Digital Signal Processing Reference
In-Depth Information
T ime domain
Spectr um
Freq. domain
Sine
Multipl.
4
2,00
3
1,75
-8 Hz
8 Hz
2
1,50
1
1,25
0
1,00
-1
0,75
-2
0,50
-3
0,25
-4
17,5
0,00
8
7
15,0
6
12,5
5
-16 Hz
16 Hz
10,0
4
7,5
3
5,0
2
2,5
1
0,0
0
50
150
250
350
450
550
650
750
850
950
-20
-15
-10
-5
0
5
10
15
20
25
ms
Hz
Illustration 143:
Multiplication of identical sinusoidal signals
The multiplication of a sinusoidal signal by itself may be used as a technique for doubling the frequency.
The output signal contains a different frequency from the input signal(s). It is thus a non-linear process.
The output signal is always positive. The frequency domain shows that it consists of a sinusoidal signal
(16 Hz) and an offset („zero frequency“ 0 Hz).
Multiplication of two signals
What happens when two signals are multiplied with each other? Let us proceed systema-
tically. As representative of all signals as a result of
FP
we select two sinusoidal signals,
initially of the same frequency, amplitude and phase size.
Illustration 143 shows the astonishing result in the time and frequency domain. In the time
domain we see a sinusoidal signal of twice the frequency, which has a direct voltage
superimposed on it. Further experiments show the following: the level of the direct
voltage depends on the phase displacement of the two sinusoidal signals in relation to
each other. In the frequency domain we see a line in the doubled frequency - thus it is
really a sinusoidal signal.
