Introduction
In this lab, I know the principle of DSB/SSB modulation and demodulation and Hilbert transform. And I draw the LabVIEW program diagram for DSB/SSB modulation and demodulation. By observing and analyzing the performance of different signals in time domain and frequency domain, I have known the process of DSB/SSB modulation and demodulation. At the last of the lab, I use the knowledge of SSB modulation and demodulation to design a SSB walkie-talkie.
Lab results & Analysis：
- The waveform compositions:
The compositions of waveform are t0, dt and y, the function of these three variables are:
- t0 is the trigger time of the waveform.
- dt is the time interval in seconds between data points in the waveform, we can also call dt as sampling frequency.
- y is the data values of the waveform.
- The Hilbert transformation:
The principle of Hilbert transform is taking a function, u(t) of a real variable and produces another function of a real variable H(u)(t). This linear operator is given by convolution with the function 1/ (πt
).
And in the signal processing, Hilbert transform is still correct. I will show this result in the following figure:
Figure 1 The program diagram of verify Hilbert transform
Figure 2 The waveform of two signals
And in Figure 2, the waveform which was draw by red line is the signal that was get by Hilbert transform. And we can get that the red waveform has just 90-degree difference in phase with the white waveform.
- The results of DSB modulation and demodulation:
First of all, let’s check the parameters of the signals:
Figure 3 The parameters of the signals
The LabVIEW program diagram is showed in this figure:
Figure 4 The LabVIEW program diagram
The function and name of variables are noted on the top of the elements.
The principle of DSB modulation and demodulation we have learnt in the class. Then we can check the result of DSB modulation and demodulation, and analysis the condition occurred in the figure: And in the figure 5, the red line is modulated signal, the signal draw by the white dot line is baseband signal.
Figure 5 The waveform of DSB modulation
And in the figure 5, the red line is modulated signal, the signal draw by the white dot line is baseband signal. We can see the modulated signal is the waveform which we expected.
Figure 6 The waveform of DSB demodulation
And in the figure 6, the red line is demodulated signal, the signal draw by the white line is baseband signal. We can see the demodulated signal is the waveform which we expected.
Figure 7 The DSB wave FFT
And in the figure 7, we can see the bandwidth of DSB and the center frequency is about 10000HZ. And the upper band is about 12000HZ, the lower band is about 8000HZ.
- The results of SSB
First of all, let’s check the parameters of the signals:
Figure 8 The parameters of the signals
The LabVIEW program diagram of SSB modulation and demodulation is showed in this figure:
Figure 9 The LabVIEW program diagram
Figure 10 the waveform of SSB signal
Figure 11 demodulated signal
Figure 12 The DSB-SC FFT
We can see that the center frequency is about 10000HZ.
Figure 13 The demodulated SSB FFT
We can see that the frequency of demodulated SSB is about 2000HZ clearly. This frequency is as same as the baseband signal frequency. So that we can conclude that we do the modulation and demodulation successfully.
Figure 14 The SSB FFT
But the case we have discussed was under the condition which is frequency offset is 0. So we need to see how the figure changes when we change the value of frequency offset. When we change the value of frequency offset to 900, we can get:
Figure 15
Figure 16 The signals in frequency domain
- The SSB walkie-talkie:
The LabVIEW program diagram of SSB walkie-talkie is showed in this figure:
Figure 17 The LabVIEW program
The LabVIEW program diagram of SSB walkie-talkie is shown in this figure:
Figure 18 the sound signal in time domain
Figure 19 the sound signal in the frequency domain
Figure 20 the SSB in the time domain
Figure 21 the SSB in the frequency domain
Figure 22 demodulated signal in time domain
Figure 23 demodulated signal in frequency domain
Then we put the demodulated signal and signal in one diagram to compare the difference between these two signals.
Figure 24 compare two signals
And we find that two signals are similar in the time domain. It tells us our SSB walkie-talkie is made successfully! The sound signal had been transmitted successfully by our modulation and demodulation system.
6. Feedback:
- Why we do not directly implement a 90º phase shift for a single frequency signal?
In my opinion, maybe it’s very difficult to implement a 90º phase shift for a single frequency signal directly. So, we need to use the Hilbert transform.
- In SSB case, we need to restrain one side of the signal, but what will occur when the restrained side has some remnant signal, this part may also influence the result of the system.
- In the process of Hilbert transform, we have a complex term, how we transfer this term in our modulation and demodulation system?
- In this lab, we do not take care of the complex term, because the useful signal will not be distortion without complex term. But how to handle this problem in other cases?
Experience
In this lab, I know the principle of DSB/SSB modulation and demodulation and Hilbert transform. And I draw the LabVIEW program diagram for DSB/SSB modulation and demodulation. By observing and analyzing the performance of different signals in time domain and frequency domain, I have known the process of DSB/SSB modulation and demodulation. At the last of the lab, I use the knowledge of SSB modulation and demodulation to design a SSB walkie-talkie. And the result in figure 24 show that the performance of the SSB walkie-talkie is pretty well.
By observing figure 7 and figure 14, I find that the bandwidth of SSB signal is only half of DSB signal. And I have known the definition of bandwidth better: The difference between the upper and lower frequencies in a continuous set of frequencies.