Ce informatii ascunde spectrograma unui semnal electric?

[morpheus]

Cum am mai facut in cateva randuri in ultima vreme, postez si aici o intrebare mai veche din sectiunea Q&A a site-ului la care nu exista inca un raspuns.

http://www.scientia.ro/intrebarile-scientia/details/Ce-informatii-ascunde-spectrograma-unui-semnal-electric-_670.html

[AlexandruLazar]

Spectrograma unui semnal electric "oarecare" nu ascunde propriu-zis niciuna, dar pentru un semnal electric real pot fi foarte multe. Vezi, de exemplu, la http://www.dspguide.com/ch9/1.htm , comentariile la figura 9-2 (le reproduc mai jos ca să fie mai ușor de găsit pe urmă -- capitolul e destul de mare):

Figure 9-2 shows an example spectrum from our undersea microphone, illustrating the features that commonly appear in the frequency spectra of acquired signals. Ignore the sharp peaks for a moment. Between 10 and 70 hertz, the signal consists of a relatively flat region. This is called white noise because it contains an equal amount of all frequencies, the same as white light. It results from the noise on the time domain waveform being uncorrelated from sample-to-sample. That is, knowing the noise value present on any one sample provides no information on the noise value present on any other sample. For example, the random motion of electrons in electronic circuits produces white noise. As a more familiar example, the sound of the water spray hitting the shower floor is white noise. The white noise shown in Fig. 9-2 could be originating from any of several sources, including the analog electronics, or the ocean itself.

Above 70 hertz, the white noise rapidly decreases in amplitude. This is a result of the roll-off of the antialias filter. An ideal filter would pass all frequencies below 80 hertz, and block all frequencies above. In practice, a perfectly sharp cutoff isn't possible, and you should expect to see this gradual drop. If you don't, suspect that an aliasing problem is present.

Below about 10 hertz, the noise rapidly increases due to a curiosity called 1/f noise (one-over-f noise). 1/f noise is a mystery. It has been measured in very diverse systems, such as traffic density on freeways and electronic noise in transistors. It probably could be measured in all systems, if you look low enough in frequency. In spite of its wide occurrence, a general theory and understanding of 1/f noise has eluded researchers. The cause of this noise can be identified in some specific systems; however, this doesn't answer the question of why 1/f noise is everywhere. For common analog electronics and most physical systems, the transition between white noise and 1/f noise occurs between about 1 and 100 hertz.

Now we come to the sharp peaks in Fig. 9-2. The easiest to explain is at 60 hertz, a result of electromagnetic interference from commercial electrical power. Also expect to see smaller peaks at multiples of this frequency (120, 180, 240 hertz, etc.) since the power line waveform is not a perfect sinusoid. It is also common to find interfering peaks between 25-40 kHz, a favorite for designers of switching power supplies. Nearby radio and television stations produce interfering peaks in the megahertz range. Low frequency peaks can be caused by components in the system vibrating when shaken. This is called microphonics, and typically creates peaks at 10 to 100 hertz.

Now we come to the actual signals. There is a strong peak at 13 hertz, with weaker peaks at 26 and 39 hertz. As discussed in the next chapter, this is the frequency spectrum of a nonsinusoidal periodic waveform. The peak at 13 hertz is called the fundamental frequency, while the peaks at 26 and 39 hertz are referred to as the second and third harmonic respectively. You would also expect to find peaks at other multiples of 13 hertz, such as 52, 65, 78 hertz, etc. You don't see these in Fig. 9-2 because they are buried in the white noise. This 13 hertz signal might be generated, for example, by a submarines's three bladed propeller turning at 4.33 revolutions per second. This is the basis of passive sonar, identifying undersea sounds by their frequency and harmonic content.

Similar, pentru semnalele modulate în frecvență, spectrograma include chiar informația care trebuie transmisă. În cazul în care semnalele sunt forme de undă dintr-o rețea electrică de putere mare, abaterile de la forma sinusoidală (care apar ca niște componente spectrale în plus față de vârful de la 50 sau 60 Hz) pot da informații despre calitatea energiei furnizate prin rețea, despre consumatori și uneori chiar despre eventuale defecte.