Digital Signal Processing Reference
In-Depth Information
Ti me domain
Sp ect r um
Fr eq. domai n
Rectangular
Integr al
8
6
7
5
6
4
5
3
+
+
+
+
+
+
+
+
4
2
3
1
2
0
1
-
-
-
-
-1
0
4,0
-2
2,25
2,00
3,5
1,75
3,0
1,50
2,5
1,25
2,0
1,00
1,5
0,75
1,0
0,50
0,5
0,25
0,0
0,00
50
150
250
350
450
550
650
750
850
950
50
150 250 350 450 550 650 750 850 950
ms
ms
Illustration 137:
Closer examination of the „measurement of areas“ and the forming of the mean value
On the left a rectangular signal is integrated which lies entirely in the positive sphere. In accordance with
Illustration 135 the area increases linearly from 0 to 125 ms. After that it remains constant to 250 ms
because the rectangular curve is zero at this point. On the right however the area decreases linearly
because from 125 ms the curve of the signal lies in the negative sphere.
If one continued to carry out the integration of the periodic rectangular signal, the curve of the signal
would increase more and more in both cases and tend towards infinity. Where does the mean value lie?
The mean value of the input signal top left lies at four - as can be seen without difficulty - that of the input
signal top right lies at two. The curve of integration shows precisely these values after 1 s.
The results in Illustration 137 show:
If the curve of the signal lies predominantly in the positive (or
negative sphere), the integrated signal rises more and more (or
falls more and more). In the case of signals of this kind in pure
integration the correct mean value is indicated exactly after 1 s!
