Stochastic resonance (SR) in an overdamped linear system with periodically modul ated noise is studied. The explicit expressions of the first two moments and sig nal-to-noise ratio (SNR) are obtained when we introduce the asymmetric dichotomo us noises to the system. Through analyzing the SNR, we find the bona fide SR and conventional SR. Meanwhile, the effects of the asymmetry and correlation time o f the multiplicative noise and cross_correlated noise intensity on the SNR are d iscussed.