i = 0
|bi ×x( t - i)|
This application was implemented using the IIRFilter class
Below we see an unit impulse input at t=2
Next we see the response with b0=1.0, and a1=-0.8.
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 and thus does not contribute to the response. However, the feedback portion applied to the response value at t=2 (=1.0) gives us a response of 0.8 for t=3. For t=4, we get 0.8 of 0.8 or .064, etc. Next we see change the sign of font face=symbol>a1 from -0.8 to 0.8 and we obtain a response of
Next, for the fun we have an imput of the word "three"