Convolution Example 1: Smoothing a Rectangular Pulse
Filter input signal .
Filter impulse response .
Filter output signal .
Figure 7.3 illustrates convolution of
as graphed in Fig.7.3(c). In this case, can be viewed as a ``moving three-point average'' filter. Note how the corners of the rectangular pulse are ``smoothed'' by the three-point filter. Also note that the pulse is smeared to the ``right'' (forward in time) because the filter impulse response starts at time zero. Such a filter is said to be causal (see  for details). By shifting the impulse response left one sample to get
Convolution Example 2: ADSR Envelope
Convolution as a Filtering Operation