Abstract:

As one of important fundamental graduate courses in University of Electronic Science and Technology of China, “Theory and algorithm of digital signal processing” focuses mainly on statistical modeling of signals, power spectrum density estimation, adaptive filtering and so on [1]. Many classical theories and useful algorithms are introduced in this course. Among them, discrete Fourier transform and minimum variance distortless response are two of most important filters and power spectrum density estimators and have been the subjects of extensive research for its potential applications in science and technology, especially in radar and acoustic signal processing, wireless communication, geophysical exploration, image enhancement and image recognition [2]. Though they have been well known in the field of signal processing, discrete Fourier transform and minimum variance distortless response are usually introduced separately and the students are hard to find the intrinsic relationship between them [3]. In this lecture note, discrete Fourier transform is introduced as the least squares solution to the problem of data fitting based on unit-sparse data model. On the other hand, minimum variance distortless response is regarded as the semi-definite linear program solution to the problem of covariance fitting based on unit-sparse covariance model. It will enable the students to understand the similarity and difference between discrete Fourier transformation and minimum variance distortless response. From this viewpoint, the performance of both methods are compared to bring students a new insight.This lecture note is organized as follows. Section 2 briefly formulate the problem of data model and covariance model. Discrete Fourier transform is introduced as the least squares solution to the problem of data fitting based on unit-sparse data model in Section 3. Section 4 presents minimum variance distortless response as the semi-definite linear program solution to the problem of covariance fitting based on unit-sparse covariance model. Section 5 provides a concluding remark to summarize the lecture note.

Keywords:

Discrete Fourier Transform, Minimum Variance Distortless Response, Unit-sparse Model, Data and Covariance Fitting.