隨著數位音訊處理日益成熟，越來越多的相關議題也隨之浮出檯面。破壞性資料壓縮演算法往往將較不重要的資訊由其中移除並犧牲一些品質以求取較高之壓縮比，但這也帶來一些新的問題。”zero band”這種失真雜訊便是其中之一。其成因是在使用極低位元率進行壓縮時，許多參數將不會被壓縮而在解碼端得到零值，而當一個頻帶間充斥著零時便會造成可聽到的失真雜訊。在此便用一個基於修正式離散餘弦轉換對於純正弦曲線分析結果的估測方法應用在現存的編解碼器上以去除零值。
一個普通的音訊通常是由數個正弦波曲線組合而成。而又由於一個由數個正弦波曲線組合而成的訊號其修正式離散餘弦轉換分析結果等於這些正弦波曲線各自修正式離散餘弦轉換分析結果之總和。由先前的研究，一個正弦波訊號的修正式離散餘弦轉換分析結果可以由一個常數，一個餘弦函數與一個衰減函數的乘積所逼近。利用這樣的規律，一個在解碼端利用被壓縮參數來估測其他未被壓縮係數的估測方法便可以被實現。這樣的估測方法不需要在訊號流中增加任何其他的資訊，而且可以被應用在任何使用修正式離散餘弦轉換做為分析工具的編解碼器上。
接著這個估測方法被應用到一個現存的頻譜導向樹狀結構（Spectral Oriented Trees）編解碼器。被預期能夠在解碼端被準確估測的參數便會在編碼端先行移除以節省資料量，而這些被移除的參數則會在解碼端被估測回來。這樣的估測方法不需要在訊號流中增加任何其他的資訊，而節省下來的資料量便可以用來壓縮或修正其他的參數以增進音訊品質。這個頻譜導向樹狀結構編解碼器中使用的壓縮法也經過些微修改以得到更好的效率。

As digital audio signals processing becomes more mature, more related issues come to the surface. Lossy compression algorithms usually remove the unimportant data and sacrifice some quality to reach a better compression ratio, but this brings up some new issues. The “zero band” artifact is one of them. The reason this artifact happens is that in very low bitrate coding many coefficients are not encoded and a band that is full of coefficients with the value of zero cause audible noises. An estimation method based on the MDCT analysis results of pure sinusoids is applied to an existing coder to remove zero coefficients.
A common audio signal is usually a tonal signal which is a combination of several sinusoids. It is known that the MDCT analysis results of a signal composed by several sinusoids is the same as the sum of the MDCT analysis results of these sinusoids. Previous studies have shown that the MDCT analysis results of pure sinusoids can be approximated by using the product of a constant, a cosine function, and a decay function. Using this law, an estimation method using the encoded coefficients to estimate other non-encoded coefficients on the decoder side is implemented. This estimation method does not need to add any side information into the bitstream and can be applied to any coder using MDCT and IMDCT as their analysis and synthesis tool.
The estimation method is later applied to a Spectral Oriented Trees based coder. The coefficients which are expected to be accurately estimated on the decoder side are removed in the encoding process to save bits, and the removed coefficients are estimated on the decoder side further in the process. There is no need to add any side information into the bitstream and the saved bits can be used to encode or refine other coefficients in order to improve audio quality. The coding method in the chosen SOT-based coder is modified to achieve better performance.

[1] McKinney, J. C., & Hopkins, R. (1995). Digital audio compression standard (AC-3). Advanced Television System Committee.
[2] ISO/IEC 11172-3 (1992). Coding of moving pictures and associated audio for digital storage media at up to about 1.5 Mbit/s (part 3: MPEG-audio).
[3] ISO/IEC 13818-7 (1997). Coding of moving pictures and associated audio (MPEG-2 advanced audio coding AAC).
[4] ISO/IEC 14496-3 (1998). Information technology – coding of audiovisual objects – part 3: audio – subpart 4: time/frequency coding.
[5] Liu, C. M., Hsu, H. W., & Lee, W.C. (2008). Compression artifacts in perceptual audio coding. IEEE Transactions Audio, Speech, and Language Processing, 16(4), 681-695.
[6] Prince, J. P., Johnson, A. W., & Bradley, A. B. (1987). Subband/transform coding using filter bank designs based on time domain aliasing cancellation. IEEE Transactions Acoustics, Speech, Signal Processing, 2161–2164.
[7] Prince, J. P., & Bradley, A. B. (1986). Analysis/synthesis filter bank design based on time domain aliasing cancellation. IEEE Transactions Acoustics, Speech, Signal Processing, assp-34 (5).
[8] Daudet, L., & Sandler, M. (2004). MDCT analysis of sinusoids: exact results and applications to coding artifacts reduction. IEEE Transactions on Speech and Audio Processing, 12(3), 302-312.
[9] ftp://kiwi:kiki@140.116.82.177:399/new/
[10] ITU-R BS.1387-1 (2001). Method for objective measurements of perceived audio quality.
[11] Chang, W. C., Wang, J. X., & Su, Alvin W. Y. (2008). SOT audio coder using reference frame ordering method. Submit to Journal of Audio Engineering Society.
[12] Said, A., & Pearlman, W.A. (1996). A new fast and efficient image codec based upon set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology, 6, 243–250.
[13] Wang, J. X., Chang, F. H., & Su, A. W. Y. (2004). Concurrent encoding in hierarchical trees for wavelet based image compression. International Conference on Image Processing, 5, 3173- 3176.