  This paper introduces a new fast algorithm for the 8-point discrete cosine
transform (DCT) based on the summation-by-parts formula. The proposed method
converts the DCT matrix into an alternative transformation matrix that can be
decomposed into sparse matrices of low multiplicative complexity. The method is
capable of scaled and exact DCT computation and its associated fast algorithm
achieves the theoretical minimal multiplicative complexity for the 8-point DCT.
Depending on the nature of the input signal simplifications can be introduced
and the overall complexity of the proposed algorithm can be further reduced.
Several types of input signal are analyzed: arbitrary, null mean, accumulated,
and null mean/accumulated signal. The proposed tool has potential application
in harmonic detection, image enhancement, and feature extraction, where input
signal DC level is discarded and/or the signal is required to be integrated.
