Digital Signal Processing Reference
In-Depth Information
Noise
FFT
Bandpass 1Hz
IFFT
Time domain
FFT01
Freq. domain
Symmetric spectrum
7,5
5,0
0,30
0,25
2,5
0,0
0,20
0,15
-2,5
-5,0
0,10
0,05
-7,5
0,125
0,100
0,075
0,050
0,025
0,000
-0,025
-0,050
-0,075
-0,100
-0,125
0,125
0,100
0,075
0,050
0,025
0,000
-0,025
-0,050
-0,075
-0,100
-0,125
0,20
0,15
0,10
0,05
0,00
-0,05
-0,10
-0,15
-0,20
0,00
0,055
0,050
0,045
0,040
0,035
0,030
0,025
0,020
0,015
0,010
0,005
0,000
0,06
0,05
0,04
0,03
0,02
0,01
0,00
0,09
0,08
0,07
0,06
0,05
0,04
0,03
0,02
0,01
0,00
-500
-250
0
250
500
0 50
150
250
350
450
550
650
750
850
950
Hz
ms
Illustration 120:
Does noise really contain all the frequencies?
This can be checked easily by using our "supercircuit". Any four frequencies are filtered out in the
frequency domain - in this Illustration 32, 100 and 160 Hz from top to bottom.
That sounds simple but at the same time quite amazing. Where do filters exist - bandpasses - whose band
width only lets a
single
frequency pass, or the steepness of whose sides tends "towards infinity". Our filter
bank is only limited by the
UP
: in the case of a signal duration of 1 s the bandwidth or the frequency
uncertainty must be at least 1 Hz. You will have noticed that the frequencies filtered out or the sinusoidal
oscillations have different amplitudes. If you construct and operate the circuit yourself you will note that
the amplitude and phase position fluctuate (magnifying glass). It is not possible to see any regularity as
noise is a stochastic or random signal. When, do you think, will these fluctuations be greater - in the case
of a short noise signal or in the case of a very, very long one?
