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Least Squares Theory and Design of Optimal Noise Shaping Filters

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Signal requantization to reduce the word-length of an audio stream introduces distortions. Noise shaping can be applied to make requantization distortions minimally audible. The psychoacoustically optimal noise shaping curve depends on the time-varying characteristics of the input signal. Therefore, the noise shaping filter coefficients are to be computed and updated on a regular basis. We present a new theory for optimal noise shaping of audio. It provides more straightforward proof of properties of dithered and non-dithered noise shaping. In contrast with standard theory, it does show how optimum noise shaping filters can be designed in practice. Experimental results illustrate the method. The link with two popular noise shaping requantization techniques (F-weighted noise shaping and Super Bit Mapping) is also discussed.

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