DCT kernel based finite discrete Gabor expansion and transform implemented by filterbanks

DCT kernel based finite discrete Gabor expansion (DGE) and discrete Gabor transform (DGT) implemented by filterbanks are presented. An analysis filterbank is designed for the finite DGT and a synthesis filterbank is designed for the finite DGE. The parallel channel in each of the two filterbanks has a unified structure and can apply the fast DCT (discrete cosine transform) algorithm to reduce its computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate of the DGT. The computational complexity of the proposed parallel method is analyzed and compared with that of the existing major parallel algorithms for the finite DGT and DGE. The results show that the proposed parallel implementation of the DCT kernel based finite DGE and DGT is attractive for real time signal processing.