An apparatus and a method for processing signal are provided. The signal processing apparatus comprises an input interface and a processing unit. The input interface receives smoothing parameters and a to-be-separated signal. The processing unit establishes an upper extreme envelope and a lower extreme envelope of the to-be-separated signal, and calculates a mean envelope between the upper extreme envelope and the lower extreme envelope. The processing unit performs smoothing according to the smoothing parameters and the mean envelope to generate a smoothed mean envelope, and determines a trend component or a non-trend component according to the smoothed mean envelope.