The Art of Doing Science and Engineering: Learning to Learn

by Richard Hamming

Therefore we are going to analyze the signals in terms of the Fourier functions, and I need not discuss with electrical engineers why we usually use the complex exponents as the frequencies instead of the real trigonometric functions. We have a linear operation, and when we put a signal (a stream of numbers) into the filter, then out comes another stream of numbers. It is natural, if not from your linear algebra course then from other things such as a course in differential equations, to ask what functions go in and come out exactly the same except for scale. Well, as noted above, they are the complex exponentials; they are the eigenfunctions of linear, time-invariant, equally spaced sampled systems. Lo and behold, the famous transfer function is exactly the eigenvalues of the corresponding eigenfunctions! Upon asking various electrical engineers what the transfer function was, no one has ever told me that! Yes, when pointed out to them that it is the same idea they have to agree, but the fact it is the same idea never seemed to have crossed their minds! The same, simple idea, in two or more different disguises in their minds, and they knew of no connection between them! Get down to the basics every time!