Convolution - Signal Processing of Random Physiological Signals - page 86

3.5

Y

3

2.5

2

1.5

1

0.5

0

- T -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 T

FIGURE 10.1 : A signal represented in terms of a continuum of impulses in the interval,
− T to + T

examine how the convolution integral is used to obtain the system impulse response of
a simple RC circuit or low pass filter as shown in Fig. 10.2.
If a single unit pulse of width T and amplitude 1 / T is applied, the output

voltage increases exponentially toward the value 1 / T ; when the pulse terminates at

T , the output voltage decays toward zero as shown in Fig. 10.3.
If the impulse is taken to its limit as t 0, then the impulse ap-

➡

proaches a theoretical impulse; the delta function , δ , and the response to the impulse

R

v 0 ( t )

v i ( t )

C

FIGURE 10.2 : Low-pass RC filter circuit