Digital Signal Processing Reference
In-Depth Information
T ime domain
Spectrum
Freq. domain
Nois e
LP filter
* C
2,5
2,0
1,5
1,0
0,5
0,0
-0,5
-1,0
-1,5
-2,0
-2,5
250
200
150
100
5
0
-50
-100
-150
-200
-250
0,025
0,020
0,015
0,010
0,005
0,000
-0,005
-0,010
-0,015
-0,020
-0,025
0,3000
0,2250
0,1500
0,0750
0,0000
30,0000
22,5000
15,0000
7,5000
0,0000
0,0030
0,0023
0,0015
0,0007
0,0000
0
100 200 300 400 500 600 700 800 900
0
50 100 150 200 250 300 350 400
Hz
ms
Illustration 125:
Multiplication by a constant: amplification or damping
The top series shows the original signal - filtered noise - in the time and frequency domains. In the centre:
the signal after amplification by one hundred, and finally at the bottom, the signal after damping by one
hundred (multiplied by 0.01).
Amplification and damping are given in dB (decibels), a logarithmic scaling. The factor one hundred here
equals 40 dB.
It may come as a surprise that there are mostly extremely simple mathematical operations
behind these processes which, at first glance, have little to do with communications
engineering. Besides, our aim was to leave mathematics out of it.
Multiplication of a signal by a constant
This sounds and is very easy. But behind it there are important concepts such as amplifi-
cation and damping. A hundredfold amplification means the multiplication of all instan-
taneous values of variables by the factor 100, and in the frequency domain stretching the
amplitude response by one hundred.
