I found this online tool that looks promising: Interactive Digital Filter Design: Butterworth / Bessel / Chebyshev Filters
You just enter your requirements:
- Filter design: Butterworth / Bessel / Chebyshev
- Filter type: Lowpass / Highpass / Bandpass / Bandstop
- Filter order
- Corner frequency/frequencies
Click submit, and it computes the following information:
- Gains, poles, zeros
- Recurrence relation
- C code implementing the recurrence relation
- Plots of magnitude, phase, impulse and step responses
You can implement a filter in C# directly from the recurrence relation.
If you only need a few constant filters, you're done. However, if you need to be able to adjust the filter parameters at run time, you will need to do more. Luckily, the professor provided the source code for his tool, and it should be possible to convert to C#.