finitely many local extrema, i.e., that the function changes its variation only finitely many times. (Dirichlet required in addition that the function have only finitely many discontinuities, but this constraint is unnecessarily stringent.) Any signal that can be physically produced in a laboratory satisfies these conditions. As in the pointwise case of the Jordan test, the condition of boundedness can be relaxed if the function is assumed to be absolutely integrable (i.e., ) over a period, provided it satisfies the other conditions of the test in a neighborhood of the point where the limit is taken. See also Dini test References External links Fourier series Theorems in analysis