Based on one-sided Fourier transformation, a general method is presented to research the spontaneous decay dynamics of an emitter in homogeneous media, non-leaky cavity, leaky cavity and photonic band gap material. It is found that the spontaneous decay properties of the emitters are strongly dependent on the local density of states. The spontaneous emission properties of the emitters can be manipulated through engineering the local density of stats and the high-performance optoelectronic device and quantum information processing device are obtained. This method can be used in Markovian or non-Markovian bath-reservoir environments.