Time-Domain System Example Two 2.7 2000/08/09 2004/08/10 13:30:55.059 GMT-5 Don Johnson dhj@rice.edu Melissa Selik mselik@alumni.rice.edu Don Johnson dhj@rice.edu equation difference Domain Time filter boxcar Defines Finite Impulse Response systems.

The plot shows the unit-sample response of a length-5 boxcar filter.

A somewhat different system has no "a" coefficients. Consider the difference equation y n 1 q x n … x n q 1 Because this system's output depends only on current and previous input values, we need not be concerned with initial conditions. When the input is a unit-sample, the output equals 1 q for n 0 … q 1 , then equals zero thereafter. Such systems are said to be FIR (Finite Impulse Response) because their unit sample responses have finite duration. Plotting this response () shows that the unit-sample response is a pulse of width q and height 1 q . This waveform is also known as a boxcar, hence the name boxcar filter given to this system. (We'll derive its frequency response and develop its filtering interpretation in the next section.) For now, note that the difference equation says that each output value equals the average of the input's current and previous values. Thus, the output equals the running average of input's previous q values. Such a system could be used to produce the average weekly temperature ( q 7 ) that could be updated daily.