Ministry of General and vocational education 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
YEKATERINBURG 2001
Introduction
Calculation of the acf of a given signal
Conclusion
List of symbols
Bibliographic list
abstract
Information has always been valued, and with the development of mankind, information is becoming more and more. Information flows have turned into huge rivers.
As a result, several communication problems arose.
Information has always been valued for its reliability and completeness, so there is a struggle to transmit it without loss and distortion. With one more problem at a choice of an optimum signal.
All this is transferred to radio engineering, where receiving, transmitting and processing these signals are developed. The speed and complexity of the transmitted signals is constantly becoming more complex 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 packet is considered, consisting of N trapezoidal (top duration is equal to one third of the base duration) radio pulses, where:
a) carrier frequency, 1.11 MHz
b) pulse duration (base duration), 15 μs
c) repetition rate, 11.2 kHz
d) number of impulses in a pack,9
For a given signal type, it is necessary to produce (bring):
ACF calculation
Calculation of the amplitude spectrum and energy spectrum
Calculation of impulse response, matched filter
Spectral density - there is a 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 frequency f0.
The spectral representation of signals opens up 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 width of the spectrum of a particular signal. To quantify the degree of signal difference U(t) and its time-shifted copy U(t- t) accepted to introduce ACF.
We fix an arbitrary moment of time and try to choose the function in such a way that the value reaches the maximum possible value. If such a function really exists, then the corresponding linear filter is called a matched filter.
Introduction
Coursework on the final part of the subject "Theory radio signals and circuits" covers sections of the course devoted to the fundamentals of signal theory and their optimal linear filtering.
The objectives of the work are:
study of time and spectral characteristics pulsed radio signals used in radar, radio navigation, radio telemetry and related fields;
acquisition of skills in calculation and analysis of 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:
ACF calculation.
Calculation of the amplitude spectrum and energy spectrum.
Impulse response of a matched filter.
This course work considers a rectangular coherent pack of trapezoidal radio pulses.
Signal parameters:
carrier frequency (radio fill frequency), 1.11 MHz
pulse duration, (base duration) 15 µs
repetition rate, 11.2 kHz
number of impulses in a pack, 9
Autocorrelation function (ACF) of a signal U(t) serves to quantify the degree of signal difference U(t) and its time-shifted copy 
(0.1)
and at t= 0 ACF becomes equal to the signal energy. ACF has the simplest properties:
parity property:
Those. K U( t) =K U( - t).
for any value of the time shift t ACF modulus does not exceed signal energy: ½ K U( t) ½£ K U( 0 ), which follows from the Cauchy-Bunyakovsky inequality.
So, the ACF is represented by a symmetrical 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: 
; (0.2)
where ½ G
(w) ½ square modulus of spectral density. Therefore, it is possible to evaluate 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 in terms of the possibility of accurately measuring the moment of its onset.
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 ½ G (w) ½ of frequency.
Filters matched with 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 linear filters the matched filter gives the output the maximum ratio of the peak value of the signal to the RMS value of the noise.
Calculation of the acf of a given signal
Fig.1. Rectangular coherent burst of trapezoidal radio pulses
In our case, the signal is a rectangular packet of trapezoidal (top duration equal to one third of the base duration) radio pulses ( see fig 1) in which the number of pulses N=9, and the pulse duration T i =15 μs.
Fig.2. Shift copy of the signal envelope
|
|
|
For the shift value 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 a copy of the signal envelope:
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 property (parity) of the ACF (see introduction) and the relation connecting the ACF of the radio signal and the ACF of its complex envelope: 
we have the 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):
in which the incoming functions have the form:
Thus, on figure 3 the main lobe of the ACF of the radio pulse and its envelope is shown, i.e. when as a result of a shift of a copy of the signal, 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 the maximum is necessarily at 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, finally the ACF will look like figure 4 ( 16 petals, differing from the main one only in amplitudes) given that , that in this figure T=T ip .:
Rice. 3. ACF of the main lobe of a radio pulse and its envelope
Rice. 4. ACF of a rectangular coherent burst of trapezoidal radio pulses
Rice. 5. Envelope of a burst of radio pulses.
Spectral Density and Energy Spectrum Calculation
To calculate the spectral density, we will use, as in ACF calculations, the functions of the radio signal envelope ( see fig.2), which look like:
and Fourier transform to obtain spectral functions, which, taking into account the limits of integration for the nth pulse, will be calculated by the formulas:
for the radio pulse envelope and:
for the radio pulse, respectively.
The graph of this function is shown in ( 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; at frequency w =0.
The energy spectrum is equal to the square of the spectral density and therefore the spectrum graph looks like ( pic 6) those. very similar to a 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 = ±wo, i.e. the spectrum of the video pulse (envelope of the radio signal) is transferred to the region high frequencies 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.
Calculation of the impulse response and recommendations for building a matched filter
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 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 optimally (from the standpoint of the average risk minimum criterion) make a decision about the presence or absence of a useful signal.
There is no doubt that this operation can be implemented by a linear filter.
Indeed, the signal at the output of the impulse response filter g(t) looks like:
As can be seen, when the condition g(r-x) = K ×S (r- t) these expressions are equivalent and then after the replacement t = r-x we get:
where To is constant, and to is the fixed time at which the output signal is observed.
A filter with this impulse response g(t)( see above) is called consistent.
In order to determine the impulse response, a signal is needed S(t) shift to to to the left, i.e. get the function S (to + t), and the function S (to - t) obtained by mirroring the signal relative to the coordinate axis, i.e. impulse response of the matched filter will be equal to the input signal, and at the same time we obtain the maximum signal-to-noise ratio at the output of the 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 shown in ( Fig.9).
Rice. 10. Link for the formation of a radio pulse with a given envelope.
At the input of the radio pulse formation link with a given envelope (see Fig. 9), the signal of the radio signal envelope is applied (in our case, a trapezoid).
In the oscillatory link, a harmonic signal with a carrier frequency wо is formed (in our case, 1.11 MHz), 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 filling frequency wо, i.e. signal g(t).
 |
Since we need to get a coherent pack of 9 trapezoidal video pulses, it is necessary to send a signal g (t) to the link for forming such a pack with a circuit that looks like in (Fig. 10):
Rice. 11. Link for the formation of a coherent packet.
The signal g (t) is fed to the input of the coherent burst formation link, which is a trapezoidal radio pulse (or a sequence of trapezoidal radio pulses).
Next, the signal goes to the adder and to the delay block, in which the input signal is delayed for the period of the pulses in the burst tip multiplied by the pulse number minus one, i.e. ( N-1), and from the exit side of the delay again to the adder .
Thus, at the output of the coherent burst formation link (i.e., at the output of the adder), we have a rectangular coherent burst of trapezoidal radio pulses, which was required to be implemented.
Conclusion
In the course of the work, the corresponding calculations were carried out and graphs were built on them, one can judge the complexity of signal processing. To simplify the mathematical calculation, the packages MathCAD 7.0 and MathCAD 8.0 were carried out. this work is a necessary part training course so that students have an idea about the features of the use of various pulsed radio signals in radar, radio navigation and radio telemetry, and can also design the optimal filter, thereby making their modest contribution to the “struggle” for information.
List of symbols
wo - frequency of radio filling;
w- frequency
T, ( t)- time shifting;
Ti - the duration of the radio pulse;
tip - the period of repetition of radio pulses in a pack;
N - number of radio pulses in a pack;
t - time;
Bibliographic list
1. Baskakov S.I. "Radio circuits and signals: A textbook for universities on special "Radio engineering"". - 2nd ed., revised. and additional - M.: Higher. school, 1988 - 448 p.: ill.
2. "ANALYSIS OF RADIO SIGNALS AND CALCULATION OF CHARACTERISTICS OF OPTIMAL MATCHED FILTERS: Guidelines to the term paper on the course "Theory of radio signals and circuits" "/ Kibernichenko V.G., Doroinsky L.G., Sverdlovsk: UPI 1992.40 p.
3. "Amplifying devices": Textbook: a guide for universities. - M.: Radio and communication, 1989. - 400 p.: ill.
4. Buckingham M. "Noises in electronic appliances and systems "/ Translated from English - M .: Mir, 1986
The main parameters of the radio signal. Modulation
§ Signal strength
§ Specific signal energy
§ Signal duration T determines the time interval during which the signal exists (different from zero);
§ Dynamic range is the ratio of the highest instantaneous signal power to the lowest:
§ Width of the signal spectrum F - the frequency band within which the main energy of the signal is concentrated;
§ The signal base is the product of the signal duration and the width of its spectrum. It should be noted that there is an inverse relationship between the spectrum width and signal duration: the shorter the spectrum, the longer the signal duration. Thus, the value of the base remains practically unchanged;
§ The signal-to-noise ratio is equal to the ratio of the useful signal power to the noise power (S/N or SNR);
§ The amount of transmitted information characterizes throughput communication channel needed to transmit the signal. It is defined as the product of the width of the signal spectrum and its duration and dynamic range
§ Energy efficiency (potential noise immunity) characterizes the reliability of the transmitted data when the signal is exposed to additive white Gaussian noise, provided that the symbol sequence is restored by an ideal demodulator. It is determined by the minimum signal-to-noise ratio (E b /N 0), which is necessary for data transmission through the channel with an error probability not exceeding a given one. Energy efficiency defines the minimum transmitter power required for acceptable performance. A characteristic of the modulation method is the energy efficiency curve - the dependence of the error probability of an ideal demodulator on the signal-to-noise ratio (E b /N 0).
§ Spectral efficiency - the ratio of data transfer rate to the used bandwidth of the radio channel.
- AMPS: 0.83
- NMT: 0.46
- GSM: 1.35
§ Stability to the effects of the transmission channel characterizes the reliability of the transmitted data when the signal is exposed to specific distortions: fading due to multipath propagation, bandwidth limitation, noise concentrated in frequency or time, the Doppler effect, etc.
§ Requirements for the linearity of amplifiers. To amplify signals with some types of modulation, non-linear class C amplifiers can be used, which can significantly reduce the power consumption of the transmitter, while the level of out-of-band radiation does not exceed the permissible limits. This factor is especially important for mobile communication systems.
Modulation(lat. modulatio - regularity, rhythm) - the process of changing one or more parameters of a high-frequency carrier oscillation according to the law of a low-frequency information signal (message).
The transmitted information is embedded in the control (modulating) signal, and the role of the information carrier is performed by a high-frequency oscillation called the carrier. Modulation, therefore, is the process of "landing" an information wave on a known carrier.
As a result of modulation, the spectrum of the low-frequency control signal is transferred to the high-frequency region. This allows you to set up the operation of all transceivers at different frequencies when organizing broadcasting so that they do not “interfere” with each other.
Oscillations of various shapes (rectangular, triangular, etc.) can be used as a carrier, but harmonic oscillations are most often used. Depending on which of the parameters of the carrier oscillation changes, the type of modulation is distinguished (amplitude, frequency, phase, etc.). Modulation discrete signal called digital modulation or keying.
Radio signals are called electromagnetic waves or electrical high frequency vibrations that encapsulate the transmitted message. To generate a signal, the parameters of high-frequency oscillations are changed (modulated) using control signals, which are voltages that change according to a given law. Harmonic high-frequency oscillations are usually used as modulated ones:
where w 0 \u003d 2π f 0 – high carrier frequency;
U 0 is the amplitude of high-frequency oscillations.
The simplest and most commonly used control signals are harmonic oscillation
where Ω is a low frequency, much less than w 0 ; ψ is the initial phase; U m - amplitude, as well as rectangular pulse signals, which are characterized by the fact that the voltage value U ex ( t)=U during the time intervals τ and, called the duration of the pulses, and is equal to zero during the interval between pulses (Fig. 1.13). Value T and is called the pulse repetition period; F and =1/ T and is the frequency of their repetition. Pulse Period Ratio T and to the duration τ and is called the duty cycle Q impulse process: Q=T and /τ and.
Fig.1.13. Rectangular pulse train
Depending on which parameter of the high-frequency oscillation is changed (modulated) with the help of a control signal, amplitude, frequency and phase modulation is distinguished.
With amplitude modulation (AM) of high-frequency oscillations by a low-frequency sinusoidal voltage with a frequency of Ω mod, a signal is formed, the amplitude of which changes with 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 factor expressed as a percentage (i.e. m×100%) is called the amplitude modulation depth.
Rice. 1.14. Amplitude modulated radio signal
With phase modulation (PM) of a high-frequency oscillation by 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 - coefficient of proportionality. A high-frequency signal with phase modulation according to a sinusoidal law has the form
At frequency modulation(FM) control signal changes the frequency of 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 \u003d w 0 + k World Cup U m sinW mod t, where k FM - coefficient of proportionality. The greatest change in frequency w with respect to its average value w 0 equal to Δw М = k World Cup U m, is called the frequency deviation. The frequency modulated signal can be written as follows:
The value equal to the ratio of the frequency deviation to the modulation frequency (Δw m / W mod = m FM) is called the frequency modulation ratio.
Figure 1.14 shows high-frequency signals for AM, PM and FM. In all three cases, the same modulating voltage is used. U mod, changing according to the symmetrical 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 (Fig. 1.15, a).
With AM, the signal frequency remains constant (w 0), and the amplitude changes according to the law of the modulating voltage U AM ( t) = U 0 k Maud t(Fig. 1.15, b).
The frequency modulated signal (Fig. 1.15, c) is characterized by a constant amplitude and a smooth change in frequency: w( t) = w0 + k World Cup t. In the time span from t=0 to t 1 the oscillation frequency increases from the value w 0 to the value w 0 + k World Cup t 1 , and on the segment from t 1 to t 2 the frequency decreases again to the value w 0 .
The phase-modulated signal (Fig. 1.15, d) has a constant amplitude and frequency hopping. Let's explain this analytically. With FM under the influence of modulating voltage
Fig.1.15. Comparative view of modulated oscillations with AM, FM and FM:
a - modulating voltage; b – amplitude modulated signal;
c – frequency-modulated signal; d - phase modulated signal
signal phase receives an additional increment Δy= k FM t, therefore, a high-frequency signal with phase modulation according to the sawtooth law has the form
Thus, on the interval 0 t 1 the frequency is w 1 >w 0 , and on the segment t 1 t 2 it is equal to w 2 When transmitting a sequence of pulses, for example, a binary digital code (Fig. 1.16, a), AM, FM and FM can also be used. This type of modulation is called keying or telegraphy (AT, CT and FT). Fig.1.16. Comparative view of manipulated oscillations in 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 the rest of the time (Fig. 1.16, b). With frequency telegraphy, a high-frequency signal is formed with a constant amplitude and a frequency that takes two possible values (Fig. 1.16, c). With phase telegraphy, a high-frequency signal is formed with a constant amplitude and frequency, the phase of which changes by 180 ° according to the law of the modulating signal (Fig. 1.16, d). Lecture #5
T
theme #2:
Transmission of DISCRETE messages Lecture topic:
DIGITAL RADIO SIGNALS AND THEIR For data transmission systems, the requirement for the reliability of the transmitted information is most important. This requires logical control of the processes of transmission and reception of information. This becomes possible when digital signals are used to transmit 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), as a rule, the so-called digital communication channels are used. Message carriers in digital communication channels are digital signals or radio signals if radio communication lines are used. The information parameters in such signals are amplitude, frequency and phase. Among the accompanying parameters, the phase of the harmonic oscillation occupies a special place. If the phase of the harmonic oscillation on the receiving side is precisely known and this is used when receiving, then such a communication channel is considered coherent. AT incoherent In the communication channel, the phase of the harmonic oscillation on the receiving side is not known and it is assumed that it is distributed according to a uniform law in the range from 0 to 2
.
The process of converting discrete messages into digital signals during transmission and digital signals into discrete messages during reception is illustrated in Fig. 2.1. Fig.2.1. The process of converting discrete messages during their transmission Here it is taken into account that the main operations for converting a discrete message into a digital radio signal and vice versa correspond to the generalized block diagram of the discrete message transmission system discussed in the last lecture (shown in Fig. 3). Consider the main types of digital radio signals. Amplitude shift keying (AMn). Analytical expression of the 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 the AMn radio signal,
(t) – primary digital signal (discrete information parameter). Another form of writing 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 in a time interval equal to one clock interval T. Because s(t)
=
0 at
=
0, then the AMn signal is often referred to as a signal with a passive pause. The implementation of the AMn radio signal is shown in Fig. 2.2. Fig.2.2. Implementation of the AM radio signal The spectral density of the AMn signal has both a continuous and a discrete component at the carrier frequency
. 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 takes place 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 also characteristic of other types of manipulation. Figure 2.3 shows the spectral density of the AMn radio signal. Fig.2.3. Spectral density of the AMn radio signal with a random, uniform distributed in the interval [-
;
] initial phase
The average power of the AM radio signal is equal to To form the AMn radio signal, a device is usually used that provides a change in the amplitude level of the radio signal according to the law of the transmitted primary digital signal
(t) (for example, an amplitude modulator). Amplitude modulation (AM) is the simplest and most common method in radio engineering of putting information into high-frequency oscillations. With AM, the envelope of the amplitudes of the carrier oscillation changes according to a law that coincides with the law of change in the transmitted message, while the frequency and initial phase of the oscillation are maintained unchanged. Therefore, for an amplitude-modulated radio signal, the general expression (3.1) can be replaced by the following: The nature of the envelope A(t) is determined by the type of the transmitted message. With continuous communication (Fig. 3.1, a), the modulated oscillation takes on the form shown in Fig. 3.1b. The envelope A(t) coincides in form with the modulating function, i.e. with the transmitted message s (t). Figure 3.1, b is built on the assumption that the constant component of the function s(t) is equal to zero (otherwise, the amplitude of the carrier oscillation during modulation may not coincide with the amplitude of the unmodulated oscillation). The largest change A(t) "down" cannot be greater than . The change "up" can, in principle, be greater. The main parameter of the amplitude-modulated oscillation is the modulation coefficient. Rice. 3.1. Modulating function (a) and amplitude-modulated oscillation (b) The definition of this concept is especially clear for tone modulation, when the modulating function is a harmonic oscillation: In this case, the envelope of the modulated oscillation can be represented as where is the modulation frequency; - the initial phase of the envelope; - coefficient of proportionality; - the amplitude of the envelope change (Fig. 3.2). Rice. 3.2. An oscillation modulated in amplitude by a harmonic function Rice. 3.3. Oscillation modulated by the amplitude of the pulse train Attitude is called the modulation factor. Thus, the instantaneous value of the modulated oscillation With undistorted modulation, the oscillation amplitude varies from minimum to maximum. In accordance with the change in amplitude, the power of the modulated oscillation averaged over the period of high frequency also changes. The peaks of the envelope correspond to a power that is 14 times greater than the power of the carrier wave. The average power over the modulation period is proportional to the mean square of the amplitude A(t): This power exceeds the power of the carrier wave by only a factor of 1. Thus, at 100% modulation (M = 1), the peak power is equal to and the average power (the power of the carrier wave is denoted by). It can be seen from this that the increase in the oscillation power due to modulation, which basically determines the conditions for isolating a message upon reception, does not exceed half the power of the carrier oscillation even at the limiting modulation depth. When transmitting discrete messages, which are an alternation of pulses and pauses (Fig. 3.3, a), the modulated oscillation has the form of a sequence of radio pulses shown in Fig. 3.3b. This means that the phases of high-frequency filling in each of the pulses are the same as when they are "cut" from one continuous harmonic oscillation. Only under this condition, shown in Fig. 3.3, b, the sequence of radio pulses can be interpreted as an oscillation modulated only in amplitude. If the phase changes from pulse to pulse, then we should speak of mixed amplitude-angle modulation.Features Introduction
2.1. Understanding Discrete Messaging
2.2. Characteristics of digital radio signals
2.2.1. Amplitude-shift keyed radio signals (aMn)
. This power is equally distributed between the continuous and discrete components of the spectral density. Consequently, in the AMn radio signal, the share of the continuous component due to the transmission of useful information accounts for only half of the power emitted by the transmitter.
Loading...