N. S. Jayant and P. Noll. Digital Coding of Waveforms. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1st edition, 1984. Home/Search Document Not in Database Summary Related Articles Check |
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....denoted as R k bits coefficient, such that # 1) An overall bit rate RR k = 4 1 4 (3) is satisfied and # 2) The reconstruction distortion is minimized. Since uniform scalar quantization is used, the distortion or error energy introduced by the quantizer in each subband can be modeled by [8], 9] ## # r k R y k k 222 , 4) where # y k is the variance of coefficients in each subband, R k is the subband bit rate, and# k is a parameter which depends on the probability distribution in the subbands (Gaussian or Laplacian or uniform, etc. Equation (4) makes intuitive sense ....
....(3) and (5) can be combined to form a constrained minimization problem which can be solved using Lagrange multipliers [29] where the Lagrangian to be minimized is JRR R y k = # # # ## ### 4 22 1 1 4 . Minimization of this function results in the best bit allocation of [8], 9] RR k yk k M yk = # 2 1 log . 6) Equation (6) is not valid in all cases, for example when it result in R k s that are negative, but methods have been derived to handle these technicalities [10] Using the optimal bit rates, the coefficients in each of the subbands are ....
N. Jayant and P. Noll, Digital Coding of Waveforms. Englewood Cliffs, NJ: Prentice-Hall, 1984.
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