User manual

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
-
quency decreases towards 0Hz, but when we
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
negative
frequencies
frequency shifting vs. frequency scaling
0
4000 6000

Amplitude
8000 10001000
1
0.8
0.6
0.4
0.2
0
Spectrum of original signal
0
4000 6000

Amplitude
8000 10001000
1
0.8
0.6
0.4
0.2
0
Spectrum of frequency shifted signal
0
4000 6000

Amplitude
8000 10001000
1
0.8
0.6
0.4
0.2
0
Spectrum of frequency scaled signal
reflecting negative frequency back to positive
-500
500 1000

Amplitude
1500 20000-200 200
1
0.8
0.6
0.4
0.2
0
Frequency shifted signal
Signal as we hear it
Original signal