IEEE Signal Processing Society Japan Chapter 講演会

Digital Signal Processing inherently requires the discrete-time representation of continuous-time signals. Traditionally this is accomplished through uniform sampling based on the Nyquist sampling theorem. This talk will discuss some alternatives to uniform Nyquist sampling. One such alternative is sampling on a non-uniform grid. Such a sampling grid might be imposed by a natural sampling process or because of intended or unintended erasures of samples on a uniform grid. Reconstruction of signals sampled on a non-uniform grid will be discussed in general and for the case of compensation for erasures as could be required in systems such as image displays with faulty picture display elements. Another context for nonuniform sampling is sampling strategies based on the concept of local or time-varying bandwidth. Several potential definitions for local bandwidth will be suggested along with the associated issues. A third context is the concept of randomized sampling or downsampling as a strategy for decorrelating aliasing or undersampling error. The talk will also describe the general view of discrete-time representation of signals through a basis expansion that does not require that the analog signal be bandlimited. This expansion introduces a nonlinear warping of the frequency scale which in some contexts offers advantages.

ディジタル信号処理では，連続時間信号の離散時間での表現を必要とする． 離散時間表現を得るための伝統的な手法は，ナイキストのサンプリング定理に 基づいた等間隔でのサンプリングである． 本講演では，等間隔ナイキストサンプリングに代わる手法をいくつか紹介する． その内のひとつは，不等間隔のグリッドでのサンプリングである． 不等間隔のサンプリンググリッドは，ナチュラルサンプリングの過程や，等間隔サンプリングによる サンプル点を(故意によるか否かによらず)消去する事，などで発生することがある． 不等間隔のグリッドでサンプリングされた信号の復元に関する一般的な議論，および 消去されたグリッドの補償としての復元についての議論を行う．後者は， 欠陥のある画像表示素子を含んだ画像ディスプレイなどのシステムで要求される． 次に不等間隔サンプリングが必要となる文脈として，局所的(時変)帯域幅の概念に基づくサンプリング 方策を取り上げる． 局所帯域幅の定義として可能なものをいくつか，関連する論点とともに提起する． 三番目の文脈として，エリアジングやアンダーサンプリングによる誤差を無相関化するための一方策である， 不規則サンプリングおよび不規則ダウンサンプリングを取り上げる． 本講演では，アナログ信号の帯域制限を必要としない基底展開を用いた，信号の離散時間表現に関する 紹介も行う．この展開は，ある文脈では利点となりうる周波数スケールの非線型な歪みを引き起こす．

Alan V. Oppenheim received the S.B. and S.M. degrees in 1961 and the Sc.D. degree in 1964, all in electrical engineering, from the Massachusetts Institute of Technology. He is also the recipient of an honorary doctorate from Tel Aviv University. In 1964, Dr. Oppenheim joined the faculty at MIT, where he is currently Ford Professor of Engineering and a MacVicar Faculty Fellow. Since 1967 he has been affiliated with MIT Lincoln Laboratory and since 1977 with the Woods Hole Oceanographic Institution. His research interests are in the general area of signal processing and its applications. He is coauthor of the widely used textbooks Discrete-Time Signal Processing and Signals and Systems. He is also editor of several advanced books on signal processing. Dr. Oppenheim is a member of the National Academy of Engineering, a fellow of the IEEE, a member of Sigma Xi and Eta Kappa Nu. He has been a Guggenheim Fellow and a Sackler Fellow. He has also received a number of awards for outstanding research and teaching, including the IEEE Education Medal, the IEEE Centennial Award, the IEEE Third Millennium Medal, the Society Award, the Technical Achievement Award and the Senior Award of the IEEE Society on Acoustics, Speech and Signal Processing. He has also received a number of awards at MIT for excellence in teaching, including the Bose Award and the Everett Moore Baker Award.