TDLT: Fast Lapped Transform via Time-domain Pre- and Post-Processing


Several fast lapped transforms via time-domain pre- and post-processing of the DCT have been developed. Both orthogonal and biorthogonal versions are available. The new transforms enjoy excellent frequency response and the blocking artifact can be eliminated.

Please check here for the type-I orthogonal and biorthogonal TDLT.

1. Fast Orthogonal TDLT

Fig. 1 shows the structure of the type-II fast orthogonal TDLT, which is very similar to Dr. Malvar's type-I fast lapped orthogonal transform (LOT-I).


Fig. 1. General structure of the TDLOT-II.


Fig. 2. Frequency response of the optimized 8x12 TDLOT-II.


Fig. 3. (a) Frequency response of the optimized 8x16 TDLOT-II; (b) Impulse response.

2. Fast Biorthogonal TDLT

Fig. 4 shows the structure of the type-III biorthogonal TDLT, which has much better frequency response than the orthogonal version and is more powerful for image compression.


Fig. 4. General structure of the TDLBT-III.


Fig. 5. (a) Frequency response of the analysis filter banks of the optimized 8x16 TDLT-III; (b) Impulse response of both analysis and synthesis banks..

For more information, please check the paper:

J. Liang, C. Tu, and T. D. Tran, "Lapped transform via time-domain pre- and post-filtering. Part II: fast algorithms," submitted to IEEE Trans. on Signal Processing, Oct. 2001. PostScript | PDF