Main advantages are as below
Reliability and Repeatability.
The main advantage of Digital filter lies with it's easy programmability using software. Design process involves certain techniques through which filter coefficients are designed. With the designed Filter coefficients, the frequency response in magnitude and phase can be seen. Techniques to design these filter coefficients will be discussed further.
Corresponding Analog filter cannot be represented in software(see Practical usage).
Reliability and Repeatability :
Digital filter is more reliable than analog filters by the same reason. In analog the component drift and tuning drift may be possible.Component precision can also influence the analog filter. These Problems are not there with the digital filter making it more reliable and repeatable than the analog filter.
Digital Filters make practical designs possible which are impractical and impossible
by analog filters.
Ex: Audio Frequency range
At this range the filter design was thought to be impossible as the tuning drift and also the component drift has a very sound effect. But with the digital filter, which don't have these problems, the design is shown to be possible.
Main disadvantages of digital filter are
The number of stages involved in the digital filter design.
High Power consumption in the filter because of the stages involved.
Cost involved with the hardware design.