Customer Reviews

Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications (Dover Books on Mathematics)

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This is a good second or third book on generalized functions which are otherwise known as "distributions". A good first book is "Fourier Analysis and Generalised Functions" by Lighthill. This book is based on a graduate course and provides a good introduction to distribution theory and generalized Fourier analysis. You need to have a good background in advanced calculus and be comfortable with Lebesgue theorems concerning interchangeable limit processes. The examples are quite good, but the notation is intense and the way that it is packed in small font onto a page doesn't help. The writing is compact and thorough.

I recommend this book to anyone who has had the standard digital signal processing course where the Delta function (distribution) is used freely and who has wondered what it really means.

Just a note for readers of these reviews: there are two delta functions used in signal processing. In digital signal processing the Kronecker delta is used, which is simple. In continuous-time signal processing the Dirac delta is used, which is a generalized function and causes sophomores no end of headaches. Zemanian's book will be helpful for those wishing to know more about generalized functions such as the Dirac delta. Those just wishing to know a little more might find the articles on Wikipedia about Dirac delta more helpful.

This an an excellent, clear book which is widely referenced. It was much clearer than Lighthill to me. I was comfortable with dirac delta functions in the intuitive presentation from my EE linear systems courses, but I needed to understand the theory to do correct proofs for my dissertation. This book filled the gap excellently, while being easy to follow.