Filterbank-based fast parallel algorithms for real-valued discrete gabor expansion and transform

Novel and fast parallel algorithms for the DHT-based real-valued discrete Gabor expansion (DGE) and discrete Gabor transform (DGT) are presented based on filterbanks. An analysis interbank is designed for the DHT-based real-valued DGT and a synthesis interbank is designed for the DHT-based real-valued DGE. The parallel channel in each of the two filterbanks has a unified structure and can apply the fast DHT (discrete Hartley transform) to reduce its computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate. The computational complexity of the proposed parallel algorithms is analyzed and compared with that of the existing major parallel algorithms for the DGT and DGE. The results indicate that the proposed parallel algorithms are attractive for real time signal processing.