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Transform coding is a type ofdata compression for "natural" data likeaudiosignals or photographicimages. 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).
In transform coding, knowledge of the application is used to choose information to discard, thereby lowering itsbandwidth. The remaining information can then be compressed via a variety of methods. When the output is decoded, the result may not be identical to the original input, but is expected to be close enough for the purpose of the application.
One of the most successful transform encoding system is typically not referred to as such—the example beingNTSC colortelevision. After an extensive series of studies in the 1950s,Alda Bedford showed that the human eye has high resolution only for black and white, somewhat less for "mid-range" colors like yellows and greens, and much less for colors on the end of the spectrum, reds and blues.
Using this knowledge allowedRCA to develop a system in which they discarded most of the blue signal after it comes from the camera, keeping most of the green and only some of the red; this ischroma subsampling in theYIQcolor space.
The result is a signal with considerably less content, one that would fit within existing 6 MHz black-and-white signals as a phase modulated differential signal. The average TV displays the equivalent of 350 pixels on a line, but the TV signal contains enough information for only about 50 pixels of blue and perhaps 150 of red. This is not apparent to the viewer in most cases, as the eye makes little use of the "missing" information anyway.
The PAL and SECAM systems use nearly identical or very similar methods to transmit colour. In any case both systems are subsampled.
The term is much more commonly used indigital media anddigital signal processing. The most widely used transform coding technique in this regard is thediscrete cosine transform (DCT),[1][2] proposed byNasir Ahmed in 1972,[3][4] and presented by Ahmed with T. Natarajan andK. R. Rao in 1974.[5] This DCT, in the context of the family of discrete cosine transforms, is the DCT-II. It is the basis for the commonJPEGimage compression standard,[6] which examines small blocks of the image and transforms them to thefrequency domain for more efficient quantization (lossy) anddata compression. Invideo coding, theH.26x andMPEG standards modify this DCT image compression technique across frames in a motion image usingmotion compensation, further reducing the size compared to a series of JPEGs.
Inaudio coding, MPEG audio compression analyzes the transformed data according to apsychoacoustic model that describes the human ear's sensitivity to parts of the signal, similar to the TV model.MP3 uses a hybrid coding algorithm, combining themodified discrete cosine transform (MDCT) andfast Fourier transform (FFT).[7] It was succeeded byAdvanced Audio Coding (AAC), which uses a pure MDCT algorithm to significantly improve compression efficiency.[8]
The basic process ofdigitizing an analog signal is a kind of transform coding that usessampling in one or more domains as its transform.