scaled 10x (bilinear).
Basis functions of the discrete cosine transformation with corresponding coefficients (specific for our image).
 DCT of the image =
.
On the left is the final image. In the middle is the weighted function (multiplied by a coefficient) which is added to the final image. On the right is the current function and corresponding coefficient. Images are scaled (using bilinear interpolation) by factor 10×.

The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression.

- Discrete cosine transform

Most forms of lossy compression are based on transform coding, especially the discrete cosine transform (DCT).

- Data compression
Comparison of spectrograms of audio in an uncompressed format and several lossy formats. The lossy spectrograms show bandlimiting of higher frequencies, a common technique associated with lossy audio compression.

20 related topics with Alpha

Overall

Lossy compression

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In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content.

The most widely used lossy compression algorithm is the discrete cosine transform (DCT), first published by Nasir Ahmed, T. Natarajan and K. R. Rao in 1974.

MP3

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Coding format for digital audio developed largely by the Fraunhofer Society in Germany, with support from other digital scientists in the United States and elsewhere.

Coding format for digital audio developed largely by the Fraunhofer Society in Germany, with support from other digital scientists in the United States and elsewhere.

With regard to audio compression (the aspect of the standard most apparent to end-users, and for which it is best known), MP3 uses lossy data-compression to encode data using inexact approximations and the partial discarding of data.

The discrete cosine transform (DCT), a type of transform coding for lossy compression, proposed by Nasir Ahmed in 1972, was developed by Ahmed with T. Natarajan and K. R. Rao in 1973; they published their results in 1974.

Video coding format

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Content representation format for storage or transmission of digital video content (such as in a data file or bitstream).

Content representation format for storage or transmission of digital video content (such as in a data file or bitstream).

It typically uses a standardized video compression algorithm, most commonly based on discrete cosine transform (DCT) coding and motion compensation.

Nasir Ahmed in 2012

Nasir Ahmed (engineer)

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Indian and American electrical engineer and computer scientist.

Indian and American electrical engineer and computer scientist.

Nasir Ahmed in 2012

He is best known for inventing the discrete cosine transform (DCT) in the early 1970s.

The DCT is the most widely used data compression transformation, the basis for most digital media standards (image, video and audio) and commonly used in digital signal processing.

MDCT window functions: blue: Cosine, red: Sine-Cosine, green: modified Kaiser-Bessel

Modified discrete cosine transform

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MDCT window functions: blue: Cosine, red: Sine-Cosine, green: modified Kaiser-Bessel

The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are overlapped so that the last half of one block coincides with the first half of the next block.

As a result of these advantages, the MDCT is the most widely used lossy compression technique in audio data compression.

Comparison of JPEG images saved by Adobe Photoshop at different quality levels and with or without "save for web"

Image compression

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Comparison of JPEG images saved by Adobe Photoshop at different quality levels and with or without "save for web"

Image compression is a type of data compression applied to digital images, to reduce their cost for storage or transmission.

Discrete Cosine Transform (DCT) – The most widely used form of lossy compression. It is a type of Fourier-related transform, and was originally developed by Nasir Ahmed, T. Natarajan and K. R. Rao in 1974. The DCT is sometimes referred to as "DCT-II" in the context of a family of discrete cosine transforms (see discrete cosine transform). It is generally the most efficient form of image compression.

Advanced Video Coding

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Video compression standard based on block-oriented, motion-compensated coding.

Video compression standard based on block-oriented, motion-compensated coding.

Block diagram of H.264
A YouTube video statistics with AVC (H.264) video codec and Opus audio format

This was achieved with features such as a reduced-complexity integer discrete cosine transform (integer DCT), variable block-size segmentation, and multi-picture inter-picture prediction.

AVC-Intra is an intraframe-only compression format, developed by Panasonic.

Block Diagram of HEVC

High Efficiency Video Coding

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Video compression standard designed as part of the MPEG-H project as a successor to the widely used Advanced Video Coding (AVC, H.264, or MPEG-4 Part 10).

Video compression standard designed as part of the MPEG-H project as a successor to the widely used Advanced Video Coding (AVC, H.264, or MPEG-4 Part 10).

Block Diagram of HEVC
HEVC has 33 intra prediction modes

In comparison to AVC, HEVC offers from 25% to 50% better data compression at the same level of video quality, or substantially improved video quality at the same bit rate.

While AVC uses the integer discrete cosine transform (DCT) with 4×4 and 8×8 block sizes, HEVC uses integer DCT and DST transforms with varied block sizes between 4×4 and 32×32.

A photo of a European wildcat with the compression rate decreasing and hence quality increasing, from left to right

JPEG

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Commonly used method of lossy compression for digital images, particularly for those images produced by digital photography.

Commonly used method of lossy compression for digital images, particularly for those images produced by digital photography.

A photo of a European wildcat with the compression rate decreasing and hence quality increasing, from left to right
The 8×8 sub-image shown in 8-bit grayscale
Zigzag ordering of JPEG image components
This image shows the pixels that are different between a non-compressed image and the same image JPEG compressed with a quality setting of 50. Darker means a larger difference. Note especially the changes occurring near sharp edges and having a block-like shape.
The original image
The compressed 8×8 squares are visible in the scaled-up picture, together with other visual artifacts of the lossy compression.
Visual impact of a jpeg compression on Photoshop on a picture of 4480x4480 pixels
An example of a stereoscopic .JPS file

JPEG uses a lossy form of compression based on the discrete cosine transform (DCT).

In video compression MCUs are called macroblocks.

Advanced Audio Coding

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Advanced Audio Coding (AAC) is an audio coding standard for lossy digital audio compression.

The discrete cosine transform (DCT), a type of transform coding for lossy compression, was proposed by Nasir Ahmed in 1972, and developed by Ahmed with T. Natarajan and K. R. Rao in 1973, publishing their results in 1974.