
Convolution 2.


Cuthbert Nyack
The mathematical expression for the convolution of 2 functions
f_{1}(t) and f_{2}(t) is given by the equation below:
The 2 functions f_{1}(t) and f_{2}(t) are shown below along with
f_{1}(t  t) and f_{2}(t  t).
The analytic expressions for the convolution are shown
below with their range of validity.
The applet below shows the convolution as t is changed.
The purple line is f_{1}(t),
the orange line is f_{2}(t  t)
and moves as t is changed by the scrollbar. f_{2}(t  t) is
shifted upwards slightly to distinguish it from
f_{1}(t). The red line at
the bottom shows the convolution of the 2 functions. As t
is changed, the filled green area shows the area under the
product function
f_{1}(t)f_{2}(t  t)
and the green line at the
bottom shows the value(area of green shading) of the convolution
at the current value of t. The gain scrollbar can be used to
expand the plot of the convolution.
The Applet below shows the convolution of the same 2 functions
as above. In this case f_{2} is fixed and f_{1} is moved. Although
the shaded green area may appear reversed or shifted, its
magnitude is the same as in the above case for any given
value of t. As above the shifted applet is displaced upwards
slightly to avoid overlap with the stationary one.
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COPYRIGHT © 1997 Cuthbert Nyack.