digital filter with pic16f877

Hello anyone.
I am a student of electronic engineering and I will graduate after 3 months.
Hence I am studying about my thesis. I must make a box with these specifications:
I must input
1-sampling time (T)
2-Order of transfer function
3-coefficients of numerator and denominator of transfer function, by keyboard and see them on the LCD screen.

For example we want system operates as this transfer function:

y(z)/u(z)=(3z+1)/(z^2+4z+2)
After using z-transform:
y(t)=3u(t-T)+u(t-2T)-4y(t-T)-2y(t-2T)

I think that PIC microcontrollers is good for this project because it has Harvard architecture.
I want to use PIC16F877 and pic basic professional compiler for making this device. But I must start studying about this micro initially so any suggestion for helping me is very lively for me.
Please guide me about algorithm of software that I should write and download in micro and introduce sites or articles about making digital filters.
I am awaiting your helpful reply.
Thanks alot.
Regards

Might this get you started?

http://www.emesystems.com/BS2math5.htm

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