The Complex LMS algorithm applied to the DFT and adaptive filtering

Abstract

Widrow's Least Mean Square (LMS) Spectrum Analyzer (or the LMS/DFT Algorithm) uses the complex LMS algorithm to compute the Discrete Fourier Transform (OFT) of a signal. In this thesis, this idea is extended to the two dimensional (20) case. It is shown that the 2D OFT of a digital image and also the 2D OFT of a sequence of images may be computed using the complex LMS algorithm. A 2D LMS/DFT Algorithm is developed using a vectorized approach. This algorithm allows a high level of parallelism and is therefore promising for VLSI circuit implementation. In addition, a Partial LMS/DFT Algorithm is investigated, which leads to a very efficient spectral estimation method for narrow-band signals. The possibility of using the LMS/DFT Algorithm (both 1 D and 2D) to implement a Frequency Domain Adaptive Filter (FDAF) is also verified.