linguistic:paraphrasing
 x

As stated previously, the coefficients of (x + 1) are the nth row of the triangle. Now the coefficients of (x − 1) are the same, except that the sign alternates from +1 to −1 and back again. After suitable normalization, the same pattern of numbers occurs in the Fourier transform of sin(x) / x. More precisely: if n is even, take the real part of the transform, and if n is odd, take the imaginary part. Then the result is a step function, whose values (suitably normalized) are given by the n th row of the triangle with alternating signs. For example, the values of the step function that results from:

compose the 4th row of the triangle, with alternating signs. This is a generalization of the following basic result (often used in electrical engineering):

is the boxcar function. The corresponding row of the triangle is row 0, which consists of just the number 1.

If n is congruent to 2 or to 3 mod 4, then the signs start with −1. In fact, the sequence of the (normalized) first terms corresponds to the powers of i, which cycle around the intersection of the axes with the unit circle in the complex plane: + i, − 1, − i, + 1, + i, … {\displaystyle +i,-1,-i,+1,+i,\ldots }