Radio signals are electromagnetic waves or high-frequency electrical vibrations that carry the transmitted message. To generate a signal, the parameters of high-frequency oscillations are changed (modulated) with the help of control signals, which represent a voltage that changes according to a given law. Harmonic high-frequency oscillations are usually used as modulated ones:
where w 0 = 2π f 0 - high carrier frequency;
U 0 - amplitude of high-frequency oscillations.
The simplest and most commonly used control signals are harmonic oscillation.
where Ω - low frequency much less than w 0; ψ - initial phase; U m - amplitude, as well as rectangular pulse signals, which are characterized by the fact that the voltage value U control ( t)=U during the time intervals τ and, called the pulse duration, and is equal to zero during the interval between pulses (Fig. 1.13). The quantity T and is called the pulse repetition period; F and = 1 / T and - the frequency of their repetition. Pulse repetition ratio T and to the duration τ and is called the duty cycle Q impulse process: Q=T and / τ and.
Figure 1.13. Sequence of rectangular pulses
Depending on which parameter of the high-frequency oscillation is changed (modulated) with the help of the control signal, amplitude, frequency and phase modulation are distinguished.
With amplitude modulation (AM) of high-frequency oscillations with a low-frequency sinusoidal voltage with a frequency of Ω modes, a signal is formed, the amplitude of which changes over time (Fig. 1.14):
Parameter m=U m / U 0 is called the amplitude modulation factor. Its values are in the range from one to zero: 1≥m≥0. Modulation ratio expressed as a percentage (i.e. m× 100%) is called the AM modulation depth.
Rice. 1.14. Amplitude modulated radio signal
With phase modulation (PM) of a high-frequency oscillation with a sinusoidal voltage, the signal amplitude remains constant, and its phase receives an additional increment Δy under the influence of the modulating voltage: Δy = k FM U m sinW mod t, where k FM is the coefficient of proportionality. A high-frequency signal with sinusoidal phase modulation has the form
With frequency modulation (FM), the control signal changes the frequency of the high frequency oscillations. If the modulating voltage changes according to a sinusoidal law, then the instantaneous value of the frequency of the modulated oscillations w = w 0 + k World Cup U m sinW mod t, where k FM is the coefficient of proportionality. The greatest change in frequency w in relation to its average value w 0, equal to Δw М = k World Cup U m is called frequency deviation. A frequency modulated signal can be written as follows:
A value equal to the ratio of the frequency deviation to the modulation frequency (Δw m / W mod = m FM) is called the frequency modulation factor.
Figure 1.14 shows the high frequency signals for AM, PM, and FM. In all three cases, the same modulating voltage is used. U mod, changing according to the symmetric sawtooth law U mod ( t)= k Maud t, where k mod> 0 on time interval 0 t 1 and k Maud<0 на отрезке t 1 t 2 (Figure 1.15, a).
With AM, the signal frequency remains constant (w 0), and the amplitude changes according to the modulating voltage law U AM ( t) = U 0 k Maud t(Figure 1.15, b).
A frequency-modulated signal (Figure 1.15, c) is characterized by a constant amplitude and a smooth change in frequency: w ( t) = w 0 + k World Cup t... At a time interval from t= 0 to t 1 the vibration frequency increases from the value w 0 to the value w 0 + k World Cup t 1, and on the interval from t 1 to t 2, the frequency decreases again to the value w 0.
The phase-modulated signal (Figure 1.15, d) has a constant amplitude and a jump-like frequency change. Let us explain this analytically. With FM under the influence of a modulating voltage
Figure 1.15. Comparative type of modulated oscillations at AM, FM and FM:
a - modulating voltage; b - amplitude-modulated signal;
c - frequency modulated signal; d - phase modulated signal
the signal phase receives an additional increment Δy = k FM t, therefore, the high-frequency signal with phase modulation according to the sawtooth law has the form
Thus, on the segment 0 t 1 frequency is equal to w 1> w 0, and on the interval t 1 t 2 it is equal to w 2 When transmitting a sequence of pulses, for example, a binary digital code (Figure 1.16, a), AM, FM and FM can also be used. This type of modulation is called keying or telegraphy (AT, CT and FT). Figure 1.16. Comparative view of manipulated oscillations at AT, PT and FT With amplitude telegraphy, a sequence of high-frequency radio pulses is formed, the amplitude of which is constant during the duration of the modulating pulses τ and, and is equal to zero all the rest of the time (Figure 1.16, b). With frequency telegraphy, a high-frequency signal is formed with a constant amplitude, and a frequency that takes two possible values (Figure 1.16, c). With phase telegraphy, a high-frequency signal is formed with constant amplitude and frequency, the phase of which changes by 180 ° according to the law of the modulating signal (Figure 1.16, d). As a carrier of messages, high-frequency electromagnetic oscillations (radio waves) of the corresponding range are used, which can propagate over long distances. The oscillation of the carrier frequency emitted by the transmitter is characterized by: amplitude, frequency and initial phase. In the general case, it is presented in the form: i = I m sin (ω 0 t + Ψ 0), where: i- instantaneous value of the current of the carrier oscillation; I m- amplitude of the current of the carrier oscillation; ω 0
- the angular frequency of the carrier wave; Ψ 0 –
the initial phase of the carrier wave. The primary signals (transmitted message converted into electrical form) that control the operation of the transmitter can change one of these parameters. The process of controlling high-frequency current parameters using a primary signal is called modulation (amplitude, frequency, phase). For telegraphic transmissions, the term "manipulation" is used. In radio communication, for the transmission of information, radio signals are used: radiotelegraph; radiotelephone; phototelegraph; telecode; complex types of signals. Radiotelegraph communication differs: according to the method of telegraphy; by the method of manipulation; on the use of telegraph codes; by the way of using the radio channel. Depending on the method and speed of transmission, radiotelegraph communications are divided into manual and automatic. In manual transmission, manipulation is carried out with a telegraph key using the MORSE code. The transmission speed (for auditory reception) is 60–100 characters per minute. In automatic transmission, the manipulation is carried out by electromechanical devices, and the reception is carried out with the help of printing machines. Transfer rate 900-1200 characters per minute. According to the method of using the radio channel, telegraph transmissions are divided into single-channel and multi-channel. By the method of manipulation, the most common telegraph signals include signals with amplitude shift keying (АТ - amplitude telegraph - A1), with frequency shift keying (ChT and DCHT - frequency telegraphy and dual frequency telegraphy - F1 and F6), with relative phase shift keying (OFT - phase telegraphy - F9). For the application of telegraph codes, telegraph systems with the MORSE code are used; start-stop systems with 5 and 6-digit codes and others. Telegraph signals are a sequence of rectangular pulses (messages) of the same or different duration. The smallest message in duration is called elementary. Basic parameters of telegraph signals: telegraphy speed (V); manipulation frequency (F); spectrum width (2D f). Telegraphing speed V equal to the number of chips transmitted per second, measured in baud. At a telegraphing rate of 1 baud, one elementary message is transmitted per second. Manipulation frequency F numerically equal to half the speed of telegraphy V and is measured in hertz: F = V / 2
. Amplitude-shift keyed telegraph signal has a spectrum (Fig. 2.2.1.1), which, in addition to the carrier frequency, contains an infinite set of frequency components located on either side of it, at intervals equal to the manipulation frequency F. three spectrum components located on either side of the carrier. Thus, the width of the spectrum of the amplitude-shift keyed CW RF signal is equal to 6F. The higher the keying frequency, the wider the spectrum of the HF CW signal. Rice. 2.2.1.1. Time and spectral representation of the AT signal At frequency shift keying the current in the antenna does not change in amplitude, but only the frequency changes in accordance with the change in the manipulating signal. The spectrum of the FT signal (DCF) (Fig. 2.2.1.2) is, as it were, a spectrum of two (four) independent amplitude-manipulated oscillations with their own carrier frequencies. The difference between the frequency of "pressing" and the frequency of "pressing" is called the frequency separation, it is denoted ∆f and can be in the range of 50 - 2000 Hz (most often 400 - 900 Hz). The width of the FT signal spectrum is 2∆f + 3F. Fig. 2.2.1.2. Time and Spectral Representation of the FT Signal To increase the throughput of a radio link, multichannel radiotelegraph systems are used. In them, on one carrier frequency of a radio transmitter, two or more telegraph programs can be transmitted simultaneously. A distinction is made between frequency division multiplexing, time division multiplexing and combined systems. The simplest two-channel system is the dual frequency telegraphy (DFC) system. Frequency-keyed signals in the DCT system are transmitted by changing the carrier frequency of the transmitter due to the simultaneous action of the signals of two telegraph sets on it. In this case, it is used that the signals of two devices operating simultaneously can have only four combinations of transmitted messages. With this method, at any moment of time, a signal of one frequency is emitted, corresponding to a certain combination of manipulated voltages. The receiving device has a decoder, with the help of which DC telegraph messages are generated through two channels. Frequency densification means that the frequencies of individual channels are located in different parts of the total frequency range and all channels are transmitted simultaneously. With time division of channels, a radio line is provided to each telegraph apparatus sequentially using distributors (Figure 2.2.1.3). Fig. 2.2.1.3. Multi-channel time division system For the transmission of radiotelephone messages, mainly amplitude-modulated and frequency-modulated high-frequency signals are used. LF modulating signal is a collection of a large number of signals of different frequencies located in a certain band. The bandwidth of a standard LF telephone signal is typically 0.3–3.4 kHz. 1 Classification of modulation types, basic characteristics of radio signals. To carry out radio communication, it is necessary to somehow change one of the parameters of the radio frequency oscillation, called the carrier, in accordance with the transmitted low-frequency signal. This is achieved by modulating the RF waveform. It is known that the harmonic oscillation characterized by three independent parameters: amplitude, frequency and phase. Accordingly, there are three main types of modulation: Amplitude, Frequency, Phase. Amplitude modulation (AM) is called this type of influence on the carrier wave, as a result of which its amplitude changes according to the law of the transmitted (modulating) signal. We assume that the modulating signal has the form of a harmonic oscillation with a frequency W much less than the frequency of the carrier wave w. As a result of modulation, the amplitude of the carrier oscillation voltage should change in proportion to the voltage of the modulating signal uW (Fig. 1): UAM = U + kUWcosWt = U + DUcosWt, (1) where U is the voltage amplitude of the carrier radio frequency oscillation; DU = kUW - amplitude increment. The equation of amplitude-modulated oscillations, in this case, takes the form UAM = UAM coswt = (U + DUcosWt) coswt = U (1 + cosWt) coswt. (2) The current iAM will change according to the same law during modulation. The value characterizing the ratio of the magnitude of the change in the amplitude of the oscillations DU to their amplitude in the absence of modulation U is called the modulation coefficient (depth) It follows from this that the maximum amplitude of oscillations is Umax = U + DU = U (1 + m) and the minimum amplitude is Umin = U (1-m). As it is easy to see from equation (2), in the simplest case, the modulated oscillations are the sum of three oscillations UAM = U (1+ mcosWt) coswt = Ucoswt U / 2 + cos (w - W) t U / 2 + cos (w + W) t. (4) The first term is the oscillations of the transmitter in the absence of modulation (silent mode). The second are side frequency oscillations. If modulation is carried out by a complex low-frequency signal with a spectrum from Fmin to Fmax, then the spectrum of the received AM signal has the form shown in Fig. The frequency band occupied by the AM signal is independent of m and is equal to Δfс = 2Fmax. (five) The occurrence of oscillations of side frequencies during modulation leads to the need to expand the bandwidth of the transmitter (and, accordingly, the receiver) circuits. She must be where Q is the quality factor of the circuits, Df - absolute detuning, Dfk - loop bandwidth. In fig. spectral components corresponding to the lower modulating frequencies (Fmin) have lower ordinates. This is due to the following circumstance. For most types of signals (for example, speech) entering the input of the transmitter, the amplitudes of the high-frequency components of the spectrum are small compared to the components of the low and medium frequencies. As for the noise at the detector input to the receiver, their spectral density is constant within the passband receiver. As a result, the modulation coefficient and signal-to-noise ratio at the input of the detector of the receiver for high frequencies of the modulating signal are small. To increase the signal-to-noise ratio, the high-frequency components of the baseband signal during transmission are emphasized by amplifying the high-frequency components by a greater number of times compared to the components of the low and middle frequencies, and when received before or after the detector, they are attenuated by the same amount. The attenuation of high-frequency components before the detector occurs almost always in the high-frequency resonant circuits of the receiver. It should be noted that artificial emphasis of the upper baseband frequencies is acceptable as long as it does not result in overmodulation (m> 1). Ministry of General and Professional Education of the Russian Federation USTU-UPI named after S.M. Kirov Theoretical foundations of radio engineering ANALYSIS OF RADIO SIGNALS AND CALCULATION OF CHARACTERISTICS OF OPTIMAL MATCHED FILTERS COURSE PROJECT EKATERINBURG 2001 Introduction Calculation of akf of a given signal Conclusion List of symbols Bibliographic list Information has always been appreciated, and with the development of mankind, information becomes more and more. Information flows have turned into huge rivers. In this regard, several problems arose in the transmission of information. Information has always been valued for its reliability and completeness, therefore, a struggle is being waged to transmit it without loss or distortion. With one more problem when choosing the optimal signal. All this is transferred to radio engineering, where receiving transmitting and processing these signals are being developed. The speed and complexity of the signals transmitted is constantly complicated by the equipment. To obtain and consolidate knowledge on the processing of the simplest signals in the training course there is a practical task. In this term paper a rectangular coherent burst is considered, consisting of N trapezoidal (the duration of the top is equal to one third of the duration of the base) radio pulses, where: a) carrier frequency, 1.11 MHz b) pulse duration (base duration), 15μs c) repetition rate, 11.2 kHz d) the number of pulses in a packet, 9 For a given type of signal, it is necessary to produce (bring): ACF calculation Calculation of the amplitude spectrum and energy spectrum Calculating the impulse response of a matched filter Spectral density is the coefficient of proportionality between the length of a small frequency interval D f and the corresponding complex amplitude of the harmonic signal D A with the frequency f 0. Spectral representation of signals opens a direct path to the analysis of the passage of signals through a wide class of radio circuits, devices and systems. The energy spectrum is useful for obtaining various engineering estimates that establish the actual spectrum width of a given signal. To quantify the degree of signal difference U (t) and its time-shifted copy U (t-
t) it is customary to introduce ACF. Let us fix an arbitrary moment in time and try to choose the function so that the value reaches the maximum possible value. If such a function really exists, then the corresponding line filter is called a matched filter. Course work on the final part of the subject "Theory of radio-technical signals and circuits" covers sections of the course devoted to the basics of signal theory and their optimal linear filtering. The objectives of the work are: study of the temporal and spectral characteristics of pulsed radio signals used in radar, radio navigation, radio telemetry and related fields; acquisition of skills in calculating and analyzing the correlation and spectral characteristics of deterministic signals (autocorrelation functions, amplitude spectra and energy spectra). In the course work for a given type of signal, you must make: Calculation of the ACF. Calculation of the spectrum of amplitudes and energy spectrum. Impulse response of the matched filter. In this course work, a rectangular coherent bundle of trapezoidal radio pulses is considered. Signal parameters: carrier frequency (radio frequency), 1.11 MHz pulse duration, (base duration) 15 μs repetition rate, 11.2 kHz number of pulses in a burst, 9 Autocorrelation function (ACF) of the signal U (t) serves to quantify the degree of signal difference U (t) and its time-shifted copy parity property: Those. K U ( t) =K U ( -
t). at any value of the time shift t ACF module does not exceed signal energy: ½ K U ( t) ½£ K U ( 0
), which follows from the Cauchy - Bunyakovsky inequality. So, the ACF appears to be a symmetric curve with a central maximum, which is always positive, and in our case, the ACF also has an oscillatory character. It should be noted that the ACF is related to the energy spectrum of the signal: It is often more convenient to first obtain the autocorrelation function, and then, using the Fourier transform, find the energy spectrum of the signal. Energy spectrum - is a dependence of ½ G
(w) ½ of the frequency. Filters matched to the signal have the following properties: The signal at the output of the matched filter and the correlation function of the output noise have the form of the autocorrelation function of the useful input signal. Among all line filters, the matched filter gives the maximum peak-to-rms noise ratio at the output. Fig. 1. Rectangular coherent trapezoidal radio burst In our case, the signal is a rectangular bundle of trapezoidal (the top duration is equal to one third of the base duration) radio pulses ( see fig 1) in which the number of pulses is N = 9, and the pulse duration is T i = 15 μs. Fig. 2. Shift of the signal envelope copy For the magnitude of the shift T belonging to the interval from zero to one third of the pulse duration, it is necessary to solve the integral: Solving this integral, we obtain an expression for the main lobe of the ACF of a given shift of the signal envelope copy: For T belonging to the interval from one third to two thirds of the pulse duration, we obtain the following integral: Solving it, we get: For T, which belongs to the interval from two-thirds of the pulse duration to the pulse duration, the integral has the form: Therefore, as a result of the solution, we have: Taking into account the symmetry (parity) property of the ACF (see the introduction) and the relationship between the ACF of a radio signal and the ACF of its complex envelope: in which, the incoming functions are of the form: Thus, on Figure 3 depicts the main lobe of the ACF radio pulse and its envelope, i.e. when, as a result of the shift of the signal copy, when all 9 pulses of the burst are involved, i.e. N = 9. It can be seen that the ACF of the radio pulse has an oscillatory character, but a maximum is obligatory in the center. With a further shift, the number of intersecting pulses of the signal and its copy will decrease by one, and, consequently, the amplitude after each repetition period T ip = 89.286 μs. Therefore, the final ACF will look like Figure 4 ( 16 petals differing from the main one only in amplitudes) considering that ,
that in this figure T = T ip
.: Rice. 3. ACF of the main lobe of the radio pulse and its envelope Rice. 4. ACF of a Rectangular Coherent Trapezoidal Radio Pulse Bundle Rice. 5. Envelope of a burst of radio pulses. To calculate the spectral density, we will use, as in the calculation of the ACF, the radio signal envelope functions ( see fig. 2), which look like: and the Fourier transform to obtain spectral functions, which, taking into account the limits of integration for the n-th pulse, will be calculated by the formulas: for the envelope of the radio pulse and: for a radio pulse, respectively. The graph of this function is presented on ( fig. 5). in the figure, for clarity, a different frequency range is considered Rice. 6. Spectral density of the radio signal envelope. As expected, the main maximum is located in the center, i.e. at frequency w = 0. The energy spectrum is equal to the square of the spectral density and therefore the spectrum graph looks like on ( Figure 6) those. very similar to the spectral density plot: Rice. 7. Energy spectrum of the radio signal envelope. The form of the spectral density for the radio signal will be different, since instead of one maximum at w = 0, two maxima will be observed at w = ± wо, i.e. the spectrum of the video pulse (the envelope of the radio signal) is transferred to the high-frequency region with a halving of the absolute value of the maxima ( see fig. 7). The form of the energy spectrum of the radio signal will also be very similar to the form of the spectral density of the radio signal, i.e. the spectrum will also be transferred to the high-frequency region and two maxima will also be observed ( see fig. 8). Rice. 8. Spectral density of a burst of radio pulses. As you know, along with the useful signal, noise is often present and therefore, with a weak useful signal, it is sometimes difficult to determine whether there is a useful signal or not. To receive a signal shifted in time against the background of white Gaussian noise (white Gaussian noise "BGS" has a uniform distribution density) n (t) i.e. y (t)= + n (t), the likelihood ratio when receiving a signal of a known shape has the form: where No.- spectral density of noise. Therefore, we come to the conclusion that the optimal processing of the received data is the essence of the correlation integral The resulting function is the essential operation that should be performed on the observed signal in order to make a decision on the presence or absence of a useful signal in the optimal (from the standpoint of the criterion of the minimum average risk) way. There is no doubt that this operation can be implemented with a line filter. Indeed, the signal at the output of the impulse response filter g (t) looks like: As you can see, when the condition g (r-x) = K
× S (r-
t) these expressions are equivalent and then after replacing t = r-x we get: where TO- constant, and to- fixed time at which the output signal is observed. A filter with such an impulse response g (t) ( see above) is called consistent. In order to determine the impulse response, you need a signal S (t) shift to to to the left, i.e. we get the function S (to + t), and the function S (to - t) get by mirroring signal relative to the coordinate axis, i.e. impulse response of the matched filter will be equal to the input signal, and thus the maximum signal-to-noise ratio is obtained at the output of the matched filter. Rice. 10. A link for the formation of a radio pulse with a given envelope. The signal of the envelope of the radio signal (in our case, a trapezoid) is fed to the input of the link of the formation of a radio pulse with a given envelope (see Fig. 9). A harmonic signal with a carrier frequency wо (in our case, 1.11 MHz) is formed in the oscillatory link, therefore, at the output of this link, we have a harmonic signal with a frequency wо. From the output of the oscillatory link, the signal is fed to the adder and to the link of the signal delay line at Ti (in our case, Ti = 15 μs), and from the output of the delay link, the signal is fed to the phase shifter (it is needed so that after the end of the pulse there is no radio signal at the output of the adder) ... After the phase shifter, the signal is also fed to the adder. At the output of the adder, finally, we have trapezoidal radio pulses with a radio frequency wо, i.e. signal g (t). Rice. 11. A link in the formation of a coherent pack. The signal g (t), which is a trapezoidal radio pulse (or a sequence of trapezoidal radio pulses), is fed to the input of the coherent burst formation link. Then the signal goes to the adder and to the delay unit, in which the input signal is delayed for the pulse repetition period in the packet Tip multiplied by the pulse number minus one, i.e. ( N-1), and from the output of the delay again to the adder .
Thus, at the output of the link for the formation of a coherent packet (i.e., at the output of the adder), we have a rectangular coherent packet of trapezoidal radio pulses, which was required to be implemented. In the course of the work, the corresponding calculations were carried out and graphs were built from them, one can judge the complexity of signal processing. For simplicity, the mathematical calculation was carried out using the MathCAD 7.0 and MathCAD 8.0 packages. this work is a necessary part of the curriculum so that students have an understanding of the features of the use of various pulsed radio signals in radar, radio navigation and radio telemetry, and can also design an optimal filter, thereby making their modest contribution to the "struggle" for information. wо
- radio frequency; w -
frequency T, (
t) -
time shifting; Ti
- the duration of the radio pulse; Tip
- the repetition period of radio pulses in a packet; N
- the number of radio pulses in the bundle; t
- time; 1. Baskakov S.I. "Radio circuits and signals: Textbook for universities on the special." Radio engineering ". - 2nd ed., Rev. and add. - M .: Higher. shk., 1988 - 448 p .: ill. 2. "ANALYSIS OF RADIO SIGNALS AND CALCULATION OF THE CHARACTERISTICS OF OPTIMAL MATCHED FILTERS: Methodological instructions for the course work on the course" Theory of radio signals and circuits "/ Kibernichenko V.G., Doroinsky L.G., Sverdlovsk: UPI 1992.40 p. 3. "Amplifying devices": Textbook: manual for universities. - M .: Radio and communication, 1989. - 400 p .: ill. 4. Buckingham M. "Noises in electronic devices and systems" / Per. from English - M .: Mir, 1986 Lecture number 5
T
ema number 2:
Transmission of DISCRETE messages Lecture topic:
DIGITAL RADIO SIGNALS AND THEIR For data transmission systems, the requirement of the reliability of the transmitted information is most important. In this case, logical control of the processes of transmitting and receiving information is necessary. This becomes possible when digital signals are used to transfer information in a formalized form. Such signals make it possible to unify the element base and use correction codes that provide a significant increase in noise immunity. Currently, for the transmission of discrete messages (data), so-called digital communication channels are used, as a rule. The carriers of messages in digital communication channels are digital signals or radio signals, if radio communication lines are used. Informational parameters in such signals are amplitude, frequency and phase. Among the accompanying parameters, a special place is occupied by the phase of the harmonic oscillation. If the phase of the harmonic oscillation on the receiving side is precisely known and this is used during reception, then such a communication channel is considered coherent... IN incoherent the communication channel, the phase of the harmonic oscillation on the receiving side is not known and it is considered that it is uniformly distributed in the interval from 0 to 2
.
The process of converting discrete messages into digital signals during transmission and digital signals into discrete messages during reception is explained in Figure 2.1. Figure 2.1. The process of converting discrete messages in transit It is taken into account here that the basic operations of converting a discrete message into a digital radio signal and vice versa correspond to the generalized structural diagram the system of transmission of discrete messages considered at the last lecture (shown in Fig. 3). Let's consider the main types of digital radio signals. Amplitude Shift Keying (AMn). Analytical expression of AMn signal for any moment of time t looks like: s AMn (t,
)= A 0
(t)
cos(
t
)
,
(2.1) where A 0
,
and
- amplitude, cyclic carrier frequency and initial phase of AMn radio signal,
(t) - primary digital signal (discrete information parameter). Another notation is often used: s 1
(t)
=
0
at
=
0,
s 2
(t)
= A 0
cos(
t
) at
=
1,
0
t
T,(2.2) which is used in the analysis of AMn signals over a time interval equal to one clock interval T... As s(t)
=
0 at
=
0, then the AMn signal is often referred to as a passive pause signal. The implementation of the AMn radio signal is shown in Fig. 2.2. Figure 2.2. Implementation of AMn radio signal The spectral density of the AMn signal has both a continuous and a discrete component at the frequency of the carrier wave
... The continuous component is the spectral density of the transmitted digital signal
(t) transferred to the carrier frequency region. It should be noted that the discrete component of the spectral density occurs only at a constant initial phase of the signal
... In practice, as a rule, this condition is not met, since as a result of various destabilizing factors, the initial phase of the signal randomly changes in time, i.e. is a random process
(t) and is uniformly distributed in the interval [-
;
]. The presence of such phase fluctuations leads to “blurring” of the discrete component. This feature is typical for other types of manipulation. Figure 2.3 shows the spectral density of the AMn radio signal. Figure 2.3. Spectral density of AMn radio signal with random, uniformly distributed in the interval [-
;
] the initial phase
The average power of the AMn radio signal is For the formation of an AMn radio signal, a device is usually used that provides a change in the amplitude of the radio signal according to the law of the transmitted primary digital signal
(t) (for example, an amplitude modulator).
abstract
Introduction
(0.1)
and at t= 0 ACF becomes equal to the signal energy. ACF has the simplest properties:
; (0.2)
where ½ G
(w) ½ the square of the modulus of the spectral density. Therefore, it is possible to estimate the correlation properties of signals based on the distribution of their energy over the spectrum. The wider the signal bandwidth, the narrower the main lobe of the autocorrelation function and the more perfect the signal from the point of view of the possibility accurate measurement the moment it began.
Calculation of akf of a given signal
S3 (t)
S2 (t)
The repetition period of pulses in the burst T ip »89.286 μs. Therefore, the duty cycle q = T ip / T i = 5.952. To calculate the ACF, we use the formula ( 0.1)
and a graphical representation of a time-shifted copy of the signal using a single trapezoidal pulse (envelope) as an example. To do this, turn to Figure 2. To calculate the main lobe of the ACF of the signal envelope (trapezoid), consider three intervals: S1 (t)
we have functions for the main lobe of the ACF of the envelope ko (T) of the radio pulse and the ACF of the radio pulse Ks (T):
Calculation of spectral density and energy spectrum
Impulse response calculation and recommendations for constructing a matched filter
With our input signal, to build such a filter, you must first create a link for the formation of one trapezoidal pulse, the circuit of which is shown in ( fig. 9).
Since we need to obtain a coherent pack of 9 trapezoidal video pulses, the signal g (t) must be fed to the link for forming such a pack, a circuit that looks like in (Fig. 10):
Conclusion
List of symbols
Bibliographic list
Features Introduction
2.1. Understanding the Transmission of Discrete Messages
2.2. Characteristics of digital radio signals
2.2.1. Amplitude Shift Keying (AMN) RF Signals
... This power is equally divided between the continuous and discrete components of the spectral density. Consequently, in the AMn radio signal, the continuous component due to the transmission of useful information accounts for only half of the power emitted by the transmitter.
