Running discrete cosine transform

Abstract

The discrete cosine transform (DCT) has become an important tool in digital signal processing because its performance is close to the optimal Karhunen-Loeve transform. In this work the running discrete cosine transform (RDCT) is introduced. Using the properties of the discrete Fourier transform kernel $\text{W =}\text{exp}\text{(}\text{−2π}\text{j}\text{N}\text{)}$, a fast recursive algorithm was developed for real-time computation of the RDCT coefficients. For N-point RDCT the present algorithm needs only 2N real multiplications. The hardware implementations of the RDCT algorithm and applications in realtime data processing are discussed.