This application was implemented using the FIRFilter class
Below we see an unit impulse input at t=2
Next we see the response with the coefficients 1.0, 0.8. 0.6, 0.4. 0.2, that is b0=1.0, b1=0.8, etc.
Note at t=2, the we first encounter the impulse and our response is b0=1.0. Next, at t=3, the impulse is now one unit back in time and hence b1=0.8 is applied to the unit value to obtain 0.8 at t=3. Etc.
Next, for the fun we have an imput of the word "three"
and applying the above filter we obtain
Note, the noise has been modulateD.