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Signals and Systems | Signals and Systems Vijay K. Madisetti Georgia Institute of Technology Douglas B. Williams Georgia Institute of Technology 1 Fourier Series Fourier Transforms and the DFT W Kenneth Jenkins Introduction Fourier Series Representation of Continuous Time Periodic Signals The Classical Fourier Transform for Continuous Time Signals The Discrete Time Fourier Transform The Discrete Fourier Transform Family Tree of Fourier Transforms Selected Applications of Fourier Methods Summary 2 Ordinary Linear Differential and Difference Equations . Lathi Differential Equations Difference Equations 3 Finite Wordlength Effects Bruce W. Bomar Introduction Number Representation Fixed-Point Quantization Errors Floating-Point Quantization Errors Roundoff Noise Limit Cycles Overflow Oscillations Coefficient Quantization Error Realization Considerations THE STUDY OF SIGNALS AND SYSTEMS has formeda cornerstone for the development of digital signal processing and is crucial for all of the topics discussed in this Handbook. While the reader is assumed to be familiar with the basics of signals and systems a small portion is reviewed in this chapter with an emphasis on the transition from continuous time to discrete time. The reader wishing more background may find in it any of the many fine textbooks in this area for example 1 - 6 . In the chapter Fourier Series Fourier Transforms and the DFT by W Kenneth Jenkins many important Fourier transform concepts in continuous and discrete time are presented. The discrete Fourier transform DFT which forms the backbone of modern digital signal processing as its most common signal analysis tool is also described together with an introduction to the fast Fourier transform algorithms. In Ordinary Linear Differential and Difference Equations the author . Lathi presents a detailed tutorial of differential and difference equations and their solutions. Because these equations are the most common structures for both implementing and modelling systems this .

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