The key operation we perform, both in the theoretical development and in the implementation of filtering, is convolution. This applet allows students to understand the process of convolution. First they create a signal and a filter function to convolve. Then, they place the filter function when they see the product function of the two original signals. In a final graph below, they build up the convolution, seeing the area under the product curve correspond to the value of the convolution at that point.
This applet is useful in understanding both how convolution works and what the effects are of specific signals being convolved together.
Students interested in gaining a better understanding of how two functions are convolved.
Click and drag in the top graph window to create an input function. Click and drag in the middle window to create a filter with which to convolve the input function. Slide the slider in the middle to "slide" the filter function over the input function. Notice that the third window contains the immediate product of the input function and the filter function. Note also that the immediate magnitude of the convolved function (in the bottom window) is equal to the area of the product signal.