A Fast Algorithm Of DGT And Its Applications

There are a number of ways to represent a signal, in which the most important and fundamental variables are time and frequency. The bridge between the time-domain representation and the frequency-domain representation for stationary signals is the Fourier transform. But most signals in the real world are often non-stationary. The Fourier transform is not suitable for the representation of the non-stationary signals because it can not reveal any time information in the frequency domain. In order to overcome this problem, many joint time-frequency analysis techniques has been developed and widely used, such as windowed Fourier transform, wavelet transform, etc. The Gabor transform is one of the most important methods in the joint time-frequency analysis. It has been considered as an effective time-frequency analysis technique in diverse areas such as speech and image processing, radar, sonar and seismic data processing and interpretation; however, its real time applications were limited due to its high computational complexity. How to compute the Gabor transform efficiently has became a significant problem. In this paper, fast algorithms and applications of the discrete Gabor transform (DGT) are developed. Firstly, block time-recursive algorithms for the efficient and fast computation of the 1-D DGT coefficients and for the fast reconstruction of the original signal from the DGT coefficients will be discussed in both the critical sampling case and the oversampling case; secondly, unified parallel lattice structures for the implementation of the algorithms will be studied. The computational complexity and the advantages of the proposed algorithms will be discussed and compared. And finally, the DGT is applied in analysis and processing of speech signals and watermarking of digital images. Its highlights in applications have been illustrated.