2003/01/01 by Xinjian Chen, Qionghai Dai, Chunwen Li · 1 citation
Computer Science · Mathematics · #Algorithm #Computation #Computer science #Digital Filter Design and Implementation #Digital signal processing #Discrete Fourier transform (general) #Discrete Hartley transform #Discrete cosine transform #Discrete mathematics #Discrete sine transform #Fourier analysis #Fourier transform #Fractional Fourier transform #Inverse #Lapped transform #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix decomposition #Matrix multiplication #Modified discrete cosine transform #Numerical Methods and Algorithms #Pure mathematics #Signal processing #Tensor product #Transform coding
paper · doi:10.1109/tsp.2002.806558
openalex publication_date 2003/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
This paper presents a new algorithm for the fast computation of multidimensional (m-D) discrete cosine transform (DCT) with size N/sub 1//spl times/N/sub 2//spl times//spl middot//spl middot//spl middot//spl times/N/sub m/, where N/sub i/ is a power of 2 and N/sub i//spl les/256, by using the tensor product decomposition of the transform matrix. It is shown that the m-D DCT or inverse discrete cosine transform (IDCT) on these small sizes can be computed using only one-dimensional (1-D) DCTs and additions and shifts. If all the dimensional sizes are the same, the total number of multiplications required for the algorithm is only 1/m times of that required for the conventional row-column method. We also introduce approaches for computing scaled DCTs in which the number of multiplications is considerably reduced.