Xaoc Devices KOSZALIN Manual page 5

negative
frequencies
1
Amplitude
0.8
0.6
0.4
0.2
0
0
1000
1
Amplitude
0.8
0.6
0.4
0.2
0
0
1000
1
Amplitude
0.8
0.6
0.4
0.2
0
0
1000
1
Amplitude
0.8
0.6
0.4
0.2
0
-500
-200
NeGAtIVe freQueNcIeS?
Consider a point rotating on a circle at X
rpm. When observed along one dimension, it
would oscillate sinusoidally with a frequency
of X/60 Hz (because there are 60 seconds in
a minute). If we slow down the circle, the fre-
quency decreases towards 0Hz, but when we
4000
4000
4000
fig. 2: frequency shifting vs. frequency scaling
0 200 500
fig. 3: reflecting negative frequency back to positive
6000
6000
6000
1000
stop the circle and change the direction, the
frequency starts rising again—towards the
negative frequency values.
Sinusoids with negative frequencies are in-
distinguishable from those with positive
frequencies, except when crossing zero. This
zero-crossing is why through-zero frequency
5
Spectrum of original signal
Frequency (Hz)
8000 1000
Spectrum of frequency shifted signal
Frequency (Hz)
8000 1000
Spectrum of frequency scaled signal
Frequency (Hz)
8000 1000
Original signal
Frequency shifted signal
Signal as we hear it
Frequency (Hz)
1500 2000