The behavior of a linear, time-invariant discrete-time system with input signal*x[n]*
and output signal *y[n]* is described by the *convolution sum*

The convolution summation has a simple graphical interpretation.First, plot
*h[k]* and the "flipped and shifted" *x[n - k]*on the *k*
axis, where *n* is fixed. Second, multiply thetwo signals to obtain a plot of
the summand sequence indexed by *k*.Summing the values of this sequence with
respect to *k*yields *y[n]*. These operations can be repeatedfor every
value of *n* of interest.

To explore graphical convolution, selectsignals
*x[n]* and *h[n]* from the provided examples below,or use the mouse to
draw your own signal or to modify a selectedsignal. Then click at a desired value
of *n* on the first*k* axis. After a moment, *h[k]* and *x[n - k]*
will appear. Drag the *n* symbol along the *k* axis to change thevalue of
*n*. For each *n*, the corresponding summand*h[k]x[n - k]* and
output value *y[n]* will bedisplayed in their respective windows.

Applet by Steve Crutchfield |