Digital filters - Signals, Processes, and Systems - page 308

Time domain Spectrum Freq. domain

Ram p Gen . (V C O) T ime domain Spectrum F req. domain

Ram p Ge n . (V C O) Diff.+ Int.

Diff.+ Int.

Time domain

Frequency domain

4
3
2
1
0
-1
-2
-3
-4
5000

0,45
0,40
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
-0,05
400
350
300
250
200
150
100
50
0
0,0030
0,0025
0,0020
0,0015
0,0010
0,0005
0,0000
0,40
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00

Sweep signal

Amplitude
constant

Differentiated
sweep signal

2500

0

-2500

-5000
0,20

( ∗ 2 π f )

0,13

Integrated
sweep signal

0,05

-0,03

-0,10
4
3
2
1
0
-1
-2
-3
-4

( ∗ 1/ 2 π f )

Differentiated
and integrated
sweep signal

25 75 125 175 225

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

Hz

ms

Illustration 204: Analog filters: differentiation and integration as frequency-dependent processes

In the differentiation of a sweep signal the amplitude increases linearly (proportionally) to the frequency
and in the case of integration it is inversely proportional to the frequency. This can be seen in the Illustra-
tion both in the time and frequency domain. Note the effect of the Uncertainty Principle in the frequency
domain (see in this connection Illustration 104).

In the case of an analog resonance circuit consisting of a coil and a capacitor or an analog bandpass the
voltage u and current i are linked by these two processes differentiation and integration. Only in this way
can the resonance circuit effect be achieved.

The faster the current i in a coil changes the greater the instanta-
neous induced voltage u ( law of induction ).

The faster the voltage u changes at a capacitor the greater the
current i which the condenser discharges or charges ( law of
capacity ).