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A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies.The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression.
The most widely used transform coding technique in this regard is the discrete cosine transform (DCT), [1] [2] proposed by Nasir Ahmed in 1972, [3] [4] and presented by Ahmed with T. Natarajan and K. R. Rao in 1974. [5] This DCT, in the context of the family of discrete cosine transforms, is the DCT-II.
By applying Euler's formula (= + ), it can be shown (for real-valued functions) that the Fourier transform's real component is the cosine transform (representing the even component of the original function) and the Fourier transform's imaginary component is the negative of the sine transform (representing the odd component of the ...
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.
A DCT variant, the modified discrete cosine transform (MDCT), is used in modern audio compression formats such as MP3, [21] Advanced Audio Coding (AAC), and Vorbis (OGG). The discrete sine transform (DST) is derived from the DCT, by replacing the Neumann condition at x=0 with a Dirichlet condition.
Motion compensation is one of the two key video compression techniques used in video coding standards, along with the discrete cosine transform (DCT). Most video coding standards, such as the H.26x and MPEG formats, typically use motion-compensated DCT hybrid coding, [1] [2] known as block motion compensation (BMC) or motion-compensated DCT (MC ...
In addition to spectral analysis of signals, discrete transforms play important role in data compression, signal detection, digital filtering and correlation analysis. [2] The discrete cosine transform (DCT) is the most widely used transform coding compression algorithm in digital media, followed by the discrete wavelet transform (DWT).
Rao, along with Nasir Ahmed and T. Natarajan, introduced the discrete cosine transform (DCT) in 1974 which has since become very popular in digital signal processing. DCT, INTDCT, directional DCT and MDCT (modified DCT) have been adopted in several international video/image/audio coding standards such as JPEG/MPEG/H.26X series and also by SMPTE ...