Digital Signal Processing Reference
In-Depth Information
4,00
2,00
0,00
-2,00
-4,00
0,40
0,20
0,00
-0,20
-0,40
0,40
0,20
0,00
-0,20
-0,40
0,40
0,20
0,00
-0,20
-0,40
0,40
0,20
0,00
-0,20
-0,40
25
75
125
175
225
275
325
375
425
475
ms
0,08
StepFunction
Time domain
Spectrum
LP filter
HP f ilter
Freq. domain
0,06
0,04
0,02
0,00
50
100
150
200
250
300
350
400
450
500
550
600
650
Hz
Illustration 113:
Does the step function contain all the frequencies?
A step function is connected with an extremely narrow band pass filter (formed from LP and HP) which
only lets through one frequency. Hence the step responses are „brief sinusoidal signals“. Only the center
frequency is varied without changing the sensitivity (Quality Q) of the filter. The spectrum - the FT of the
step responses - shows that the low frequencies are much more strongly represented in the spectrum than
the high ones. Put more precisely - if the frequency is doubled, the height of the amplitude spectrum of the
step response is halved. This suggests: U ~ 1/f.
This property will be exploited in an experiment presented in Illustration 113 to obtain
information on the curve of the amplitude spectrum of the step function.
