Digital Signal Processing Reference
In-Depth Information
Time domain
Step funct.
Differential
5,0
2,5
Correlation between step
function and delta pulse:
the derivative of the step
function creates
the
0,0
-2,5
-5,0
20000
17500
15000
12500
10000
7500
5000
2500
0
δ−
pulse!
25
50
75 100
150
200
250
300
350
400
45
ms
Time domain
Spectrum
F r eq . do ma in
Step funct.
LP f i lt e r
Differential
7,5
0,15
This is the
step
response!
Die
FT
of the
step
response
cannot be interpreted
5,0
0,11
Note: LP filtering and
differentiation arel
inear
processes; that´s why the
sequence of LP filtering
and differentiation can be
changed!
2,5
0,07
0,0
0,04
-2,5
0,00
17,50
-5,0
3000
2500
2000
1500
Therefore: the derivative of
the response of step function
creates the pulse response
h(t)!
But the
FT
of the pulse
response is the desired
transfer function of the filter
13,13
1000
500
8,75
0
-500
-1000
4,38
0,00
-1500
0
250
500
750
1000
0
0
25
25
50
50
75
75
100
100
125
125
15
15
Hz
ms
ms
Illustration 115:
Optimisation of system analysis: differentiation of the step response
If the differentiated step function produces a
-pulse, the differentiated step response also produces the
pulse response h(t). This follows from the fact that both the low pass and differentiation represent
linear
processes. Therfore the order of the sequence can be changed. The step function which has sufficient
energy is directed at the lowpass circuit or the system. The step response is differentiated, the pulse
response h(t) is obtained. The system was thus indirectly tested by a
δ
δ
-pulse. This process cannot be under-
stood without the theoretical background.
