With the increasing of clock frequency and the decreasing of supply voltage, power integrity becomes a critical issue. The effect of the transition time of load currents was taken into account, and a more realistic worst-case noise prediction was obtained. In addition, a dynamic programming algorithm is introduced for the time-domain impulse response of the power distribution system, and a modified Knuth-Yao quadrangle inequality speedup method is developed which reduces the time complexity of the algorithm from O(n₂m) to O(mnlogn).