In a block adaptive filtering procedure, the filter coefficients are adjusted once per each output block while maintaining performance comparable to that of widely used Least Mean Square (LMS) adaptive filtering in which the filter coefficients are adjusted once per each output data sample. In this block adaptive filtering procedure, the output values and gradient estimate are given as convolution and correlation, respectively. Accordingly, an efficient implementation of block adaptive filters is possible by means of discrete transform technique which has cyclic convolution property and fast algorithms.
In this thesis, the block adaptive filtering using Fermat Number Transform (FNT) is studied to exploit the computational efficiency and less quantization effect on the performance compared with finite precision FFT realization. It is shown that the block adaptive filters using FNT have advantages over those using FFT in terms of computational complexity and adaptation accuracy. And this has been verified by computer simulation for several applications including adaptive channel equalizer (PAM and QAM), adaptive line enhancer, and system identification.
In addition, we have formulated a two dimensional block adaptive filtering procedure in which the number theoretic transform such as FNT can be used efficiently.
본 논문에서는 Fermat Number Transform 을 이용한 block adaptive filter 의 성능에 관하여 고찰하였다.
성능을 알아보기 위해서 몇몇 응용 예에 대하여 FFT를 이용한 방법과 FNT를 이용한 방법으로 computer simulation 을 통하여 그 성능을 비교하였다. 그 응용 예는 channel equalizer, system identification, adaptive line enhancer 등이다.
word length 가 제한된 digital machine 들로 block adaptive filter 를 실현시켰을 때 FNT를 이용한 방법이 computational efficient면에서 좋고 또한 FFT를 이용한 것보다 quantization effect 의 영향이 적어진다. 따라서 FNT를 이용한 것이 FFT를 이용한 것보다 computational complexity 면에서나 adaptation accuracy 면에서 우수하다는 것을 simulation 결과를 통해 알아 보았다.
또한 본 논문에서는 two dimensional signal 에 대한 block adaptive filtering 방법을 formulate하여 보았다. formulation 결과 FFT algorithm을 이용하여 implement 할 수 있으며, number theoretic method가 효과적으로 이용되어 짐을 알 수 있다.
