Single upright radio pulse. The structure of the mathematical model of a rectangular coherent pack of rectangular radio pulses

On the top of the spectrum of the Dzvonyarskiy packs, the spectra of rectangular packs may have the shape of a pelust, but itself.

Spectrum of packs of direct-current radio-pulses

· The shape of the ASF arches is based on the shape of the ASF impulses.

· The shape of the ASF pelus is based on the shape of the ASF pack.

· Spectrum of packets of video pulses roztashovani on the axis of frequencies in the vicinity of the lower frequencies, and the spectrum of packets of radio pulses - in the vicinity of non-significant frequencies.

The numerical value of the spectral power of a pack of impulses starts from the energy, yak, in its own circle, directly proportional to the amplitude of the pulses in the part of the triviality of the pulses and the number of pulses in the batches Before(Triviality of the pack) and non-proportional to the period of passing of the pulses

When there are a few pulses in the pachtsi base signal (coefficient of wide bean) =

1.5.2. Signals from internal pulse modulation

In the theory of radar locating, it has been brought that for increasing the range of radar stations it is necessary to increase the number of sounding pulses, and for improving the distribution of health - to expand the range of cycles of pulses.

Radio signals without an intra-pulse modulation ("smooth"), which are stagnant in the quality of the probes, cannot be satisfied with one another at once, because the triviality and the width of the spectrum are proportional to one to one.

To that, in the early days in radio locating, it is becoming more and more difficult to know the probes of radio pulses with an intra-pulse modulation.

Radio pulse with line frequency modulation

An analytic virase of such a radio signal to a matime viglyad:

de - the amplitude of the radio pulse,

Triviality to an impulse,

The middle is not a freaky frequency,

frequency change;

The law of frequency change.

The law of frequency change.

The graph of the radio signal from the chirp and the law of the frequency change and the signal in the middle of the pulse (images on the little one are 1.63 radio pulses with the increasing frequency per hour) aimed at the little one 1.63

The amplitude-frequency spectrum of such a radio pulse is approximately straight-forward shape (Fig. 1.64)

For lowering the ASF readings of a single direct-current radio pulse without internal-pulse frequency modulation. At the connection, the triviality of the radio pulse from the chirp is great, it can be cleverly broken into the frequency of radio pulses without the chirp, the frequencies of which vary according to the stepwise law shown on the little 1.65

The spectrum of cutaneous radio impulses without JICHM will be transformed into cutaneous at its own frequency: .

signal. It is not important to show that the form of ASF will be taken into account by the form of the outbound signal.

Phase-kodo-man_pulivan_impulsi (FKM)

FKM radioimpulses are characterized by a streak-like change in phase and in the middle of an impulse behind the singular law, for example (Fig. 1.66):

Signal Trochelement code

phase law

Three-element signal

or a seven-element signal (Fig. 1.67)

With such a rank, you can create visnovki:

· AShS signals from chirp є sutsilny.

· Scho oginaє AShS is formed by the form of an obvidnoy signal.

· The maximum value of ASF is due to the energetic signal, which is directly proportional to the amplitude and triviality of the signal.

The width of the door spectrum de-deviation of the frequency and do not lie in the triviality of the signal.

Base signal maybe bootie n>> 1. Tom chirp signals are called shirokosmugovymi.

FKM radioimpulses triviality represent the success of the offensive one by one without intervals of elementary radioimpulses, the triviality of the skin of them is the same and expensive ... Amplitude and frequency of the elementary impulses are the same, but the cob phases can be seen on (or, be it, the meaning). The law (code) of the cob phase delineation is assigned to a signal. For FKM radio pulses, which are vikorovvanih in the radar breakdown of different codes, for example:

1, +1, -1 - three-element codes

- two options chotirochelementny code

1 +1 +1, -1, -1, +1, -2 - seven-element code

The spectral power of the coded impulses starts, the vicious power of the additivity is the transformation of Fur'є, the spectral density of the elementary radio pulses is in the view of the sumi.

ASF graphs for Three-element and seven-element impulses aiming at a little one 1.68

Yak can be seen from hovering signals, the width of the spectrum of the FCM radio signals in the form of a trivial elementary radio pulse

abo.

kofіtsієnt wide beige , de N-Number of elementary radio-pulses.

2. Analysis of processes by time-based methods. Country houses about the transition processes in electric lances and the classic method and analysis

2.1. Understand the transition regime. Legislate the commotion and the ear

processes in electric lancers They can be stationary and non-stationary (transient). Transition, a process in the electric lancers call such a process, with any structure and springs not permanent or periodic functions for an hour. Switching processes can be detected in the lances, so that the reactive elements can be replaced when the signals are connected or connected to the power supply, the strip-like change of the circuit and the parameters of the input elements (and the clock) On the diagrams, the commutation is indicated at the key viewer (Fig. 2.1), it is transmitted, the commutation is displayed mittєvo. The moment of communication is cleverly taken as an ear for an hour. In lantsyugah, do not take revenge on energy elements L and C when switching between

Visiting processes. In lancers with energy-saving elements, the transition processes take a decade, so the energy is stored in a capacitor for inductiveness you can’t change with a streak, so it’s worthwhile to get energy from endless exertion. The connection from the cymbal, the pressure on the capacitors and the strum through the inductance of the striking, cannot change. meaning

ASF is suspicious and changes behind the law, the maximum value of ASF at f= 0 .

The maximum value of ASF of the first bicho plyustka one thing todi yak at a single straight-field video pulse .

The width of the spectrum at equal 90% of the signal energy .

· FShS at all frequencies road 0.

The base of the signal, at which the triviality and the width of the spectrum are assigned at the level of 90% of the energy, road , Tobto signal є forgive.

1.2.2 Single radio signals і їх spectrum.

Single direct-current radioimpulse (Opri)

Determination (Fig. 1.38) can be corrected by means of the amplitude modulation of the high-frequency collation with direct video pulses.

Analytical viraz Def:

The spectral power of the signal is known by the way of calculating the integral

Zvidsi ,

.

For the analysis of graphs, hovering over the little one 1.39 next:

· ASF of a single direct-current radioimpulse sutsilny, zooseredzhenii in the outskirts of non-scientific frequency.

· That the limit of the spectrum changes from the law.

The maximum value of ASF at .

Spectrum width at equal 90% of the signal energy .

· FShS in the fringes of unpaired pelyus dorіvnyuє, in the fringes of guys.

Base signal , Tobto signal є forgive. If the spectrum of the modulating function is visible, then the spectrum of the radio signal is shaped like this:

§ ASF modulating function is replaced by the frequency of the non-linear vibration.

§ The maximum value of the modulus of spectral intensity (ASF) is reduced by a factor of two.

§ Formations of such a rank, the spectrum is mirrored to the wrong frequency.

Single dzonovy radioimpulse (Окрі)

Okri (Fig. 1.40) can be offset by the amplitude modulation of the high-frequency collation of bell-shaped video pulses.

Analytical viraz Okra:

de , at k= e .

The spectral power of such a signal of the little ones is 1.41 and the rate of calculation of the integral Fur'є.

;

, at k= e, .

To analyze the graphs hovering over the little one 1.41 next:

· AShS of a single dzone radio pulse of suspicion and transmission in the vicinity of a nonsense frequency.

· Scho oginaє AShS madzonovu form.

The maximum value of ASF at one

The width of the spectrum at equal 90% of the signal energy (k= e).

· FShS at all ranges of frequencies dorіvnyuє.

Base signal at triviality of the pulse and width of the spectrum to the signal at the level of 90% of the energy , Tobto signal є forgive.

1.3. PERIODICHNI SIGNAL I ЇX SPECTRUM

Periodic after-time of direct-current video impulses (PPPVI).

Periodic sequencing of direct-current video pulses є modulating function for the formation of periodical sequencing of direct-current radio pulses (PPPVI), such as probing signals for detecting and changing the coordinates of the collision. Therefore, according to the spectrum of the modulating function (PPPVI), it is possible to quite simply and quickly and in the value of the spectrum of the probing signal (PPPRI). When the probing signal is displayed as a malfunctioning cycle, the frequency and spectrum of the harmonics of a non-random number change (Doppler effect). In any case, you can see a brown signal, when it hits it from a rudimentary cycle, on the background you can see (interference) sounds, see it from non-sound objects (micro-objects), but also little-educated objects (meteorological objects).

PPPVI (Fig. 1.42) is the number of single rectangular video impulses, which follow one after one through equal intervals for an hour. Analytical viraz to the signal.

Amplitude of pulses;

The triviality of impulses;

Period of passing of impulses;

Pulse frequency, ;

Shparuvat.

For the calculation of the spectral stock of periodical endpoints of pulses, a number of Fur'є should be used. With the visible spectra of single impulses, where the periodical last is established, it is possible to speed up the sound with a spectral education pulses and complex amplitudes in the following series:

.

For a single direct-current video pulse, the spectral gap is described by the formula

.

Having shrunk with the sound between the spectral gap of a single pulse and complex amplitudes in a series, we know

,

de = 0; ± I; ± 2; ...

Amplitude-frequency spectrum (Fig. 1.43) will be represented by the number of warehouses:

,

with a lot of positive values, the values ​​indicate zero cob phases, and negative ones - cob phases, rivni.

In such a rank, the analogous viraz PPPVI dorivnuvatime

.

For the analysis of graphs, hovering over the little one 1.43 next:

The spectrum of PPPVI is discrete and can be stored in the vicinity of harmonics with frequency .

· Scho the fire of the ASF is changed by the law.

· The maximum value of the enclosure with one, the value of the post-warehouse.

Otrimani earlier virazi, which is based on the frequency and impulse characteristics of the narrow filter, give the ability to know the physical structure of the attachment for optimal filtering of the signal of the form. Below on specific butts will be shown actions for this synthesis.

Weather filter for rectangular video pulse.

A clear-cut pulse signal is a video-pulse of a direct-current form with a similar triviality and a high amplitude. The structure of the filter, narrowed with such a signal, is known by the spectral method. Perch for all the numerical spectral power of the corian signal:

(16.31)

The frequency response of the narrow filter is known to be sent to the viraz (16.25).

Otrimaniyah result allows the synthesis of uzgodzheniy filters. Dіysnо, ааааааааааааааааааааааааааааааааааааааааааааааааа of a large-scale production with a performance factor k; b) the ideal integrator; c) attachment with a transfer function. Stop trying to implement the signal for the hour of the inverter, which changes the sign to the signal, and the sumator. The block diagram of the filter is shown in Fig. 16.3.

Small. 16.3. Block diagram of a narrow filter for direct-current video pulse

Weather filter for a pack of the same video pulses.

At the radio locator, it is often the case that the power of the cinnamon signal is increased, and the pulses are poured out in batches. Supposedly, at the outputs of the amplitude detector of the receiver є a pack of N identical video pulses to a trivial skin; The interval between pulses in the direction of T. Yaksho is the spectral width of the pulse, then the spectral width of the burst of pulses

Synthesizing the structure of a narrow filter for a pack of pulses, vimagatimemo, the maximum output at the moment of the end of the last pulse of the pack, a sound.

(16.34)

de - transmission efficiency of a narrow filter for a single video pulse.

Small. 16.4. Block diagram of a narrow filter for a pack of video pulses

Formula (16.34) without a foreground signifies a structural diagram of a narrow filter, shown in Fig. 16.4.

Filters for single video impulse are at the inputs of the spacers. The basis of the annex is to serve as a double line of reception, which will prevent the recording of signals at every hour. Signals from the input go into the sumator. It is easy to bachiti, as the maximum output on the summator outputs will be spared only if the brown signals from all the pulses of the pack are immediately detected at all inputs. The efficiency of the robot will attach a team that is better than a pack.

It is practical to check the signals of radio-locating signals to locate also a special non-linear threshold element, which is input from the output of the summator of the narrow filter.

The level of the trocha threshold is the mean square value of the noise per hour during the daytime of the corian signal. As soon as the splash of the filter's output signal reaches the threshold level, then at the indication of the indicator there is a strong signal, which indicates the manifestation of the pulse generated by the signal.

Weather filter for direct-current radio pulse.

Do not see the signal is a radio pulse to the mind

(16.35)

Synthesizing the narrowing of the filter for such a signal, vikoristovy and vіdomosti about the impulse characteristic of the filter.

As shown, the pulse characteristic of the narrow filter

Small. 16.5. Structural diagram of a narrow-band filter for direct radio pulse

that is, the pulse characteristic of the narrow filter repeats the input signal with an accuracy up to the amplitude multiplier.

Such an impulse characteristic can be closely realized behind the auxiliary system, the structural diagram of which is shown in Fig. 16.5.

At the input of the filter, there is a colival lanka (for example, a high-quality colival contour) with an impulse characteristic

de b is a constant value.

For this purpose, the pulse characteristic of the narrow filter is brought up to zero when the summation is transferred, to one input of which the signal from the output of the colial LAN is sent without the middle, and to the input - through the LAN of the closure for seconds, and phase wrap-around, during the cold phase. When the elements are turned on, two harmonic signals with the same amplitudes and other phases are applied at the moment of an hour before the inputs of the summer, and the signal at the outputs of the summer is turned to zero.

Weather filter for Barker's signal.

Ch. 3 The receding frequency of Barker's signals is the highest value of the cephalic dandle of the autocorrelative function and the borderline low level of the dwarf dandelion.

Small. 16.6. Block diagram of a narrow filter for the Barker signal

In fig. Fig. 16.6 shows a block diagram of a narrow filter designed for the detection of a Barker M-Junction signal with phase codes. Such a signal can be seen as a result of the last of the harmonic lines with phase faults of about 180 ° (Div. Fig. 3.7).

When synthesizing, it turns out that the impulse characteristic of the narrow filter is guilty of being a "mirror" copy of the signal being seen in an hourly order of passing around the edges.

At the entrance to the annex, there is an additional filter of narrowing signals according to the reduction to one position of the folding phase-controlled signal, i.e. to the direct-current radio pulse. At the output of the filter, the input delta-impulse is injected with a radio impulse from the bypass direct-current form. A whole impulse is supplied to the line of connection with the inputs, which is a call to the hvilyov (rozpodilena) system. Covering in hours between the drivers to the triviality of the skin position to the signal.

For the correct function of the annex, it is necessary that the last of the phase failures (div. Fig. 16.6) indicated the values ​​of the phases in the vicinity of the Barker's signal when the rakhunka comes from the signal to the cob.

Direct radio pulse, shifting bridging lines of pickup, according to zbudzhu enter the sumator, at the exit of any kind of "mirror" copy is seen by the signal.

Weather filter for chirp pulse.

On a practical level, it is necessary not only to generate a signal, but to simultaneously change the actions of its parameters, for example, the position at the time or the frequency. In a wide range of converters, signals are displayed with a sharp rotation of the maximum auto-correlation function.

Among the largest signals, which are so powerful, the radio impulses are widely distributed with a linear frequency modulation (LFM-impulses). The theory of such signals of Bula Vicladena in Ch. 4. Bulo is shown, zokrema, which is chirp-impulse type

characterized by a great base, then the spectral gap in the smuga frequency ranges with a width of a practically permanent module

і argument, to quadratically lie in the frequency:

The output of the filter is up to the frequency characteristics of the filter, narrow with the chirp signal: to ensure the maximum response to the input at the singing moment, the filter is responsible for the constant value of the frequency response in the smoothie of frequencies and the frequency response, I will describe the formula

The first addition in the right part of the virase (16.38) will summarize the recording of the output signal as a single whole by the value of Another, quadratic additionally compensate for the phase of the destruction due to the spectral folding of the signal and, such a folding

The squareness of the Phase characteristics of the narrow filter for the chirp signal can be entered from the beginning of the winter months. In the process of intra-pulse modulation, the frequency of the signal changes according to the linear law for every hour

The skin moment at the t-hour in the interval between the triviality of the pulse receives its own high-cosmic (quasi-harmonic) signal, which will be picked up in the filter for an additional hour, equal to the group hour of recording (div. Ch. 9)

In order to know the moment when the spectral warehouses appear at the entrance, until the next hour the value of t appears, that is, the moment of the spectral warehouses appears at the entrance. The sound arrives before the day, when all spectral warehouses and the chirp signal arrive at the filter's output one hour at the time of the hour

A brown signal at the output of a narrow filter with an accuracy up to a pre-amplitude multiplier before repeating the shape autocorrelation function Chirp-impulse [see. formulas (4.54) і (16.22)]:

The graph, which is generated by such a signal, is shown in Fig. 4.10. It’s not important bachiti, but the width of the cephalic pelust is a signal, you can see the zero points, Yours

That is the function of the chirp-pulse, which will take care of the ultrasonic filter: the base for the signal

proportional to the base of the chirp signal.

For the hardware implementation of visible filters, the physical phenomenon of the dispersion of spring ultrasonic needles in solid bodies is often the physical phenomenon of the dispersion of spring ultrasonic needles in solid bodies - the accumulation of fluidity is more widespread in terms of frequency. According to the law of the dispersion of needs in the ultrasonic line of pickup, it is necessary to adjust the required phase characteristic to the form (16.38). Eskiz design of the filter and dispersion characteristic of the image in Fig. 16.7, a, b.

Uzgodzhena filtering of chirp-pulses, on the basis of the optimal processing of packets of video pulses, is carried out, as a rule, on the basis of non-success at the intermediate frequencies of the receiver, i.e. before the amplitude detector.

Small. 16.7. Rozpodіleniy filter, uzgodzheniy with chirp signal: a - schematic pristіy (1 - sound line, 2 - electromechanical conversion); b - the frequency of accumulation of a group hour of accumulation of a colivan in a sound pipeline

In the presence of a tsom, one should be given a unique strangulation weak signal a strong transition, as it is inevitable that the signal and noise are not inevitably modified.

Quasi-optimal filter.

In a number of vipadkіv it is possible to achieve good results, having lost the filter three more simple design in proportion to the optimal filters. The selected attachments are taken as Quasi-Optimal Filters.

The transparent-four-pole of the integrated type, at the inputs of which there is an instantaneous noise of the spectral force of WQ and the direct video pulse, which has a low amplitude (70

Small. 16.8. Reduction of the blue signal-to-noise ratio for the RC filter in the case of an ultrasonic filter

Zokrema, for a quasi-optimal view of a direct-current radio pulse trivially, a dark-colored filter with a gaus can be used frequency characteristic, Oscillations on a non-carrier frequency. Smug the passage of such a filter should be vibrated from the performance

(16.44)

It can be shown that the programmed signal / noise ratio at the optimal warehouse filter is close to 1 dB.

Signal є direct-current radio pulse with harmonic memory (pic.4.170)

With the calculated functions of non-significance, the drops of positive and negative time-related events between pulses are clearly visible. at

When the result is similar. Cozy results

(4.96)

It is clear that the function of non-value is changed for the drop f d = 0. The result of the offensive

. (4.97)

Peretin with a surface area f d = 0 is shown in Fig. 4.171

If the area is overwhelmed with τ = 0,

(4.98)

The formula is adapted to the modulus of the spectrum of the direct-current video pulse, which is є bypass to the output signal (pic.4.172).

On the pic.4.163 the diagram of non-significance of the direct-current radio pulse is displayed

The more the triviality of the impulse, the greater the distribution of the health by frequency, and the faster the distribution of the health by the hour. The less the triviality of the impulse, the less the triviality of the power by the hour, and the higher by the frequency. Such a standard is based on the principle of non-value in radar location.

broadsmouth signals

The impulse signal is embedded in a wide-dark, like solid triviality on the width of the frequency spectrum. Є th іnshiy pіdhіd at the assigned broadband signal. So, for example, in 1990 in the United States introduced a field value for the frequency η:

As far as the signal is valid, it may cause a swamp η≤0.01 to be reported to the university; May 0.01<η≤0,25 относится к широкополосным; имеющие 0,25<η<1 относятся к сверхширокополосным (СШП).

Yak Snip can quickly change the code-pulse response, linear-frequency-modulated signals, pseudo-noise signals, video-pulses, but not high-frequency storage and radio-pulses, may not be high-frequency, low-frequency low-frequency signals. The name of the signal in the images is shown in Fig. 4.174.

The broadband signal can be reached by means of intra-pulse modulation of the phase or frequency. The wide-mug signal (radio pulse) is n times greater than the width of the spectrum, the lower the pulse is the same without intra-pulse modulation.

The processing of broad-spectrum signals is realized in optimal filters, impulses, on outputs such as the amplitude-frequency spectrum of the signal. Shirokosmugovy radioimpulses in the optimal filter squeeze, and the stronger, the more hard.

Similar information:

1. The function of chaklunstvo is accorded for individ polyagus in a socially secured channel for turning the culturally fenced off "

Single radio pulse of tasks with amplitude U= 1V, often f and trivial impulse τ values ​​in tables 1.

1. Visually the spectrum of amplitudes and phases for the variant of a single radio pulse with the values ​​in the table. Provide tables and graphs, date analysis of the results

2. Vivichi changes in the spectrum of amplitudes and phases during changes τ їm . (τ їm =0,5τ , τ їm =τ , τ їm =1,5τ ). Provide tables and graphs, date analysis of the results.

3. Vivity changes in the spectrum of amplitudes and phases at a ssuv / pulse Δt relative t = 0Δt = 0.5 τ їmΔt = 1.5 τ їm... Provide tables and graphs of date analysis of the results.

4. Visually increase the width of the spectrum to the signal up to

victorious criteria.

5. Add the width of the spectrum to the signal, which will prevent the transmission of 0.9 energy to the signal at low signal durations.

for help, the program, aiming at the dodatku

I... Periodic pulse duration

The drawing of the spectral characteristics of the periodical signal of the rectangular form can be carried out behind the help of the program by students, using the electronic tables, or by the programs "Spectrum_1.xls" brought into the electronic

version of the given order. The program "Spectrum_1.xls" has a numerical method for measuring spectral warehouses.

Formulas that can be used for rosters of the spectrum for

periodic signals

Basically, the method is based on the formulas of hovering below

(2)

(3)

(4)

de C 0 - after the warehouse,

ω 1 = 2π / T is the circular frequency of the first harmonic,

T - period of repeated function,

k – harmonica number

C k- amplitude k- th harmonica,

φ k- phase k- th harmonica.

The number of harmonious warehouses is built up to the calculation for the formulas of the approximate integration

(5)

(6)

de N- the number of discrete views per period

dulled functions f(t)

Δ t = T/ N- croc, with a good rosette function f(.).

Post_yna warehouse is behind the formula C 0 = a 0

Go to the complex form presented here, follow the guidance given by the formulas:

;
; (7)

For periodic signals with a spectrum encircled by the spectrum, it is necessary to follow the formula:

(8)

de P – tighter signal due to the spectrum n harmonics.

For the determination of the spectral analysis of the formulas, the spectral characteristics are displayed in the supplementary program. Program viconani in VBAMicrosoftExcel middleware.

The launch of the programs will go from the "Spectrum" folder to the onslaught of the two key bears on the names of the programs. A window with a program is shown in Fig. 1. When the image hovered in Fig. 1 appears. 2, next to enter the input data for the distribution in the given fields, as seen by the color

Fig 1. Launching programs

Fig. 2. Periodic signal with a period of 1000 μs i

trivial 500 microseconds

When you see the image hovered in fig. 2, next to enter the data for distribution in the given fields, as seen by the color. The range of amplitudes of phases is available until the default for the option of the latency of direct-current pulses with a period of 1000 microseconds and a trivial one of 500 microseconds. Write the introduction of the tribute in the skin field next to the key "Enter". To start the program, move the cursor to the "Calculate spectrum" button and press the bear's key.

Tables and graphs of deposition of the module of amplitudes and phases from the number of harmonics and frequency and pointing in Fig. 3 - 5

Small. 3. Table with calculation results

In fig. 3 hovering the results and drawing, select in the table on the arch 3. In the columns of the display of the coming results: 1 - harmonic number, 2 - harmonic storage frequency, 3 - cosine storage spectrum amplitude, 4 - sinus storage spectrum amplitude, 5 - 6 - amplitude phase spectral warehouse. The tables in fig. 3, the butt is aimed at the racking for the period of repetition of pulses T = 1000 μs and triviality of pulses τ = 500 μs. The number of points per period is vibrated depending on the required accuracy of the design and it can be taken twice as much as the number of numerical harmonics.

Small. 4. The module of spectral storage signals with a period of 1000 microseconds and a triviality of 500 microseconds

Small. 5. Phases of spectral storage signals with a period of 1000 μs and triviality of 500 μs

Fig. 6. The sum of the efforts of the harmony warehouses.

Updates signal representations in Fig. 7. The form of the renewed signal is initiated by the formula (1) and is based on the number of harmonics

Small. 7. Updating the signal by the sum of harmonics 1, 3, 15.