Dithering

Figure 3. Watermark embedding using Costa s seheme with a scalar component codebook (SCS). The watermark letter e is embedded after dithered uniform scalar quantization of x and the addition of the scaled quantization error as watermark Wr,.

Zachi Baharav, and Doron Shaked - Watermarking of Dither Halftoned Images. SPIE Electronic Imaging, Vol. 3657, pp. 307-313, January 1999. 

Keep moving. Don t dither around on one question. If you don t know the answer, skip the question and move on. Circle the number of the question in your test booklet in case you have time to come back to it later. 

Higher order architectures have been successfully used to build converters for digital audio applications [Adams, 1986][Hauser, 1991], However, the complexity of modulator and demodulator increases with the order. Higher order architectures also exhibit stability problems [van de Plassche, 1994], Dithering is a remedy to many of the problems of low level signals (see the previous section) and has been used in sigma delta converters as part of the noise shaping loop [Vanderkooy and Lipshitz, 1989]. 

Macon and Clements,] Macon, M. and Clements, M. Phase dithering in sine-wave analysis/synthesis. IEEE Signal Processing Letters, (submitted for publication). 

Vanderkooy and Lipshitz, 1984] Vanderkooy, J. and Lipshitz, S. (1984). Resolution below the Least Significant Bit in Digital Systems with Dither. J. Audio Eng. Society, 32 106-113. Correction, ibid., vol. 32, pp. 889, June 1987. 

Yamasaki, 1983] Yamasaki, Y. (1983). Application of large amplitude dither to the quantization of wide range audio signals. Journal of the Acoustical Society of Japan, J-39(7) 452-462. (In Japanese). 

Dither. Starting from Robert s pioneering paper [Roberts, 1976], the use of dither in audio was seriously analyzed by Vanderkooy and Lipshitz [Vanderkooy and Lipshitz, 1984], The basic idea is simple to whiten the quantization error, a random error signal is introduced. While the introduction of noise will make the signal noisier , it will also decorrelate the quantization error from the input signal (but not totally). Vanderkooy and Lipshitz also propose the use of triangular dither derived from the sum of two uniform random sources [Vanderkooy and Lipshitz, 1989],... 

Dither can be subtracted out ( subtractive dither ) after quantization and thereby whiten the signal. But in most systems this may be either difficult or impossible to do because the dither signal is not available. Therefore non-subtractive dither is the most common use of dithering. Yamasaki [Yamasaki, 1983] discusses the use of large amplitude dither (as much as 32A) in subtractive dither systems. 

A typical example of subtractive dither use in an A/D converter can be found in a Teac patent [Nakahashi and Ono, 1990], Notable features include the use of limiting and overload detectors as well as the ability to control the dither amplitude. A clever example of non-subtractive dither [Frindle, 1995][Frindle, 1992] separates the input signal into two paths. One of the paths is now inverted and then both paths are added to a random noise source. After the DAC, the two analog signals are subtracted the result is the sum of the conversion errors and twice the input signal. 

Frindle, 1992] Frindle, P. A. (1992). Digital to Analog Conversion Circuit with Dither and Overflow Prevention. U. S. Patent 5,148,163. 

Not a concern. Just attend to it and stop dithering. Garudin always spoke as if he had a sour taste in his mouth, but at times it was sharper than usual. I m done with the past for the present. He smiled, savouring his evil humour. This takes priority. History can wait. ... 

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