What is the width of the range of the electrical signal. The spectrum of viprominuvannya radio signal. Power and task for self-verification
Signal spectrum width 1. The value that characterizes the part of the spectrum of the signal
Vikoristovuetsya at the document:
Addendum No. 1 to GOST 24375-80
Telecommunication dictionary. 2013 .
Look at the "Signal Spectrum Width" in other dictionaries:
signal spectrum width- a value that characterizes a part of the spectrum of the signal, which can cover the spectral warehouses, the total intensity of which is to become a given part of the overall intensity of the signal. [GOST 24375 80] Topics of TV broadcasting, radio broadcasting, video
Signal spectrum width- 2. Width of the signal spectrum The value that characterizes a part of the spectrum of the signal, to compensate for the spectral warehouses, the total intensity of which to set a given part of the total intensity of the Dzherelo signal: GOST 24375 80 Radio communication. Terms and… …
spectrum width (optical channel signal)- 44 spectrum width (to the signal of the optical channel): A range of frequencies or a range of fluctuations, in which the main part of the average intensity of the optical signal is transmitted to the signal of the optical channel. Glossary of terms for normative and technical documentation
width of the spectrum of the output signal of the module (block) low-frequency- spectrum width Δfbread Frequency interval of the spectrum of the output module (block) of the low frequency frequency, in which the part of the tightness of the colivans is set. [GOST 23221 78] Topics of components and communication technology Key terms VHF modules, VHF blocks Synonyms width … Dovіdnik technical translation
spectrum width- A range of frequencies, in which the main energy of the signal is considered, which is vibrated, and there are frequency storages, which may have the maximum value. The width of the spectrum should be adjusted for the level of 0.5 (ZdB) according to the maximum value of the tension or for the level of 0... Dovіdnik technical translation
Width of the spectrum of the output signal of the module (block) LF- 20. Width of the spectrum of the output signal of the module (block) LF Δfwide
It is already clear to us that the less trivality of the signal, the broader spectrum.
All the fundamental provisions of the theory of signals can be established in a wild look on the basis of the transformation of Fur'є
Let's take a look at the behavior of the skin z іntegraіv zі zbіlshennyam Ω.
It seems to be true to Riemann's Lemy, which makes it clear that the function s(t) is absolutely integrated over the interval
The geometric sensation of this solidity is explained by a little, in the upper part of such an image there is a definite sufficient signal s (t) and harmonic vibration with a frequency Ω, and in the lower part - їх tvіr.
When reaching a high frequency Ω, the skin positive fold may be compensated by the closest negative fold to it and the total area under the curve s(t)cos(Ωt) or s(t)sin(Ωt) is close to zero. To increase the frequency with a high frequency, to increase the frequency Ω=2π/T, if the period T is to achieve a small resistance to the signal s(t).
Obviously, we want a short signal, a smaller one, and a period T, which inspires my mind.
In other words, if the signal is short, then the frequency limit of the spectrum of the signal is higher. The shards of the lower range reach zero frequency, then the upper range will go wider, less trivality of the signal. In this case, it appears that the increase in trivality on the "technical" width of the spectrum is a value close to one.
Previously, on the yakіsnom level, they gave a designation of equivalent trivality, more strictly it can be designated as
Moreover, the cob, at the right time, will go with the middle of the impulse, that mind will win
Similarly, the equivalent spectrum width ΔΩ=2πΔF is determined by virase
For dodatkovoy mind
Clarifying cob for frequency on the Ω axis.
This is a signal of regulation in such a way that yogo energy is healthy alone, that is.
That viraz for τ і ΔΩ, which is deposited in the form of a signal, at the same time cannot be less than ½.
In such a rank, for any signal, the mind is beaten and ΔF≥1/4π.
Zocrema, for the Gaussian impulse, basing on the previous results, we know
Vykoristovuyuchi umovu rationing
acceptable
From the first example, it is clear that with the signals of the Gaussian pulse, the smallest possible value of the additional oil τ and ΔF.
Squeezing the impulse in an hour, for example, increasing the accuracy of the timing of the moment, will inevitably be accompanied by an expansion of the spectrum of the impulse, which will suffocate the smog of the transmission of the vibrational extension. Similarly, squeezing the spectrum of the impulse, for example, with the method of increasing the accuracy of the frequency control, is inevitably accompanied by an increase in the signal per hour, which means a greater delay in the delay (modification). The impossibility of concentrating the signal in a narrow fluid at once, often in a short interval of an hour, is one of the manifestations of the principle of non-insignificance, which is familiar to the physicist.
In practical cases, the trivality of the signal and the width of its spectra in a number of fluctuations are easily adjusted by energy criteria. The active pulse duration, the active spectrum width (or) is determined as an hour interval and a frequency range, in the middle of which, a part of the total energy is more important E impulse (for example, 95%). Like a signal s(t) tasks at the interval of an hour
At the left part of the equanimity, the energy of the signal was recorded, which was recorded in the interval of hour 0 - (Fig. 4.33, a). At the right part of equality - a part (as it is determined by a given coefficient re-energize the signal.
Parseval’s parity, similarly, the width of the signal spectrum is enabled
In this way, the width of the spectrum of the signal is active, depending on the smoothness of frequencies, at the boundaries of which a part of the signal energy is laid (Fig. 4.33 b).
In times of simple video pulses (for example, recto-current, tri-current, cosine), the spectrum of such serrations in the low-frequency region can be taken into account with sufficient accuracy for practice, which
de, - a constant value, which should be deposited in the form of an impulse and the criterion for assessing the value of .
Fig.4.33. Signal (a) that spectrum (b)
As can be seen from (4.61), it is inevitable that the change in the trivality of the impulse should be brought up to an increase in the width of the spectrum, and in the same way. Corying with spіvvіdnennia (4.61), you can sort out a lot of frequencies, like taking the spectrum of the signal in the fallow period.
Rice. 4.34. Rectangular pulse (a) and iogo spectrum (b)
For more types of video impulses, the value is close to one. Zocrema, to evaluate the active width of the spectrum of a rectilinear pulse trivality (Fig. 4.34 a) as a range of frequencies f\u003d 0 to these frequency values, if the spectral width first goes to zero (Fig. 4.34, b), then if the spectral width argument (4.42) gains a value 
, then = 1. Also, for a rectilinear impulse = 1.
Corresponding to the ratios (4.60), it can be shown that the smooth (0, ) (the first pellet) has over 90% of the overall signal energy.
The task for self-verification:
Which trigonometric functions can form a periodic signal?
What is the posting of that main warehouse, the harmonies of the signal?
What formulas Fur'є vikoristovuyut for the description of periodic signals?
Write down the Four's series (4.4) in trigonometric and complex forms, using the third harmonic.
What is the spectrum of amplitudes?
Periodic signal of tasks instructed by Fur'є at the form
Give a series in trigonometric form (4.10).
Theoretically, as it was planned more, more periodic functions are the spectrum of non-obstructions, tobto. for the transmission of signals to telemechanics without changing the form, it is necessary to have an infinitely large amount of bandwidth for the communication channel and the frequency of amplitude and phase effects. Practically all communication channels can be interchanged with a lot of bandwidth, and the signal form of the transmission hour by the channel changes according to the frequency of the amplitude and phase signals of the channel. Obviously, it is important to convey that part of the spectrum to the signal, as if to avenge the harmonic warehouses of audibly great amplitudes. In connection with the cim, it is necessary to understand the practical width of the spectrum of the signal. Under the practical width of the spectrum, the signal understands that frequency range, at the boundaries of which lie harmonic warehouses of the signal with amplitudes, which shift the predetermined value.
Shards of average tension, which is seen as a signal on the active support, which is equal to 1 Ohm, is composed of pressure, which is seen on this support by harmonic warehouses,
the practical width of the spectrum from the energy point of the gap can be assigned as the frequency range, at the boundaries of which the signal intensity is more important.
As an example, the width of the spectrum of the periodic sequence of rectilinear pulses (Fig. 1.8, a) is significant for practical purposes, so it is necessary to turn all the harmonic warehouse signals, the amplitude of which is greater than 0.2 in the amplitude of the first harmonic. The number of harmonics that give shape k maybe buti otrimano z virazu
,
stars k= 5.
In this way, the practical width of the spectrum in the examined butt is equal to 5W 1 in it there are only three harmonics (first, third and fifth) and a constant warehouse.
Middle tightness P k 5, which is seen in the active support, which is 1 ohm,
The middle tension, which is seen in the very support of the entire warehouse signal, will be
in such a manner, 
%, tobto. warehouses that enter the practical spectrum, 96% of all signal intensity is seen in the active support.
Obviously, the expansion of the practical spectrum of this signal (over 5W 1) from the energy point of the gap is underestimated.
Spectrum reduction of the signal is also added to its shape. For illustration on small. Fig. 1.8 shows the change in the shape of straight-cut pulses for saving in the spectrum of the more permanent warehouse and first harmonics (Fig. 1.8, b), when the spectrum is reduced with a frequency of 3W 1 (Fig. 1.8, in) that when the spectrum is reduced with a frequency of 5W 1 (Fig. 1.8, G). Like a crying baby, the cooler the front impulse can be, the more greater harmonic warehouses can enter the warehouse signal.
A0+A 1 (t)
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A 0 +A 1 (t)+A 3 (t) A 0 +A 1 (t)+A 3 (t)+A 5 (t)
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Rice. 1.8. Form a signal when the sequence spectrum is reduced
rectilinear impulses
The analysis of the presence of the form of a periodic signal in terms of the number of summed harmonics shows that, due to the choice of the practical spectrum width, the signal cannot be separated by more energy-efficient mixing. It is necessary to protect the vimogi before the signal at the exit of the system, both from the energy point of view, and from the point of view of saving the form. In vipadku practical signal spectrum width is chosen sensibly
, (1.21)
de m = 0.5…2 – pulse shape coefficient; with m = 1, transmission of close to 90% of the signal energy is ensured.
In code-pulse systems of television, as well as in rich telecontrol systems, the skin code combination is composed of a singing sequence of direct pulses and pauses. Code combination, which confirms the given value of the parameter, which is valid, or commands, can be periodically transmitted over the communication channel. The spectrum of such a signal to fall, obviously, depends on how the same code combination is transmitted. However, the most important factor that determines the highest harmonic spectrum is the highest frequency of pulses. Therefore, for code-pulse systems, it is practically necessary to select a signal as a periodic sequence of rectangular pulses (Fig. 1.5). Parameter t choose the equal trivality of the shortest pulse of the middle amps, which are sounded in code combinations, the period of follow-up T= 2t. In this direction, the maximum frequency of passage of impulses W max = 2p/ Tі the frequency of the fundamental harmonic of the spectrum W1 = Wmax. The required width of a range of frequencies for a signal is determined by a discrete spectrum with a limited number of warehouses, and it can vary up to (1.21).
The nature of the spectrum, the initial need for a range of frequencies, lies in the form of a signal, and minds that the transmission path has. As transitional processes, which in the system for the first hour of transmission of one impulse, end up to the termination of the offensive impulse, then the replacement of the periodic sequence of impulses can be considered the transmission of independent single impulses.
The spectrum of a single impulse may look like this:
Rice. 10.16. Spectrum of a single pulse
From the spectrum of a single pulse, it is clear which is smaller, while the spectrum is wider. At ® 0 – spectrum of equalities; and with = - there can be one post warehouse on the spectrum.
This sing-along screeches out of the middle from the wildness of the transformation of Fur'є.
Come on ƒ( t) show the spectrum F(ω).
Change the scale of the function ƒ( t) along the time axis in a once and look at the spectrum of functions aƒ( at):
replace change at = z; adt = dz; t = z/a, so that the trivality of the function ƒ( t) change into a times, in the style of the time, the width of the її range.
The power of the spіvvіdnoshennia between the trivality of the impulse and the width of the yogo range of the greatest practical value. In the calculation technique, short and intense pulses are necessary and at the same time it is necessary, so that the spectrum of the pulse is already narrower, so that wide spectra are difficult to assemble.
Qіmogi super-clear.
Blame the power: why can't you know such signals, if they would be small, the spectrum would be surrounded and the trivality would be surrounded at once? The formalism of the transformation of Fur'є tsgogo is not allowed, the prote for real signals can be introduced sensible occupancy, as they allow the occupancy or Δ t, or Δƒ, or else.
The most important thing for this sensi, as we said earlier, is the energy criterion. With this, you can detect the following signal models:
1. Clock signals . spectrum - theoretical non-surfaces; physically responsible for the surroundings and less than a part of the spectrum is protected, the part of the signal energy is less important.
2. Signals so mathematically ce periodic, uncircumscribed at the hour signals. In fact, the real process of zavzhda obmezheniya at the hour, that is protected by less than an hour interval, in which I am aware of the importance of a part of all the energy of the signal.
de t 0 - often set naturally: for a symmetrical impulse t 0 = 0; for the solitary t 0 = 0 i the formula may look like:
.
3. Signals, yakі moat і trivalіst (Δ t) that spectrum width (Δƒ) is interspersed as intervals, in which the energy part of the signal is more important. Mathematical apparatus of transformation Four'є gives you different results.
With interchanges, Δ tі Δƒ it is possible to set such a task - to view such a signal shape, on the basis of tvіr Δ t· Δƒ reach min.
Such a mind inspires an impulse that can form a ringing form, as it is described Gaussian curve (Curve of normal distribution).
Rice. 10.17. Kriva Gaus
Tvir Δ t· Δƒ can be changed to less than a singing boundary:
Δ tΔƒ ≈ const > 0,
de const deposit in the choice of destination Δƒ and Δ t.
Induced value Δ tΔƒ for different types of signals in the admission, which
,
de η = 0.9.
Δ t· Δƒ - max for impulses with opening (exponential, rectangular); less for impulses with a rise in the first slow (tricutnik and cosine) and the least value for a ringing impulse, for which the function is uninterrupted with its mustaches. http://website/
The most plausible and close to real activity is a model with a substitution spectrum.
This is due to the fact that the spectrum of tightness of a real signal is slowly falling down with a frequency interval, on which the main part of the tightness falls.
In engineering practice, it is accepted (in the first place, it is independent of the form of a signal):
Δ tΔƒ ≈ 1.
In fact, regardless of the form of the signal, there is > 90% energy.
1. Yakscho T imp = 3mlsec, then how many frequencies are needed to miss the main part of the energy?
.
2. Like the triviality of television impulses, like F TV max = 6MHz?
