TABLE OF CONTENTS Working in the field of heat transfer in the early nineteenth century, Jean B. S. Fourier found that virtually all functions of time, particularly repetitive ones, could be described in a series of sine and cosine waves of various frequencies and amplitudes. His work has been described as one of the most elegant developments in modern mathematics. Whatever its stature for the world, the benefits for the radar engineer are epic. The following presentation uses the approach taken by H. H. Skilling in Electrical Engineering Circuits, Chapters 14 through 15 (New York, Wiley, 1957). George Stimson also has an excellent discussion on Fourier series and transforms in Introduction To Airborne Radar , 2nd ed., Chapters 17 and 20 (Raleigh, NC: SciTech Publishing, 1998).
The statement for the Fourier series is that any wave may be broken down into the sum of sines and cosines of various amplitudes and frequencies. In mathematical notation,
The term f(t) is a function of time here (it does not have to be), and the a i and b i terms are constants that are to be found so as to make the expression on the right equal to f(t); 1/2 a 0 is the dc component of the function, if any.
The next step is to find a way to evaluate the a i and the b i. To do this, we use the orthogonality of the sine and cosine function, which is...
