Hi Folks, I have read about the three conditions that must be satisfied before the Fourier series can be successfully used to represent any given function. Can someone please confirm that my understanding of them is correct! 1) The function must have a single defined value for each value in its domain. For every value of x there should be only one value of y. Most of the electronic (This is my field) functions will satisfy this condition. One function that wouldn't satisfy this condition is the circle function (sometimes not reffered as a function because two values are obtained for x) because that would give two values for each value of x. 2) The function must not have any infinite discontinuity of range within its domain. This condition states that the function shouldn't have an infinite number of discontinuities on its domain. It's kind of hard to come up with a function that doesn't abide to this condition. One example would be: let f be a function of x so that its value is: 1 if x is a rational number 0 if x is an irrational number This function has an infinite number of discontinuities, because in any finite interval, there is an infinite number of rational numbers, and an infinite number of irrational numbers between them! So the function would have an infinite number of "jumps" between 0 and 1. I guess if a function did have a lot of jump the Fourier representaion would be skewed by the Gibbs Phenomina. The first and second differentials of the function must be piecewise continuous over the domain. a. within each interval, the function is continuous; and b. on the "borders" of each interval, the function can be discontinuous, as long as the limit coming from each side exists. For example, the tan(x) function is NOT piecewise continuous, because near pi/2 multiples it "Points towards" infinity. Had it pointed towards any real value, it would be piecewise continuous. Thank you in advance for you guidance and help. Jag.