In an ideal design, a digital filter has a target gain in the passband and a zero gain (−∞ dB) in the stopband. In a real implementation, a finite transition region between the passband and the stopband, which is known as the transition band, always exists. The gain of the filter in the transition band is unspecified. The gain usually changes gradually through the transition band from 1 (0 dB) in the passband to 0 (−∞ dB) in the stopband http://zone.ni.com/reference/en-XX/help/371325F-01/lvdfdtconcepts/dfd_filter_spec/.
Question: If an ideal design, a digital filter has a target gain in the passband and a zero gain (−∞ dB) in the stopband. It has a role in the appearance of the ripples in some way in the stopband and passband?
Why the transition band always exists? does this is because the gradually through the transition band from the passband to the stopband?
In electronics, gain is a measure of the ability of a two-port circuit (often an amplifier) to increase the power or amplitude of a signal from the input to the output port.by adding energy converted from some power supply to the signal https://en.wikipedia.org/wiki/Gain_(electronics). I want to know how this definition is applied in the design of digital filters.