What is the need of Filters in Rectifier circuits. Please explain in detail and if possible with diagram

The ripple has a peak to peak voltage. What is the minimun voltage the ripple can sag to without causing a problem for the downstream circuit(s)? For example, when using a linear regulator, it has a "dropout voltage" where if the input voltage sags below that level, the regulator stops regulating.What are the factors deciding which filter is to be used in Rectifier circuit.?
Full wave rectification means that the filter capacitor has to hold up the voltage for half the time compared to halfwave rectification. If low ripple is critical, then use fullwave. If ripple has too much sag with just a simple filter capacitor, then add an expensive inductor. It is usually cheaper to increase the transformer secondary voltage to allow for more sag than to use an inductor (Pi filter).Where pie filter is used in Full wave rectifier circuit or half wave rectifier circuit.?