DISCRETE COSINE TRANSFORM

CONTENTS                 HOME       INTRODUCTION       METHODOLOGY       VHDL + C   CODES       BLOCK DIAGRAMS       FLOW CHARTS       PRE-LAYOUT SIMULATIONS       SYNTHESIS       POST-LAYOUT SIMULATIONS       RESULTS       CONCLUSIONS

The DCT is a loss-less and reversible mathematical transformation that converts a spatial amplitude representation of data into a spatial frequency representation. One of the advantages of the DCT is its energy compaction property, that is, the signal energy is concentrated on a few components while most other components are zero or are negligibly small. The DCT was first introduced in 1974 and since then it has been used in many applications such as filtering, transmultiplexers, speech coding, image coding (still frame, video and image storage), pattern recognition, image enhancement, and SAR/IR image coding. The DCT is widely used in image compression applications, especially in lossy image compression. For example, the 2D DCT is used for JPEG still image compression, MPEG moving image compression, and the H.261 and H.263 video-telephony coding schemes. The energy compaction property of the DCT is well suited for image compression since, as in most images, the energy is concentrated in the low to middle frequencies, and the human eye is more sensitive to the middle frequencies. The DCT is not easy to implement because it is data dependent but it provides a very good compression ratio.         Since the 2D DCT can be computed by applying 1D transforms separately to the rows and columns, we say that the 2D DCT is separable in the two dimensions.     As in the 1D case, each element F(u,v) of the transform is the inner product of the input and a basis function, but in this case, the basis functions are M x N matrices. Each 2D basis matrix is the outer product of two of the 1D basis vectors                 DCT v/s DFT     In case of the DFT, the basis sequences are the complex periodic sinusoidal sequences of exponential function, and in general the transforms yield complex even if the signal is real. DCT is an orthogonal transform representation for real sequences. DFT involves implicit assumption of periodicity, the DCT involves in implicit assumption of both periodicity and even symmetry. Computationally, the DCT is more efficient than the DFT because it is a completely real transform and does not require complex variables or arithmetic.