System analysis - Signals, Processes, and Systems - page 151

30
20
10
0

Im p u ls e

Pulse response h(t) LP 2. order (Butterworth, 100 Hz))

LP+ HP-F ilt er T i me do ma in

HP 70Hz

20
15
10
5
0
-5
-10
20
15
10
5
0
-5
-10
75
50
25
0
-25
-50
-75
75
50
25
0
-25
-50
2,0
1,5
1,0
0,5
0,0
-0,5
-1,0
-1,5
-2,0
7,5
5,0
2,5
0,0
-2,5
-5,0
-7,5

Pulse response h(t ) LP 6. order (Butterworth, 100 Hz)

Pulse response h(t) LP 10. order (Butterworth, 100 Hz)

Pulse response h(t) HP 10. order (Butterworth, 100 Hz)

Pulse response h(t) HP 10. order (Chebychef , 100 Hz)

Pulse response h(t) BP 10. order (Butterworth, 70 Hz)

Pulse response h(t) BP 10. order (Butterworth, 70-100 Hz))

25 25 50 50 75 75 100 100 125 125 150 150 175 175

ms ms

Illustration 108: From the ugly duckling….

Although we ought by now to be familiar with the properties of a -pulse - it contains all the frequencies

and sinusoidal oscillations with the same amplitude, i.e. the system is tested simultaneously with all
frequencies - the result of this measurement analysis never fails to surprise. The pulse responses at first
sight look so insignificant but do tell the expert a great deal about the frequency-related behaviour of the
filter.

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In the case of higher order filters the edge steepness is greater and consequently the conducting state
region of the filter is smaller. As a result of this the pulse response h(t) lasts longer on account of the UP .
This can be seen quite clearly in the case of the narrow band pass filter (70Hz). And, the greater the edge
steepness the greater the delay in the beginning of the pulse response.

A highpass filter is always broadband, its pulse response starts with a step and builds up to its cutoff
frequency. As a result of the high degree of edge steepness of the CHEBYCHEFF highpass filter, h(t) lasts
much longer than in the BUTTERWORTH high pass of the same order.

It seems like a miracle that the FT of these insignificant-looking pulse responses results exactly in the
transfer function H(f) according to the absolute value and phase (see Illustration 109). The phase
spectrum is however only given correctly if the

-pulse is positioned at the reference point of time t = 0. In
contrast to the traditional methods of measuring using an oscilloscope and a function generator the
computer-based measurement and evaluation only takes fractions of a second.

δ