orms for a couple of important reasons. The DCT has fast O(nlogn) Figure 7.4-3 Reconstruction periodicity of DFT VS DCT. Video compression CHAPTER 7.4 (a) Original (b) Reconstructed Figure 7.4-4 Severe blocking artifacts introduced by gross quantization of DCT coefficients. and the DCT transformed coefficient array is displayed The uniform scalar quantizer is the most fundamental in part (b). scalar quantizer. It possesses a nonlinear staircase input- The original image sub-block in (a) contains large output characteristic that divides the input range into values in every position and is not very suitable for spatial output levels of equal size. In order for the quantizer to compression in this format. The coefficient matrix (b) effectively reduce the bit rate, the number of output concentrates most of the signal energy in the top left values should be much less that the number of input quadrant. The signal frequency coordinates (u, v) = (0,0) values. The reconstruction values are chosen to be at the start at the upper left position. The DC component midpoint of the output levels. This choice is expected to equals 1255 and contains the vast majority of the signal minimize the reconstruction MSE when the quantization energy by itself. This dynamic range and concentration of energy should yield a significant reduction in non-zero values and bit rate after the coefficients are quantized. 7.4.5.3 Quantization f(i,j) = The quantization stage of the video encoder creates a lossy representation of the input. The input as discussed earlier should be conditioned with a particular method of quantization in mind. And vice versa, the quantizer should be well matched to the characteristics of the input in order to meet or exceed the rate-distortion performance requirements. As always is (a) Original Lena 8x8 image sub-block the case, the quantizer has an effect on system perfor- mance that must be taken under consideration. Simple scalar versus vector quantization implementations can have significant system performance implic