View signals: analog, digital, discrete. Form signals

per types (types) of signals are seen like this:

1. analog
2. digital
3. discrete

analog signal

analog signalє natural. It can be fixed for additional different types of sensors. For example, sensors of the middle (pressure, moisture) or mechanical sensors (acceleration, speed). Analog signals in mathematics, they are described by non-interrupted functions. The electrical voltage is described with the help of a straight line, tobto. є analogous.

digital signal

digital signal є piece, tobto. їх it is possible to take away only by way of transformation of the analog electrical signal.

The process of sequential transformation of an uninterrupted analog signal is called sampling. Discretization has two types:

1. by the hour
2. by amplitude

Discretization by the hour is called the sampling operation. And discretization for signal amplitude - quantization for equal.

over important digital signalsє light chi electric impulses. The digital signal vikoristovuyut the entire qiu frequency (smooth bandwidth). The whole signal is still filled with analog, only after the transformation is given numerical authority. І up to the new one can zastosovuvat numerical methods and power.

Discrete signal

Discrete signal– the same transformations of the analog signal, only in neobov'yazykovo quantizations per equal.

All main information about types (types) of signals.

Lecture 1

The main types of signals and their mathematical description.

Main types of signals: analog, discrete, digital.

analog- the same signal, without interruption at the hour and camp (Fig. 1a). The signal is described by a non-interruptible (or shmatkovo-non-interruptible) function X(t). If so, the argument and the function itself can accept whether the values ​​of such intervals are:

t" ≤ t ≤ t"" , x" ≤ x ≤ x"".

discrete- the same signal, discrete at the hour and without interruption by the camp (Fig. 1b). Be described by a lattice function X(n* T), de n- Number of the contact (1,2,3, ...). interval T name the discretization period, and wrap the value f q=1/ T- sampling rate. Gradual function is assigned only at the moment and hourn * T i may have less time take any value from the current interval x" ≤ x ≤ x"". The value of the lattice function, depending on the signal itself at the moment and hour n* T, Called Vіdlіkami. (A discrete signal can be both verbal and complex).

Digital- tse signal, discrete like at the hour, i camp (Fig. 1c). Signals of this type are self-described by lattice functions X c( n* T); x" ≤ x ≤ x"". Digital values ​​are called quantization equals, and other functions are called quantization.

When analyzing discrete signals, manually adjust the normalized hour
, otherwise, tobto. number for a discrete signal can be interpreted as a standard hour. When moving to the normalized hour, the discrete signal can be considered as a function of the integral change n. Tobto gave X(n) equally X(n· T).

Frequency normalization.

According to the Kotelnikov theorem, the maximum frequency of the analog signal f I'm not guilty buti more f e 2. Therefore, all discrete signals can be viewed in the range. When you ask for understanding normalized frequency

or

and see the discrete signal f in the region

or

Stopping the normalized frequency allows to maintain the frequency characteristics of discrete systems and the spectrum of discrete signals at a single frequency mix. For DSP, the absolute value of the frequency of the signal and the sampling frequency are important, as a setting, tobto. the value of the normalized frequency.

For example, for 2x discrete cosinusoid:

de

In the bag:

Discrete signals are the same, shards of equal frequency normalization, stench, more or less, will be different at the hour.

In the wild slope, a discrete cosine wave in the region of normalized frequencies can be seen:

The scheme of digital signal processing has been introduced.

The CHP process includes 3 stages:

Number Sequence Forming Machine X(n* T) from analog signal x(t) ;

The transformation of the sequence X(n* T) after setting the algorithm by the digital signal processing processor (DSP) at a new, output numerical sequence y (n* T) ;

Shaping the resulting analog signal y(t) from sequence y(n* T).

Sampling frequency f to choose: f e ≥ 2 f in.

Real signals do not satisfy me. Therefore, set the low-pass filter, which surrounds the spectrum. Since the energy of real signals changes with increasing frequency, the effect that the low-pass filter is introduced is insignificant (Fig. 3 a and b), and also the spectra are lower:

Equal quantization(Fig. 1.c.) are encoded with two numbers, so the ADC output may have a sequence of two numbers
. digital signal
winds up as a discrete
by size:

Pardon quantuvannya.

For її reduction, it is necessary to increase the amount of equal quantization. A discrete signal should be received by the CPOS, which, after the algorithm of the skin input sound, should set the output signal to be unambiguous
. In case of any number of operations (multiplier, addition, inversion, overstretching, etc.) for the removal of one case, the number of bills can be calculated annually. However, the processing period (calculation hour) cannot be longer than the sampling period . And maybe even less, like the clock frequency f T CPOS >> f D.

Gave the DAC form the analog signal steps (t), gatherings of which are smoothed by a filter, otrimuyuchi analog y(t).

Signals are called information codes, which are used by people to transmit messages in the information system. The signal can be given, but it's not obov'yazkovo. In this way, as a reminder, you can only use such a signal (or a combination of signals), some kind of acceptance and decoding otrimuvach (analog and digital signal).

One of the first methods of transmitting information without the participation of people or other living sources was a signal richness. At times of guilt, fires were successively planted from one post to the next. Gave us a way to transfer information for the help of electromagnetic signals and report back to those analog and digital signal.

Whether there is a signal, there may be representations in the visual function, as a way to describe the change of its parameters. Such is the appearance of a successful installation of attachments and systems of radio engineering. Krim signal in radio engineering, yet more noise, which is another alternative. Noise does not carry core information and creates a signal, interacting with it.

It is self-understood that it is possible to consider specific physical quantities for an hour to look at the phenomena that are encoded and decoded information. Mathematical model of the signal in the future gives the ability to rely on the parameters of the function to the hour.

Types of signals

Signals from the physical medium of carrying information are subdivided into electrical, optical, acoustic and electromagnetic.

For the method of setting, the signal can be regular or irregular. A regular signal is a deterministic function of the hour. An irregular signal in radio engineering is represented by a chaotic function and is analyzed by a moving approach.

Signals in fallow as a function, as described by their parameters, can be analog and discrete. A discrete signal that is quantized is called a digital signal.

Signal processing

The analog and digital signals are converted and converted to those that transmit and retrieve the information encoded in the signal. After the removal of information, it is possible to zastosovuvat in different purposes. In a few ways, the information is formatted.

Analogue signals are strengthened, filtered, modulated and demodulated. Digital well can still be subject to the pressure, revealed by those others.

analog signal

Our organs perceive all the information in an analog look. For example, as if mi bachimo a car, which passes by, mi bachimo yogo rush without interruption. Yakbi our brain instantly took away information about the camp once for 10 seconds, people constantly squandered the wheels. Ale, we can estimate the time more richly and the moment of the skin is clearly marked.

Absolutely the same, and with other information, we can evaluate the severity of any moment, consider the vise of our fingers to fix on objects. In other words, practically all information, as it can be vindicated in nature, may look analogous. Transmit similar information in the simplest way with analog signals, which are uninterrupted and assigned at any given moment.

To understand, as if looking at an analog electrical signal, you can show a graph on which the amplitude will be displayed on the vertical axis and hour on the horizontal axis. If we, for example, measure the change in temperature, then the schedule will appear without interruption, which shows the value at one hour. In order to transmit such a signal behind the help of an electric jet, we need to equalize the temperature value from the voltage value. So, for example, 35.342 degrees Celsius can be encoded as a voltage of 3.5342.

Analogue signals have previously been victorious in all types of ligature. In order to get rid of the pereshkod, such a signal needs to be strengthened. The more equal the noise, then the shift, the more it is necessary to sing the signal, so that it can be accepted without confusion. This method of processing the signal shows a rich energy of seeing heat. In case of strong signal, the signal can become the reason for the overshoot for other channels in the link.

At the same time, analog signals are placed at the television and radio, for the transformation of the input signal at the microphones. Ale, zahalom, tsey type of signal is seen everywhere by digital signals.

digital signal

The digital signal represents the sequence of digital values. Most of the time, two digital signals are stagnant, shards of stink vikoristovuyutsya at the two electronics and it is easier to encode.

On the front view of the signal type, the digital signal can have two values ​​"1" and "0". If we guess our butt with temperature control, then the signal will be molded otherwise. If the voltage is given by an analog signal to indicate the value of the measured temperature, then the digital signal for the skin temperature value will be given the same amount of voltage impulses. The voltage impulse itself here is equal to “1”, and the actual voltage is “0”. Apparatus for decoding the pulse and restoring the output data is available.

Having shown how visible the digital signal is on the graph, we would like to see that the transition from the zero value to the maximum value is sharp. The very peculiarity allows receiving equipment more clearly "bachiti" signal. It’s easier to blame the transfer, it’s easier to decode the signal, lower with analog transmission.

However, a digital signal with a great level of noise is impossible to see, just like an analog type with a great ability to “see” information. I will shave with the effect. The essence of the effect is that digital signals can be transmitted singly, but they simply shave off. This effect is seen everywhere and is destroyed by a simple signal regeneration. There, where the signal is being cut off, insert a repeat or change the length of the line. The repeater does not reinforce the signal, but recognizes it as an ear of the ear and sees it as an exact copy and can victorate like a charm in lance. Such methods of repeating the signal are actively used in fencing technologies.

For other analog and digital signals, the signal can be changed and the possibility of coding and encryption of information. This is one of the reasons for the transition of the mobile phone to digital.

Analogue and digital signal and digital-analogue conversion

The following is a trio of information about how analog information is transmitted by digital communication channels. I'm going back to the applications. As they said sound - tse analog signal.

What is seen in mobile phones, how do they transmit information via digital channels

The sound, drinking into the microphone, is sent to analog-to-digital conversion (ADC). This process consists of 3 steps. The values ​​of the signal are taken after the same time, the whole process is called discretization. According to Kotelnikov's theorem about the throughput of channels, the frequency of taking these values ​​can be higher, lower the frequency of the signal. So, as in our channel there is a substitution for a frequency of 4 kHz, then the sampling frequency becomes 8 kHz.

Given all selected values ​​of the signal are rounded off or, otherwise, apparently, quantized. The more equal will be done, the more accurate will be the confirmed signal on the receiver. Then all the values ​​are converted to a two code, which is transmitted to the base station and then we reach the next subscriber, which we accept. At the receiver's telephone, there is a digital-analog conversion procedure (DAC). This is a reversal procedure, which, at the exit, takes away the signal of the yacomo, which is identical to the exit one. Gave an analog signal to the sound from the phone's speaker.

analog signalє uninterrupted function of an uninterrupted argument, that is. appointed for any significance of an independent zminnoy. As a rule, analog signals are used as physical processes and phenomena, without interruption in their development (dynamic changes in the meaning of the singing powers) in the hour, in the open space, or for any other independent change, with which registration the signal is similar (similar) to the process yoga breed. An example of a mathematical record of a specific analog signal: y(t) = 4.8exp[-( t-4) 2/2.8]. An example of a graphic display of the signal is shown in Fig. 2.2.1, while both the numerical value of the function itself, so and її arguments can take on whether the value is in the range of such intervals y 1 £ y £ y 2,t 1 £ t £ t 2. Even though the intervals of the value of the signal are not interchanged, the stench is taken as equal types -¥ to +¥. A lot of possible meanings of the signal make up an uninterrupted space, in which case a point can be assigned with inexhaustible accuracy.

Rice. 2.2.1. Graphic display of the signal y(t) = 4.8exp[-( t-4) 2 /2.8].

Discrete signal for its values, it is also a non-interruptible function, but it is assigned only discrete values ​​to the argument. For the impersonality of its meaning, wine and kіtsevim (numeral) that is described by a discrete sequence y(n×D t), de y 1 £ y £ y 2, D t- interval between signals (interval of signal sampling), n = 0, 1, 2, ..., N- Numbering of discrete values. Like a discrete signal subtracting the sampling of an analog signal, the fault is the sequence of responses, the values ​​of which are equal to the accuracy of the output signal values ​​by coordinates n D t.

An example of sampling an analog signal, induced Fig. 2.2.1 representations in Fig. 2.2.2. At D t= const (even discretization of data) it is possible to describe a discrete signal by fast values y(n).

In case of uneven discretization of the signal, the recognition of discrete sequences (in text descriptions) sounds fit at the curly arch - ( s(t i)), and the values ​​of the references are displayed in the table view from the assigned coordinate values t i. For short uneven numerical sequences, such a numerical description is required: s(t i) = {a 1 , a 2 , ..., a N}, t = t 1 , t 2 , ..., t N.

digital signal quantizations for their values ​​and discrete for the argument. Vіn is described by a quantized lattice function y n = Qk[y(n D t)], de Qk- function of quantization with a quantity of equal quantization k at which interval quantization can be both equal to equal distribution, and also to uneven, for example - logarithmic. A digital signal is set, as a rule, it looks like a numeric array after the last values ​​of the argument when D t = const, ale, at a glance, the signal can be set as a table for certain values ​​of the argument.

In essence, a digital signal is a formalization of a different type of a discrete signal when the value of the remaining digits is rounded to a single number, as shown in Fig. 2.2.3. In digital systems and EOM, the signal for representations is accurate to the sing number of discharges and also digital, for the description of digital signals, the quantization function is omitted (it is possible for the description of discrete operators) .

Rice. 2.2.2. Discrete signal 2.2.3. digital signal

y(n D t) = 4.8exp[-( n D t-4) 2/2.8], D t= 1. y n = Q k, D t=1, k = 5.

In principle, quantized for their values, there may be an analog signal, registrations with similar digital equipment (Fig. 2.2.4). But you can see these signals in the okremium type there is no sensation - the stench is overlaid with analog shmatkovo-bezperervnymi signals with a quantization crock, which is considered to be an acceptable slacking off.

Most of the discrete and digital signals, with which the mother is on the right, is a discretized analog signal. Ale є signals, yakі spochatku vіdnosyatsya up to the class of discrete, for example, gamma quanti.

Rice. 2.2.4. Quantization signal y(t)= Qk, k = 5.

Spectral manifestation of signals. Krіm zvodnogo timchasovogo (coordinate) representation of signals and functions under the hour of analysis and data processing is widely used to describe the signals of the functions of frequency, tobto. behind the arguments wrapped around the arguments of the timchas (coordinate) manifestation. The possibility of such a description is due to the fact that if there is any folding behind its form, the signal can be represented by looking at a sum of more simple signals, and, zocrema, at looking at a sum of the simplest harmonic sounds, the combination of which is called the frequency spectrum of the signal. Mathematically, the spectrum of signals is described by functions of the amplitude value of the cob phases of harmonic colivans for an uninterrupted or discrete argument. frequencies. The spectrum of amplitudes is called amplitude-frequency characteristic(frequency response) to the signal, the spectrum of phase cutiv - phase response(PFC). The description of the frequency spectrum reflects the signal in such a way that it is unambiguous, like a coordinate description.

Rice. 2.2.5, a correction of the signaling function has been introduced, as it is taken out of the summation of the constant warehouse (the frequency of the constant warehouse is 0) and three harmonic sounds. The mathematical description of the signal is determined by the formula:

de A n= (5, 3, 6, 8) – amplitude; f n= (0, 40, 80, 120) – frequency (Hz); φ n= (0, -0.4, -0.6, -0.8) – cob phase cod (in radians) cob; n = 0,1,2,3.

Rice. 2.2.5. Timchasovoe representation of the signal.

The frequency of representation of this signal (the spectrum of the signal as frequency response and phase response) is shown in Fig. 2.2.6. It is best to respect that the frequency of occurrence of a periodic signal s(t);

Rice. 2.2.6. The frequency of the signal.

Graphic display analogue signals (Mal. 2.2.1) no special explanation is required. With a graphical display of discrete and digital signals, either the method of non-intermediate discrete changes in the scale difference over the entire argument (Fig. 2.2.6), or the method of origin (smooth or lamano) for the values ​​​​of Fig. 2 in point 2 (curve 2). Looking at the continuity of fields and sounding, the secondness of digital data, which are controlled by sampling and quantization of analog signals, another way of graphic display is considered to be the main one.

Metarozpovіdі show why the essence of the concept is "signal", if the signals are broader and clear and if the stink of the general characteristics.

What is a signal? On the chain of food, wind a little child, say, “it’s such a thing, for help that you can help.” For example, behind the help of a mirror, that dream can transmit signals to a direct line of sight. On the ships, if the signals were transmitted for help, the ensigns-semaphores. Specially trained signalmen were engaged in this work. In such a rank, for the help of such ensigns, information was transmitted. The yak axis can convey the word "signal":

In nature, there are silent signals. So really, be it a signal: there is a note on the table, some kind of sound - you can be a signal to the ear of a singing sip.

Garazd, since such signals made everything clear, I will move on to electrical signals, which in nature are no less than the least. But if you want, you can sort of mentally break it into groups: triangular, sinusoidal, straight-cut, saw-like, single impulse is thin. All these signals are named so for those, like the stench looks like they are depicted on the chart.

The signals can be used as a metronome for timing (as a clock signal), for the hour, as a pulse, for controlling motors, or for testing the transmission of information.

Characteristics ate. signals

The singing sensi has an electric signal - tse graph, which shows the change of the voltage or the struma with the hour. What does it mean: if you take a line and along the X axis you will indicate the hour, and along the Y axis the voltage or strum, and you will indicate the values ​​of the voltage at a specific moment of the hour with points, then the image below the bag will show the shape of the signal:

There are too many electric signals, but they can be divided into large groups:

• Single direct
• bidirectional

Tobto. in unidirectional strum flow in one bіk (or not flow vzagalі), and in bidirectional strum it changes and flows either "there", then "here".

All signals, regardless of type, may have the following characteristics:

• Period - An hour later, after a signal, start repeating to yourself. Mostly indicated T
• Frequency -- Indicates how many times the signal will be repeated in 1 second. Win at hertz. For example 1Hz = 1 repetition per second. Frequency є turning point period ( ƒ = 1/T )
• Amplitude - Vymiryuetsya in volts or amperes (depending on the type of signal: strum or voltage). Amplitude refers to the "strength" of the signal. How strong is the graph of the signal in the X axis?

See the signals

sinusoid

I think how to represent a function whose graph in the picture is no longer sensational - it’s good to know sin(x).Її period is 360 o or 2pi radian (2pi radian \u003d 360 o).

And if you add 1 second to the period T, then you know how many periods will be converted into 1 second or, in other words, how often the period is repeated. Tobto, you will designate the frequency of the signal! Before the speech, it appears in hertz. 1 Hz = 1 sec / 1 repeat y sec

Frequency and period are turned one to one. Chim dowshy period, tim less frequency and navpaki. The connection between the frequency and the period is expressed by simple expressions:

Signals, like a straight-lined shape, and called "rectangular signals". You can mentally split it into simple straight-cut signals and meanders. The meander is a straight-cut signal, which has a trivality of an impulse and a pause of equal. And in order to add up the trivality of the pause and the impulse, then we take away the period of the meander.

The strongest direct-path signal is heard in the meander time, which makes the difference between pulse and pause (pulse duration). Look at the picture below - it will say more for a thousand words.

Before speech, for straight-cut signals, there are two more terms, like a trace of the nobility. The stench is wrapped one to one (like a period and a frequency). Tse courageі filling coefficient. Speechness (S) is longer for the period until the momentum is torn and navpak for the coefficient. zapovnennya.

In this order, the meander is a straight-cut signal for sparing equal 2. So, for the new one, the duration of the wave is greater for the trivality of the impulse.

S – sprouting, D – filling coefficient, T – pulse period, – pulse trivality.

Before speech, the graphs above show ideal rectilinear signals. In life, the stench looks a little different, so that in the same annex the signal cannot change absolutely mittevo from 0 to such a value and go back to zero.

If we go up the mountain, and then immediately go down and write down the change in the height of our camp on the graph, then there is a tricky signal. Grue povnyannya, ale truthful. In tricky signals, the voltage (strum) rises a little, and then it starts to change again. І for the classic tricot signal, the hour of growth is earlier than the hour of decline (and earlier half of the period).

If such a signal has an hour of growth less or more than an hour of decay, such signals are already called saw-like. І about them below.

sawtooth signal

As I have already written above, a non-symmetrical tricot signal is called a saw-like signal. Name all the smarts and needs just for the sake of clarity.