Goertzel implementations of the forward and inverse modified discrete cosine transform

Abstract

The paper suggests the use of Goertzel digital filters to calculate the forward and inverse modified discrete cosine transform (MDCT). The forward and inverse MDCT are expressed as a discrete-time convolution sum and three Goertzel digital filter structures (Goertzel MDCT A, B and C) are obtained from the discrete-time convolution sum. These new recursive algorithms require fewer arithmetic operations and are less sensitive to coefficient quantization error than previous recursive MDCT algorithms. The algorithms proposed are well suited for low-cost fixed-point VLSI implementations.