Digital Signal Processing Reference
In-Depth Information
d- Impulses
FFT
Ka r t/Po l a r
Po l a r /Ka r t
FFT
A
Time domain
Phas eshift
50
40
30
20
10
0
3
1
-1
-3
2,0
0,5
-1,0
-2,5
1,25
0,75
0,25
-0,25
-0,75
-1,25
1,00
0,50
0,00
-0,50
-1,00
A
Simulation of pulse dispersion(
without
attenuation!) on a cable
B
0
25
50
75
100
125
150
175
200
225
250
275
300
325
ms
Ti me do ma i n
Pulse
Fi l t e r00
Fi l t e r01
Fi l t e r02
Fi l te r03
Fi l te r04
Fi l t e r05
Fi l t e r06
B
1,25
B
Simulation of cable transmission(dispersion
and
attenuation!)
with a sequence of LP filter
1,00
0,75
0,50
0,25
0,00
-0,25
2.025
2.050
2.075
2.100
2.125
2.150
2.175
2.200
2.225
2.250
2.275
2.300
s
Illustration 116:
Dispersion of pulses on cables
As far as their form is concerned needle pulses would at first sight be ideal for measuring transit time in
cables or for establishing the speed of propagation in cables. However, physical phenomena occur in
homogeneous cables which alter the pulse form: as a result of frequency-dependent dispersion - the speed
of propagation depends on the frequency- the phase spectrum changes; as a result of the frequency-
dependent absorption (damping) the amplitude spectrum of the signal changes. A different signal appears
at the output from the input.
Here the “pure case” of the dispersion of a
-pulse is represented. The cable was simulated by several
serially connected allpasses . They are purely dispersive, i.e. they do not dampen depending on frequency
but only change the phase spectrum. The
δ
δ
-pulse at l = 0 km has practically the same amplitude spectrum
as at l= 16 km. Interestingly, the
δ
-pulse disperses to become an oscillation pulse which resembles a sweep
signal.
A real cable can be easily simulated by means of a series of lowpass filters because a lowpass has
frequency-dependent damping and phase displacement (absorption and dispersion, see below).
