SC_I_06_DCT-Intro_4(1)

SC_I_06_DCT-Intro_4(1) - Signal Compression 167 Copyright...

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Unformatted text preview: Signal Compression 167 Copyright © 2005 – 2008 Hayder Radha The Discrete Cosine Transform The DCT is by far the most popular transform for image and video compression applications. DCT has been adopted by leading international standards including JPEG for still image compression and the different versions of MPEG and ITU video coding standards. Signal Compression 168 Copyright © 2005 – 2008 Hayder Radha We have seen that the KLT is optimum in terms of achieving uncorrelated transform coefficients. However, the KLT suffers from a major disadvantage and that is its signal-dependent characteristics. This makes the KLT difficult to realize in practice due to complexity and coding efficiency issues (think of the need to transmit the Signal Compression 169 Copyright © 2005 – 2008 Hayder Radha image/video covariance matrices every time the signal statistics change). The DCT represents an alternative orthonormal transform that is not signal dependent. Similar to the Discrete Fourier Transform (DFT), the DCT does not require knowledge of the signal statistics. In particular, there is no need to evaluate or transmit Signal Compression 170 Copyright © 2005 – 2008 Hayder Radha the covariance matrix X K of the random source vector when evaluating the DCT. More importantly, the DCT provides an excellent “approximation” of the KLT under certain conditions; and hence, the DCT is capable of generating of “approximately uncorrelated” S i g n a l C o m p r e s s i o n 1 7 1 C o p y r i g h t © 2 5 – 2 8 H a y d e r R a d h a t r a n s f o r m c o e f f i c i e n t s w i t h o u t b e i n g s i g n a l d e p e n d e n t . W e h a v e s e e n f e w e x a m p l e s w h e n c e r t a i n s i m p l i f y i n g a s s u m p t i o n s c a n p r o v i d e s i g n a l- i n d e p e n d e n t t r a n s f o r m s . I n p a r t i c u l a r , c a s e s w h e n w e h a v e e q u a l v a r i a n c e s , r e s u l t e d i n r e l a t i v e l y S i g n a l C o m p r e s s i o n 1 7 2 C o p y r i g h t © 2 5 – 2 8 H a y d e r R a d h a s i m p l e o r t h o n o r m a l t r a n s f o r m m a t r i c e s t h a t a r e i n d e p e n d e n t o f t h e s i g n a l s t a t i s t i c s . T h e d e v e l o p m e n t o f t h e D C T e x p l o i t s t w o u n d e r l y i n g a s s u m p t i o n s a b o u t t h e s i g n a l s t a t i s t i c a l b e h a v i o r : 1 . E q u a l v a r i a n c e s S i g n a l C o m p r e s s i o n 1 7 3 C o p y r i g h t © 2 5 – 2 8 H a y d e r R a d h a T h i s i s s i m i l a r t o t h e a s s u m p t i o...
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This note was uploaded on 10/27/2009 for the course ECE 802 taught by Professor Staff during the Fall '08 term at Michigan State University.

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SC_I_06_DCT-Intro_4(1) - Signal Compression 167 Copyright...

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