Before reading this entry consider taking a look at this previous post that provides a basic overview regarding sound wave filters.
Band-Stop Filter
Band-stop filters provide the inverse impact of the band-pass filter. It attenuates or restricts all frequencies within the stopband, which is defined by two cut-off frequencies. The frequencies beyond these edges are allowed to pass unchanged. These filters are also referred to as band-reject or band-cut filters.
Band-stop filters required the two same input parameters that are used in band-pass filters. First, the center frequency parameter defines the middle-point of the stopband. The second parameter is named “Q” or bandwidth. It determines the upper and lower cut-off frequencies by specifying how far from the center frequency the edge of the passband will reach.
High- and Low-Shelf Filters
High- and low-shelf filters enable all frequencies to pass while increasing or attenuating frequencies above (if high-shelf) or below (if low-shelf) the cut-off frequencies. Other frequencies are able to pass unchanged.
These filters require at least two separate input parameters: a cut-off frequency and slope. The cut-off frequency defines what frequencies will be targeted by the filter, while the slope determines the extent to which those frequencies will be attenuated or increased.
In Pure Data (Pd) the biquad~ object is used to create these types of filters and many others. I have little knowledge of, or experience with the biquad~ filter, though I know it is more complex, flexible and powerful than the standard filter objects from Pd (such as the high-pass hip~, low-pass lop~, and band-pass bp~ filters).