Filter response to sinusoidal input signal This question is related to Does 46 dB gain of a filter for a frequency imply 200 times more amplitude? In  the accepted answer it is mentioned that "For a sine wave input the amplitude of the steady state output is simply the amplitude of the input multiplied with the magnitude of the transfer function at that frequency" 

Above relation is derived as an integral; as a convolution between filter and the input. But in practice we have all discrete signal, therefore can we get 200 times more in practice?
The fact that a sinusoidal signal's amplitude is multiplied by the magnitude of the system's frequency response (evaluated at the input frequency) is a general property of LTI systems, regardless of whether they are continuous-time or discrete-time systems.

This is a consequence of the complex exponential being an eigenfunction of LTI systems, and the value of the frequency response evaluated at the input frequency is the corresponding eigenvalue.

For more details on eigenfunctions of LTI system check out this question and its answers. And I'm sure that there's even more information here on this site.