In applications this is usually a rational algebraic function of s. Because h (t) is zero for negative t, the integral may equally be written over the doubly infinite range and putting s = iω follows the formula for the frequency response function : H ( i ω ω ) = ∫ ∫ − − ∞ ∞ ∞ ∞ h ( t ) e − − i ω ω t d t