A simple low-pass discrete-time filter is characterized by the following linear difference equation:

y[n] = f y[n-1] +(1- f) x[n] , with 0 1

Draw and clearly label an adder-gain-delay diagram for the filter.

using the same difference equation from above.

Unit Impulse Response and Unit Step Response

Calculate and plot the unit impulse and the unit step responses of this filter, for n from 0 to 10, for f = 0.1, 0.2, 0.5 and 0.9. What are the limiting values (the values as n becomes large) of the responses?

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