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Multiresolution Signal Decomposition Transforms, Subbands, and Wavelets phần 3

LOT trong việc làm giảm các hiện vật ngăn chặn được thảo luận và cơ sở chức năng ID LOT FBR biến đổi một số sẽ được hiển thị trong hình. 2.14. Chúng tôi sẽ cho thấy LOT là một trường hợp đặc biệt của các phân hủy subband tổng quát hơn. Trong một nghĩa nào đó, LOT là một tiền thân của ngân hàng đầy giận dữ mult lọc. 2.5.2 Tài sản của các LOT | 88 CHAPTER 2. ORTHOGONAL TRANSFORMS of the LOT in reducing the blocking artifacts is discussed and the ID LOT basis functions for several transforms will be displayed in Fig. 2.14. We will show that the LOT is a special case of the more general subband decomposition. In a sense the LOT is a precursor to the multirate filter bank. 2.5.2 Properties of the LOT In conventional transform coding each segmented block of N data samples is multiplied by an N X N orthonormal matrix to yield the block of N spectral coefficients. If the vector data sequence is labeled Xq.Xi .yXị. where each X represents a block of N contiguous signal samples the transform operation produces 3 ị Xị. We have shown in Fig. 2.1 that such a transform coder is equivalent to a multirate filter bank where each FIR filter has N taps corresponding to the size of the coefficient vector. But as mentioned earlier this can lead to blockiness at the border region between data segments. To ameliorate this effect the lapped orthogonal transform calculates the coefficient vector 3ị by using all N sample values in Xị and crosses over to accept some samples from Xị_ỵ and xi 1. We can represent this operation by the multirate filter bank shown in Fig. 2.12. In this case each FIR filter has L taps. Typically L 2N the coefficient 3ị uses N data samples in j . N 2 samples from the previous block and N 2 samples from the next block xi 1. We can represent this operation by the noncausal filter bank of Fig. 2.12 where the support of each filter is the interval y N 1 4- y The time-reversed impulse responses are the basis functions of the LOT. The matrix representation of the LOT is Ỗ-M-Ì 0 Ổ1 2.220 The N X L matrix pQ is positioned so that it overlaps neighboring blocks5 typically by N 2 samples on each side. The matrices P . P2 account for the fact that the first and last data blocks have only one neighboring block. The N rows of 5In this section we indicate a transpose by p for convenience. 2.5. LAPPED ORTHOGONAL .