Digital Signal Processing Reference
In-Depth Information
Pulse
T ime domain
S pectrum
real + i mg
X/Y-Chart
Li st
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Real
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Imaginary
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X/Y C h a r t 1
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Y/t Chart 0
Y/t Chart 1
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V
y
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Illustration 101:
"Locus curve" of a one-off
δ
-pulse
The frequencies which a one-off signal contains closely follow each other. The "frequency vector pairs" in
this Illustration are all on one circle because all the frequencies of a
pulse have the same amplitude.
However, as the cosine and sine-shaped curve of the real and the imaginary component shows, the phase
varies considerably from frequency to frequency so that the neighbouring "frequency vector pairs" are
arranged in a star-shaped symmetry as in Illustration 100.
The measured signal has a duration of a total of 1 s at a scanning rate of 1024 and a block length of 1024.
As a result the frequency uncertainty is roughly 1 Hz (
UP
). The complex FOURIER transformation
provides a spectrum of 0 to 1023, i.e. 1024 "frequencies". That means 512 "frequency vector pairs" all on
this circle. The result of the number of the "periods" of the sine and cosine-shaped spectrum (roughly 42) is
that the connecting chain of all frequencies orbits the circle roughly 42 times. The angle difference
between neighbouring frequencies is thus just under (42
<
360)/1024 = 15 degrees or
δ−
/24 rad. A straight
line is drawn between two neighbouring points. As these 1024 lines overlap the circle line in this Illustra-
tion appears thicker.
Using the cursor it is easy to indicate the relevant real and imaginary components. The relevant frequency
can be determined using the chart module to a maximum accuracy of 1 Hz.
π
