A digital signal processing primer: Fundamental operations, implementation and applications

Abstract

DSP or Digital Signal Processing has been a long sought academic research topic spanning as close as forty years - at the time even long before technology was available to implement them. Hence, the fruit of the efforts of early research in the discipline was largely and fundamentally mathematical in nature. It is not surprising that early algorithms that were proposed came from people who had nothing to do with electronics, physics or even programming. For example the early version FFT is attributed to Colley and Tukey who are mathematicians who were first to publish in 1965 under the title "An Algorithm for the machine computation of complex Fourier Series" [Math. Comput. 19, 297 (1965)]. Many of these results have been actually directed for obtaining efficiency of mathematical operations involving multiplication, addition and summation of a mathematical series such as the classic Fourier series.
Although enormous and voluminous literature abound after so many years in the development of this subject in the academic world, the key operations in Digital Signal Processing (DSP) can be narrowed to the operations involving: (i) Convolution (or modulation in the context of signals and spectral analysis) (ii) Correlation (the Cross Correlation and Auto Correlation) (iii) Filtering (properly called Digital Filtering in contrast with Analog Filters) and of most importance the (iv) Discrete Fourier Transform (from which the Fast Fourier Transform was derived).
It is the purpose of this paper to provide a tutorial to the physics educator, the experimental or the industrial physicist on the practical realization of fundamental operations mentioned above to DSP CPU math processing building blocks. A 5-tap Digital Filter will be demonstrated as an application.