Digital Signal Processing Reference
In-Depth Information
Ti me do ma i n
Ramp
GAUS S osc.
Fi l t e r00
Fi l t e r01
Fi l t e r02
Fi l t e r03
Fi l t e r04
Fi l t e r05
Fi l t e r06
v
Ph
>
v
Gr
Phase velocity
v
Ph
Group velocity
v
Gr
Illustration 118:
Group and phase velocity
This GAUSSian oscillation pulse is directed here to a series of the same lowpass filters according to
Illustration 116. It is affected by damping and phase displacement.
The phase velocity is visualised here by means of the maximum value of the “short-lived” sine or the line
drawn through the three maxima. The group velocity corresponds to the velocity of the enveloping
GAUSSian function. Both velocities are not identical because neighbouring maximums do not keep the
same level.
The Si-function and the Si-oscillation pulse
The disadvantages of the
-pulse as a test signal were its low spectral energy and its
“dangerous” pulse level. In addition the energy distributes itself equally over the entire
frequency domain from 0 to
δ
∝
.
What might an ideal test signal look like? - a test signal that has all the advantages of the
δ
-pulse without its disadvantages. Let us try to describe a signal of this kind:
• The energy of the signal should be confined to the frequency range of the system to
be tested
• In this range all the frequencies (as in the case of the
-pulse) should have the same
amplitude so that the FT directly produces the transfer function H(f).
δ
