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Các âm mưu của một số trực giao biến đổi khối 8 x 8 được thể hiện trong hình. 2.7. Những mô tả các trình tự cơ sở của mỗi biến đổi trong cả thời gian và frequencydomains. Những lô chứng minh rằng các trình tự cơ sở được lan truyền trên tất cả các khe thời gian tám trong khi lô tần số tập trung hơn tám băng tần riêng biệt. Các biến thể | 5.6. BLOCK TRANSFORM PACKETS 363 a b Figure 5.18 a Mixed tertiary binary tree b Tiling pattern. Daubechies Mostregular Coiflet Scaling 9 0.314 0.143 0.086 Function 5.22 5.77 11.86 ƠTƠĨÌ 0.699 0.825 1.02 Wavelet Ớ 0.178 0.188 0.108 Function 8.97 11.70 39.36 1.596 2.199 4.25 Lowpass 0.453 0.470 0.305 PR-QMF ơl 0.987 0.996 1.059 High-Pass ơl 0.453 0.470 0.305 PR-QMF 0.987 0.996 1.059 Table 5.7 Time-frequency localizations of six-tap wavelet filters and corresponding scaling and wavelet functions. 364 CHAPTER 5. TIME-FREQUENCY REPRESENTATIONS 5.6.1 From Tiling Pattern to Block Transform Packets The plots of several orthonormal 8x8 block transforms are shown in Fig. 2.7. These depict the basis sequences of each transform in both time- and frequencydomains. These plots demonstrate that the basis sequences are spread over all eight time slots whereas the frequency plots are concentrated over eight separate frequency bands. The variation in these from transform to transform is simply a matter of degree rather than of kind. The resulting time-frequency tiling then would have the general pattern shown in Fig. 5.19 a . There are eight time slots and eight frequency slots and the energy concentration is ill the frequency bands. The basis functions of these transforms are clearly frequency-selective and can be regarded as FIR approximations to a brick wall i.e. ideal rectangular band-pass filter frequency pattern which of course would necessitate infinite sine function time responses. Figure 5.19 a Tiling pattern for frequency-selective transform b Tiling pattern for time-selective transform The other extreme is that of the shifted Kronecker delta sequences as basis functions as mentioned in Section 2.1. The time- and frequency-domain plots are shown in Fig. 5.20. This realizable block transform i.e. the identity matrix has perfect resolution in time but no resolution in frequency. Its tiling pattern is shown in Fig. 5.19 b and can be regarded as a realizable brick-wall-in-time
