Digital Signal Processing Reference
In-Depth Information
4
3
1
0
-1
-2
-
-4
4
3
2
0
-1
-2
-3
-4
2,0
1,5
1,0
0,5
0,0
-0,5
-1,0
-1,5
-2,0
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
2,00
1,75
1,50
1,25
1,00
0,75
0,50
0,25
0,00
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
50
150
250
350
450
550
650
750
850
950
50
150
250
350
450
550
650
750
850
950
Absolute value
ms
ms
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
1,50
1,25
1,00
0,75
0,50
0,25
0,00
0,10
0,08
0,05
0,02
0,00
2,75
2,25
1,75
1,25
0,75
0,25
2,00
1,75
1,50
1,25
1,00
0,75
0,50
0,25
0,00
1,00
0,75
0,50
0,25
0,00
0,10
0,08
0,05
0,02
0,00
Sinusoidal signal
Triangle
Sawtooth
Pulse
25
50
75
100
25
50
75
100
125
Hz
Hz
Illustration 147:
The absolute value response of different signals
Top left you see the input signals in the time domain, below this their frequency spectra; top right you see
the response signals in the time domain and below this their frequency spectra. In the case of the two upper
signals - sine and triangle - a generally valid principle for the formation of absolute value appears to
have been discovered in the doubling of frequency; unfortunately this does not apply to the periodic saw-
tooth which also lies in a symmetrical relationship to the zero line and which becomes a periodic triangle
of the same base frequency. But have frequencies - the even multiples - disappeared?
Finally, the sequence of
δ−
pulses remains unchanged because it lies in the positive region only on the zero
line. A linear process?
Has the sawtooth been distorted in a non-linear way or have new frequencies been added?
In a sense, yes, as the even multiples of the base frequency are now lacking. They must
have been deleted by the new frequencies. These would then have a phase position
displaced by
π
compared with the frequencies already present. Or is it a linear process
after all?
