| In 1946, Dennis Gabor presented a method of representing a function of time by both time and frequency. This method was later known as the Gabor expansion. Although the Gabor transform has been recognized as being useful in diverse areas such as biomedical signal analysis and processing, signal detection, image compression and recognition, its real time applications are limited due to difficulties associated with the high complexity of the computation of the discrete Gabor transform coefficients. Therefore, it has a great significance in theory and applications to research the fast algorithms for DCT kernel based real-valued discrete Gabor Transform (RDGT).In this thesis, firstly the development of the complex-value Gabor transform theory is briefly reviewed; then the DCT kernel based RDGT is introduced. Filter bank-based fast parallel algorithms for the DCT kernel based RDGT will be presented. An analysis filter bank is designed for the RDGT and a synthesis filter bank is designed for the inverse RDGT. The parallel channel in each of the two filter banks 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 dependent of the length of input discrete signal and points of frequency of Gabor transform. The computational complexity of the proposed parallel method is analyzed and compared with that of the existing major parallel algorithms for the RDGT and its inverse transform. The results show that the proposed parallel implementation of the DCT kernel based RDGT and its inverse transform is attractive for real time signal processing.In this paper, an application of the DCT kernel based RDGT will be given. The RDGT coefficients of the audio watermark are embedded into the image carrier of the DCT coefficients. The proposed watermarking algorithm not only has a good stability, but also has a good robustness for the outside specific attacks. |
