The behavior of a linear, continuous-time, time-invariant system with input signalx(t) and output signal y(t) is described by the convolution integral
To compute the output y(t) at a specified t, first theintegrand h(v) x(t - v) is computed as a function of v.Then integration with respect to v is performed, resulting iny(t).
These mathematical operations have simple graphical interpretations.First, plot h(v) and the "flipped and shifted" x(t - v)on the v axis, where t is fixed. Second, multiply thetwo signals and compute the signed area of the resulting function ofv to obtain y(t). These operations can be repeatedfor every value of t of interest.
To explore graphical convolution, selectsignals x(t) and h(t) 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 t on the firstv axis. After a moment, h(v) and x(t - v) will appear. Drag the t symbol along the v axis to change thevalue of t. For each t, the corresponding integrandh(v) x(t - v) and the output value y(t) will bedisplayed in their respective windows.
return to demonstrations page| Discrete-time version Applet by Steve Crutchfield |