Digital Signal Processing Reference
In-Depth Information
Real
Imaginary
Real
Imaginary
Illustration 100:
Periodic and non-periodic spectra in the GAUSSian plane
-
pulses. Please note the sine and
cosine-shaped form of the line spectrum of the real and imaginary components. If you transfer these sine
and cosine components to the GAUSSian plane you will find the first "frequency vector pair" on the
horizontal cosine axis in the positive direction, the second pair with twice the frequency at a
At the top you see - slightly spoiled by the grid - a periodic sequence of
δ
/8-angle to
the cosine axis, the next pair at double the angle etc. The amplitudes of all frequencies are identical with a
δ
π
-
pulse; the result is therefore a star-shaped symmetry.
Below that you can see a lowpass-filtered noise (cutoff frequency 50Hz), i.e. a non-periodic signal. This
type of signal does not produce any law with regard to amplitude and phase as it is of a purely random -
stochastic - nature. You can clearly see the symmetry of the "frequency vector pairs". The one higher and
one lower frequencies are directly connected to each other, i.e. one line leads to the lower frequency, the
other one to the higher frequency. This muddle makes it very difficult to find the beginning and the end of
the general line. So how do we find out the frequency value of each pair?
