The output power spectrum and signal-to-noise ratio (SNR) of the first order linear system driven by sinusoidal and white noise signal are analyzed. The result shows that the linear system under additive noise does not perform traditional stochastic resonance (SR), but it reveals the parameter-adjusted SR in a broad sense, which means that a resonance peak appears in the curve of SNR versus system parameter. The output spectrum properties under different sampling frequencies are analyzed for a signal with an arbitrary frequency, leading to a conclusion that increasing sampling frequency properly can be beneficial to the detection of the character signal.