Digital Signal Processing Mathematics
Digital signal processing mathematics M. Hoffmann DESY, Hamburg, Germany Abstract Modern digital signal processing makes use of a variety of mathematical tech- niques. These techniques are used to design and understand efficient filters for data processing and control. In an accelerator environment, these tech- niques often include statistics, one-dimensional and multidimensional trans- formations, and complex function theory. The basic mathematical concepts are presented in four sessions including a treatment of the harmonic oscillator, a topic that is necessary for the afternoon exercise sessions. 1 Introduction Digital signal processing requires the study of signals in a digital representation and the methods to in- terpret and utilize these signals. Together with analog signal processing, it composes the more general modern methodology of signal processing. Although the mathematics that are needed to understand most of the digital signal processing concepts were developed a long time ago, digital signal processing is still a relatively new methodology. Many digital signal processing concepts were derived from the analog signal processing field, so you will find a lot of similarities between the digital and analog signal pro- cessing. Nevertheless, some new techniques have been necessitated by digital signal processing, hence, the mathematical concepts treated here have been developed in that direction. The strength of digital signal processing currently lies in the frequency regimes of audio signal processing, control engineering, digital image processing, and speech processing. Radar signal processing and communications signal processing are two other subfields. Last but not least, the digital world has entered the field of accel- erator technology. Because of its flexibilty, digital signal processing and control is superior to analog processing or control in many growing areas.
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