Scaled AAN for Fixed-Point Multiplier-Free IDCT

An efficient algorithm derived from AAN algorithm (proposed by Arai, Agui, and Nakajima in 1988) for computing the Inverse Discrete Cosine Transform (IDCT) is presented. We replace the multiplications in conventional AAN algorithm with additions and shifts to realize the fixed-point and multiplier-free computation of IDCT and adopt coefficient and compensation matrices to improve the precision of the algorithm. Our 1D IDCT can be implemented by 46 additions and 20 shifts. Due to the absence of the multiplications, this modified algorithm takes less time than the conventional AAN algorithm. The algorithm has low drift in decoding due to the higher computational precision, which fully complies with IEEE 1180 and ISO/IEC 23002-1 specifications. The implementation of the novel fast algorithm for 32-bit hardware is discussed, and the implementations for 24-bit and 16-bit hardware are also introduced, which are more suitable for mobile communication devices.