filter design - Realtime filtering on a microcontroller, with dynamic cut off frequencies

Is it possible to dynamically filter a signal in realtime on a microcontroller?

What I mean by dynamically is to change the cut off frequency of the filter on the fly.

I have some DSP knowledge and realize that I probably do not have the computational power to do an FFT on the fly. Instead I should be looking at creating an IIR or FIR filter that I can continually convolve with my signal.

The issue is now whether or not I have enough computational power to generate the filter coeffecients quickly and then convolve with the signal. I'm guessing that because of this I'm going to have to be very lenient on the response of the filter which is ok for my application.

I have looked at algorithms such as the Remez Exchange algorithm and believe this may be able to work but am not sure. I wanted to check before I start the lengthy process of implementing whether or not I am on the right track.