. Because the DCT is applied to the image and a frequency domain repre- sentation is available, emphasis can be applied to the parts of the spectrum that are humanly Low Luminance High Luminance Fig. 3.7 Human spatial frequency response. Spatial Frequency (cycles/degree) Chapter 3 Digital Video Transmission important. The application of nonlinear quantization of the coefficients allows the quantity of information conveyed to be reduced while still maintaining subjective quality. Discrete Cosine Transform The Discrete Cosine Transform (DCT) separates the image into parts (or spectral subbands) of differing importance with respect to the image's visual quality. The DCT is similar to the discrete Fourier transform: It transforms a signal or image from the spatial domain to the frequency domain. With an input image, A, the coefficients for the output image, B, are N1-1N2-1 IT k1 B(k1,k2) 4 A(i,j) cos T k2 (2.j+1) (3.2) The input image is N2 pixels wide by N1 pixels high; A(i,j) is the intensity of the pixel in row i and column j; B(k1,k2) is the DCT coefficient in row k1 and column k2 of the DCT matrix. All DCT multiplications are real. This lowers the number of required multiplications as compared to the discrete Fourier transform. The input to the DCT transform is an 8 X 8 array of integers containing each pixel's gray-scale level and is typically 8 bits or 0 to 255. The output array of DCT coefficients contains integers; these can range from - -1024 to 1023. For most images, much of the signal energy lies at low frequencies; these appear in the DCT's upper left corner. The lower right values represent higher frequencies and are often small-small enough to be neglected with little visible distortion. Figure 3.8 shows the basis functions, which are the individual coefficients reconstructed in the pixel domain. Significance of the Coefficients For each 8 X 8 block of pixels contained in the image, the DCT is applied, producing an 8 X 8 grid of coefficients representing the amount of each individual basis function the