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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 .
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.
Transform coding is a type of data compression for "natural" data like audio signals or photographic images. The transformation is typically lossless (perfectly reversible) on its own but is used to enable better (more targeted) quantization , which then results in a lower quality copy of the original input ( lossy compression ).
The macroblock is a processing unit in image and video compression formats based on linear block transforms, typically the discrete cosine transform (DCT). A macroblock typically consists of 16×16 samples, and is further subdivided into transform blocks, and may be further subdivided into prediction blocks.
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).
Transform coding dates back to the late 1960s, with the introduction of fast Fourier transform (FFT) coding in 1968 and the Hadamard transform in 1969. [10] An important development in image data compression was the discrete cosine transform (DCT), a lossy compression technique first proposed by Nasir Ahmed, T. Natarajan and K. R. Rao in 1973. [11]
Transform coding dates back to the late 1960s, with the introduction of fast Fourier transform (FFT) coding in 1968 and the Hadamard transform in 1969. [34] An important image compression technique is the discrete cosine transform (DCT), a technique developed in the early 1970s. [16]