Convolution - Signal Processing of Random Physiological Signals - page 97

f 1 ( t )

3

f 1

2

f 2 ( t )

0 2 t
FIGURE 10.23 : Second step: Folding. The figure shows the two functions after folding the
pulse. It should be noted that there is no overlap of the functions when t ≤ 0

Figure 10.23 shows the two functions after folding the pulse; note that at the start,
when t ≤ 0, there is no overlap and the resulting value of the convolution integral ( f 3 )

at t 0).

Following the folding step, the exponential function, f 2 , is multiplied by the pulse
function, f 1 , with a magnitude of 3, then the area between 0

= 0iszero,( f 3 =

1 is integrated. The
result of the integration is the first value of the convolution function, f 3 , which is the
shaded area in Fig. 10.24.

< t <

6

f 2 ( t )

2

0 t

FIGURE 10.24 : Result of integration. The first value of the convolution function, f 3 , is shown
by the shaded area in the figure