This applet is part of a "virtual lab" that was written to support an Instumentation course. It can be used to demonstrate the convolution of two functions ('top hats' and 'sinc squared' functions).

• Consider two "top hat" functions, A and B. If we move the lower function along one point at a time and take the area under the product of the two functions, we have the convolution of the two.

• Convolution theorem also relates to the Fourier transform of the two functions. The theorem states:"The Fourier transform of the product of two functions is the convolution of their individual Fourier transforms". It follows that "The Fourier transform of the convolution of two functions is the product of their individual Fourier transforms". This can be seen quite intuitively if we consider the two functions A and B. It is well known result that the Fourier transform of a "top hat" is a sinc function. The product of two top hats together obviously results in another top hat function. Thus by the reckoning above, the convolution of two sinc functions must also form a sinc function, this is far less than obvious!

• This applet can be used to show the convolution of two 'top hat' or 'sinc squared' functions.
• The type of function to convolute can be selected via the choice box in the upper left corner of the applet. In the case of sinc functions, the period of the upper function can be altered with the slider. The other controls can be used to run the animation.

This applet gives a clear and quick example of the convolution theorm. Try altering the peroid of the sinc functions and observe the function that is formed.

Applet produced and written by Douglas Robertson, from an intital idea by Dr Iain McKenzie.