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A matrix-number inequality theory is proposed in this paper. Utilizing this theory, the data dynamic range for a famous DCT and IDCT algorithm is further determined. Employing the conclusion drawn from this dynamic range determination process, the average mean square error for its IDCT algorithm is decreased from 0.029422 to 0.014714. The proposed matrix-number inequality theory is applicable to any fast transform. © 2005 IEEE.
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