I hope some math-funner can help me with a DFTF question: The DTFT of a complex doubly-infinite sequence x := {x[n] in C | -oo < n < oo} is given by X(w) = sum over all integers n of x[n]*exp(i n w). A textbook I'm teaching from states that if x[n] is defined as the "unit step sequence": x[n] = 0, n < 0; x[n] = 1, n >= 0 by definition, X[w] =sum_n=0^oo exp((i n w), and that by some mystical procedure, (***) X[w] = 1/(1 - exp(iw)) + pi * sum over all integers n of delta(w + 2*pi*n) (where delta = Kronecker delta function). I don't know how to interpret this, since of course in the normal sense X(w) doesn't converge for any w. But in some generalized function sense, can someone please explain equation (***), and if possible at least hint at a rigorous foundation (just in case it has one). Thanks, Dan