ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU A New Algorithm to Compute the Discrete Cosine Transform VLSI Signal Processing 台灣大學電機系 吳安宇 1. B. G. Lee “A new algorithm to compute the discrete cosine trnsform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp , Dec W. H. Chen, C. H. Smith, and S. C. Fralick, “A fast computational algorithm for the discrete cosine transform,” IEEE Trans. Commun., vol. COM-25, pp , Sept. 77

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU N-Point IDCT – Decomposing into even and odd indexes of n, we define

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Rearrange for Decimation in Time – Using the trigonometric identity to rearrange

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU N-Point IDCT Decomposed into N/2-Point IDCT

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU N-Point IDCT Architecture Take transpose form, we can obtain DCT architecture

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Sample : 8-Point IDCT

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Complexity Comparison

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Unified Parallel Lattice Structures for Time-Recursive Discrete Cosine/Sine/Hartley Transform VLSI Signal Processing 台灣大學電機系 吳安宇 1. K. J. R. Liu and C.T. Chiu “Unified parallel lattice structures for time-recursive discrete cosine/sine/Hartley transform,” IEEE Trans. Signal Processing,vol. SP-41, pp , March 93.

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU DCT Definition

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Time-Recursive DCT – DCT at time t – Decompose in and DCT at time (t+1) (See Fig. 1)

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU DST Definition

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Time-Recursive DCT – DST at time t – Decompose in and DST at time (t+1) (See Fig. 1)

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Hardware Architecture

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Time Recursive Relationship The relationship between the and the data sequence

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Overall Architecture

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Special Case for k=0 for the DCT and k=N for the DST

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU The parallel lattice structure for DCT and DST

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Architecture Comparison Architectural Comparison LeeOur approach I/O Operation Architecture Communication Hardware cost Operating frequency PIPO Modular Global Large, O(Nlog 2 N) f s / N SIPO Modulare and Regular Local Small, O(N) f s f s : Input data rate 1. K. J. R. Liu and C.T. Chiu “Unified parallel lattice structures for time-recursive discrete cosine/sine/Hartley transform,” IEEE Trans. Signal Processing, vol. SP-41, pp , March B. G. Lee “A new algorithm to compute the discrete cosine trnsform,”, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp , Dec. 84