Fast discrete cosine transform for 1-D and 2-D signals with and without symmetry

This paper focuses on the ways of reducing the computational complexity involved in transforming the audio (1-D) and video (2-D) signals, to meet the growing need to include multimedia systems in real-time. In the first approach, computations involved in 1-D and 2-D discrete cosine transforms (DCT) are reduced considerably by eliminating some of the twiddle factors for any 1-D and 2-D signals. In the second approach, when the audio signal possesses 1-D reflection symmetry, a computational savings of 75% is obtained over the conventional 1-D algorithms. Similarly, when the 2-D signal possesses quadrantal symmetry, to compute 2-D DCT, a computational savings of 93.75% is obtained over the conventional algorithms.