Digital Signal Processing Reference
In-Depth Information
Time domain
Adder
Delta-pulse
Delay
Spectrum
Freq. domain
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
0,02
Spectrum: amplitude versus frequency
0,01
0,01
0,01
64 Hz
0,00
200
delay 156
μ
s
Spectrum: phase versus frequency
150
100
50
0
-50
-100
-150
-200
0
50
100 150 200 250 300 350 400 450 500
0
50
100
150
200
250
300
350
400
450
Hz
ms
Illustration 126:
Delay plus addition = digital comb filter
This Illustration shows a simple way of doubling a
-pulse: the input pulse is delayed (in this case by
1/64 s) and fed into an adder. On the right hand side you can see - similar to Illustration 88 and Illustra-
tion 89 - the spectrum of the two bottom
δ
δ
-pulses according to absolute value and phase.
The amplitude spectrum is cosine-shaped with a zero position interval of 64 Hz. The first zero position is at
32 Hz (the first zero position in the negative frequency range is at -32 Hz).
All digitalised signals consist of lines of numbers which can be represented as „weighted“
-pulses (see
Illustration 37 and Illustration 126 bottom). The envelope reproduces the original analog signal. If you
added to each of the
δ
-pulses - here after 1/64 s - a pulse of the same level, all the odd multiples of 32 Hz,
i.e. 32 Hz, 96 Hz, 160 Hz etc, would be filtered out of the spectrum.
δ
A filter, which, like a comb, has gaps at regular intervals, is called a comb filter. In the case of this digital
comb filter the gaps come at intervals of 64 Hz. Would you have known that it is that easy to design a
filter?
It is hardly possible to delay a given signal precisely by a planned value by means of
analog technology, but there is no problem whatsoever if digital signal processing DSP is
used.
