This page describes the convolution applet found on the CD-ROM. (Open in a new maximized window.)
You see three graph areas in this applet. From the top, the first represents the input signal, the second represents the impulse response of the system and the third represents the convolution sum.
Signals are accepted in following manner. You type in a series of numbers starting from time 0. For example if x[0]=1, x[1]=0.5, x[2]=0, x[3]=-0.5 and x[4]=-1 then type in "1 0.5 0 -0.5 -1". Press enter to update the signals in the graph. The same goes with specifying the h[n].
Convolution1 and Convolution2 buttons will illustrate two different ways to calculate the convolution sum. See Chapter 2 in the book "Fundamentals of Signals and Systems" by B. Boulet for more details.
Convolution1 is a more intuitive way of thinking about the convolution sum. It's basically the sum of the system responses to different level of inputs at different times. The grey signals in the convolution sum graph area (the bottom one) shows the system responses at each instant. The blue signals in the convolution sum graph is the sum of all the previous system responses plus the new system response at the particular time.
Convolution2 is a "calculation-friendly" way of calculating the convolution sum while being less intuitive. h[n] is inverted and shifted to the right each time. Again the grey signal show the temporary products between x[n] and h[n]. Then the all gray signals are summed up (illustrated by grey bars sweeping to the right and accumulating) and placed as y[n] in blue.
-Pil Joo (pil.joo@mail.mcgill.ca_ANTISPAM_)
remove _ANTISPAM_ to e-mail me for any mistakes or suggestions.