high frequency and therefore the components in the top left corner of Figure 3.10 are of particular importance. When the grid of coefficients has been zigzag-scanned there remains a 1D array of coefficient values. The values at the beginning of the array have the lowest spatial frequency. Quantization of Coefficients Transforming a block of pixels using the DCT transform gives rise to a block of coefficients. Performing the inverse DCT on this block of coefficients produces the original block of pixels; however, it should be noted that in performing the DCT transform no compression has taken place. Compression is almost universally achieved in image codecs by the imposi- Chapter 3 Digital Video Transmission Component Direction Fig. 3.10 Zigzag scanning of DCT coefficients. Table 3.2 Quantization Step Size Q = 16 Coefficient Final value tion of quantization. Figure 3.9(a) and (b) shows the relationship between fidelity and the number of coefficients used. If the coefficients are subjected to quantization, a reduction in bitrate can be achieved, but this is inevitably at the expense of image quality. A quantization scheme needs to con- sider a compromise between the bitrate and the resultant distortion. This is known as rate distortion (Ghanbari, 2003) and was studied by researchers prior to implementing the codecs. Therefore, most modern codecs have made this decision for us and have been designed to also take into consideration the behavior of the human visual system. Typically, bitrate is controlled by adjusting the quantizer step size. The step size is often controlled by the output buffer in an attempt to control the rate of data generation. The quantizer operates on the raw coefficients, reducing both the dynamic range and the number of coefficients to be coded. Table 3.2 shows an example of this where some arbitrary values have been quantized and indexed using a step size of Q = 16. Note particularly the presence of Os produced by the quantizer. For real-world images, typically the final values to be coded c