RE filters: I'm not sure what you wanted to know, but in DSP chipped radios, the digital filters operate similarly to analog filters, at least in effect. The DSP chip software narrows the width of the 'channel' you are listening to -- to reduce interference, mainly.
Most DSP chips (at least the SiLabs chips which datasheets I've looked at) have multi bandwidth capabilities. You can see that on the chip's datasheets. The radio's firmware, however -- the radio's "operating system", as it were -- is what determines, ultimately, which of the DSP chip's bandwidths are used. The firmware determines whether the radio will be one bandwidth, or have several bandwidths available to the user.
My Sangean PR-D5 AM-FM radio, for example, has one bandwidth -- it seems to be around 4 khz. The chip inside the radio is capable of maybe 5 different bandwidths. The firmware in the PR-D5's microprocessor isn't programmed to take advantage of that bandwidth switching feature. The ability to switch bandwidths, available on the chip itself, is not available to the radio user (me) because the radio's firmware ignores that feature on the DSP chip.
Hope this helps in some way.