同济大学-信号与系统SSB论文

“信号与系统”论文

标题：

The modulation and demodulation of Single-sideband

signal

姓名：潘路

学号：1257011

所在院系：电子与信息工程学院电气工程系

摘要:

Single sideband modulation is an amplitude modulation technique which makes good use of energy and bandwidth. The modulated signal bandwidth of modulation technology’s output is two times more than that of source signals. But SSB technique can avoid bandwidth doubled, while avoiding the energy waste in the carrier, but the equipment is complicated, the cost will increase. Besides, we can transmit messages by a single sideband signal without distortion.

SSB can be regarded as a kind of special form of AM. The spectrum of AM signal contain frequency fc and the belt of up and low, the transmitted message is contained in the two side, and each side contains transmitted message integrally. Therefore, we can transmit messages by a single sideband signal without distortion.

When we know a lot of advantages about the SSB, we must be curious about how to make out the SSB. Then, it is the single sideband modulation generating process. Bilateral upper and lower with modulation two sideband is completely symmetrical, they carry information is same, can use an edge to bring transmission all news. This transfer mode in addition to save carrier power besides, still can save half the transmission frequency band, namely for single side band modulation. With the single modulation only transfer bilateral with a modulated signal sideband. Therefore transmitted single side band signal the most direct way is to give the bilateral bring signals through a single side band filter, filter, can not sideband addressing to single side band signal. We put this method called filter, it's the simplest and most commonly used methods. Here is the detailed process about making it. Firstly, we have a signal we need, let us call it as s(t). Secondly, we make a function as s(t)·cow(ωt), then we will get the image of the function just like the picture show us. And this is the source signal we want to send. At this point, the prepare work is done.

The final signal we want is single sideband signal, so we have to eliminate the other sideband. Therefore, it is necessary to make a function like the picture shows us. When we have that function, it is easy to get the single sideband signal by put that function to plus the source signal function.

But the problem is that how do we get that function.

Next, it is a way to make that function come out. Firstly, we build a function which we call it g(t). If we make it g(t)·cos(ωt), the result of g(t)·cos(ωt) plus s(t)·cow(ωt) will not be the single sideband signal we want. Because the image of g(t)·cos(ωt) is not an even function and we can easily know that the result is wrong while clearing up the wrong side of the function. Therefore, we shouldn’t create a g(t)·cos(ωt) function but to create a function as g(t)·j·sin(ωt).

As we see in the picture, we can find the function j·g(t)·sin(ωt) is a even function, when it plus s(t)·cos (ωt), the both side near the y-axis below the x-axis are eliminated, so that the function remained is what we need.

However, a new problem is born. How do we have the g (t) function? In fact, it is not a problem. As we have the source signal function, it is easy to get its fourier transform s(jω), and then we create a new function s(jω)·sgn(ω), so that new function

is g(jω). The final step is to solve the inverse fourier transform. After that the g(t) is

created out.

Through those steps above, we can finally complete Modulation sideband filtering job. And the single sideband signal function is that:

Y = s(t)·cow(ωt)+ j·g(t)·sin(ωt)

= s(t)·cow(ωt)+[s(t)*1/(pi·t)]·sin(ωt) The s(t) is the input signal, the Y is the single sideband signal.

When we complete its modulation job and send it out, the next job we must think of is its. Under ideal conditions, we can use cos(ωt) to make it, just like Y·cos(ωt), then we will have its demodulation as (1/2)·s(t), after this step, the demodulation have been completed. But the actual situations would not as easy as the ideal conditions. Because under the ideal conditions, the equipments of the modulation are expensive very much. But in the normal situations, the equipments can not do that demodulation exactly right, it usually follows a angle θ, so the single sideband signal function will change into

Y ·cow(ωt+θ)=(1/2) ·{ s(t)·cow(ωt+θ)+[s(t)*1/(pi·t)]·sin(ωt+θ)}

Because of the θ, we will not return the source signal, so the works we have ever done are all waste. However, for the single sideband modulation has plenty of advantages. Some fields really need the signals keep exact and real but can ignore the equipments’ price are still using this technology, such as the military field and deep-sea exploration and so on.

Besides, we find that single sideband modulation will gradually replace the amplitude modulation. This is because the former has two outstanding advantages: the transmission bandwidth than the latter is not greater than the message bandwidth, is half; carrier suppressed (in amplitude modulation, the modulation index m=1, transmitting power centralized in 2/3 without a message carrier frequencies). This not only saves power, but also greatly reduces the interference between radios. In addition,

single sideband transmission influenced by the frequency selective fading in communication is amplitude modulation is small, and there is no threshold effect. These advantages make the SSB technology far beyond the scope of the short wave communication.

Through this paper, let me learn a lot of things can not get from school books, enhance my ability of self-taught. I have many advantages and disadvantages about the single sideband modulation and demodulation, it will do really good help for my following study. And I will study hard to carry forward SSB technology in the future.