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THE HISTORY OF SPECTRUM IN COMMUNICATION
The term "spectrum" is derived from the words "the spectrum", which translated from Latin means "vision". Into scientific also use the term a range was entered by Newton in 1671 - 1672 for designation of a multi-color strip similar to a rainbow, which turns out when passing a ray of sunlight through a triangular glass prism. Now in physics the range is understood as distribution of physical quantity: energies, masses, frequencies. The graphical representation of such distribution is called the spectral chart. In technique of communication the range is meant as an electromagnetic range - a frequency spectrum of an electromagnetic radiation. Research in this area has shown that the spectra can be discrete (ruled), continuous (solid) the nature of the distribution of the physical quantity values, and represent a combination (superposition) of discrete and continuous spectra.
Presently it is unknown whether the term "frequency" was applied at that time, but it is obvious that it couldn't be measured in Hertz as the Hertz lived much later. However process of fluctuation of strings musical instruments and communication of this phenomenon with a sound certainly were known. According to state standard specification 8.567-99 "Measurement of time and frequency" the term frequency is defined as "The size measured by number of identical fluctuations in unit of time". And in ancient times, it was quite obvious that the strings of different lengths fluctuate at different rates, but it was not possible to measure the frequency. After consideration of spectral features of musical instruments the question of features of a range of acoustic vibrations of the concrete piece of music arising at performance is of interest. The fact that in a brain sound information arrives in the form of a range demonstrates very difficult process of its conversion.They can change even under the influence of short-term training. So, for example, 10 years ago scientists considered that each cell of acoustical bark is once and for all configured to certain characteristics of a sound. However it has turned out that control of cages can change: some neurons become supersensitive to the sounds drawing attention of animals and which are stored at them in memory. In communication to explained there is clear a value of a pattern of a tune: processing of information in the hearing system significantly differs from simple relaying of sounds in phone or a stereosystem. Amplifiers cable line should ensure a simultaneous increase in the sum of all telephone signals. In summing significant part of the energy falls on the carrier frequencies. Excess total signal level leads to a nonlinear distortion and mutual interference in individual telephone channels.
The author also gives an answer to the question: "Why remove the carrier frequency in the spectrum of the transmitted signal?". Removing the side AM signal bandwidth enables economical use of bandwidth transmission line, and the removal of the carrier does not provide such savings, leads to the need for its recovery at the receiving end. The explanation is simple enough.
Boris P. Khromoy,
Moscow Technical University
of Communications and Informatics, Moscow, Russia,
mtuci@mtuci.ru
Keywords: spectrum, optics, frequency, music, discretization, noise, signals.
Для цитирования:
Хромой Б.П. История спектра в технике связи // T-Comm: Телекоммуникации и транспорт. 2016. Том 10. №11. С. 60-67. For citation:
Khromoy B.P. The history of spectrum in communication. T-Comm. 2016. Vol. 10. No.1 1, рр. 60-67.
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Historically, before all other spectra study of optical spectra was stalled. Isaac Newton, in his work "Optics", published in 1704, has published the results of their experiments, the degradation by the prism of white light into separate components of different color and refrangibility, that is, to obtain the spectrum of solar radiation, and explained to them the nature, showing that the color is own property of light. In fact, Newton laid the foundations of Optical spectroscopy in the "Optics", he described all three still used method of decomposition of light — refraction, interference and diffraction, and its prism with a collimator, a slit and a lens was (he first spectroscope.
In 1854 Kirchboff and Bunsen have begun to study ranges of the flame painted by vapors of metal salts and as a result they have laid the foundation of the spectral analysis, thanks to which has become possible to define qualitative composition of complex mixes by the form of their ranges in a blowtorch flame. From the middle of the XX century, with the development of radio engineering, has developed a different direction spectral studies related to the treatment and analysis of the original sound, and then any arbitrary signal.
If at an initial stage in optics and in other areas ranges were studied by experimental methods, then in technology of communication ranges theoretically have begun to be investigated. It has occurred becausc the functions describing electric signals are set in a time domain and can be described mathematically. Transformation of Fourier which birth is connected with 1822, at last, thanks to development of communication has received very effective application.
It is obvious that various transformations of a speech signal could appear only after the person has learned to transform a speech acoustic signal to a signal electric, and it has occurred rather recently. However studying of a range of a sound musical signal has begun in an extreme antiquity, Pythagoras nearly 2500 years ago. Usually the name of Pythagoras is connected with mathematics and it is a little known that Pythagoras was also a magnificent musician.
Presently it is unknown whether the term "frequency" was applied at that time, but it is obvious that it couldn't be measured in Hertz as the Hertz lived much later. However process of fluctuation of strings musical instruments and communication of this phenomenon with a sound certainly were known. According to state standard specification 8.567-99 "Measurement of lime and frequency" the term frequency is defined as "The size measured by number of identical fluctuations in unit of time". And in ancient times, it was quite obvious that the strings of different lengths fluctuate at different rates, but it was not possible to measure the frequency.
But to musicians communication of length of a string with radiated by it sound tone was well-known. Features of simultaneous sounding of several strings which could be harmonic (coordinated) were well also known or make impression of a dissonance [1].
Now in connection with development of electronics without difficulties it is possible to put two sine signals with the relation of frequencies equal 75 and on the scrccn of an oscillograph and to see aperiodic oscillations. In other cases in case of the close
values of frequencies it is possible to watch the phenomenon of beats. It is obvious that the musical sound in this case cannot be received. Certainly, all these phenomena were observed by musicians, but it was possible to study them only by measurement of length of a string. This method was rather effective as the frequency of fluctuations and all phenomena of musical acoustics is unambiguously connected with length of a string [2, 3].
Pythagoras made experiments by means of the device which carried the name of monochords (fig. 1): Monos - one, ehorde -a siring. The ends of strings it was strongly attached to a box by means of motionless supports. One support was mobile.
— ^ —
Figure 1
Operation with monokhordy showed that the siring, fluctuating, forms standing waves. Length of standing wave shall makes an integer part from length of the fluctuating body. Thus, the string fluctuates not only entirely, but also parts, forming harmonicas, making some frequency assembly. A whole string forms the first harmonic, the string half of the 2nd, the third part of the third string, etc. How many limes less than the fluctuating part of the string as many times higher than the oscillation frequency. As an example the natural natural harmonics for the string fluctuating with a frequency of 24 Hz are presented in table 1.
Table 1
1 1/2 1/3 1/4 1/5 1/6 w 1/8 1/9 1/10 1/11 1/12 1/13 1/14 1/15 1/16
24 ru 48 r4 72 ru 96 120 r4 144 I'M 168 ru 192 I'M 216 ru 240 ru 264 ru 288 Tq 312 ru 336 ru 360 TM 384 ru
The top line of the table defines part from total length of the tluctuating string, and lower frequencies of the harmonicas corresponding to them. In bottom line the frequencies which are octave boundaries are selected. It is necessary to mark that the same ratios turn out if not the solid body, but air in a certain volume fluctuates. Follows from the table that the natural harmonics have logarithmic structure, if the first harmonica has the frequency of 24 Hz, then the second - 48 Hz. The first and second harmonica form an octave. It is known that the octave has the boundary frequencies differing twice. The second octave is formed by the frequencies of 48 Hz and 96 Hz. Between boundary values the intermediate frequency of 72 Hz appeared. The third octave (frequency of 96 Hz - 192 Hz) already contains three intermediate frequencies, and the fourth seven frequencies.
Considering a natural scale the many-stringed instrument would seem it is necessary to adjust in compliances with 1 ratios given in the table. Really the performer can elicit from a many-stringed instrument at the same time sounds by means of several
T-Comm Vol.10. #11-2016
strings. The combination of sounds at certain ratios can cause a dissonance. On the other hand addition of strings becomes for the purpose of increase in a sound palette.
We will note that according to table 1, frequency intervals between tlie next sounds (24 Hz) are rattier big. It is known what in the low-frequency range of people distinguishes two tones differing on I Hz, in the mid-frequency range of 2-3 llz, in the high-frequency range oil 5 Hz. sound palette. In the range in which musical instruments (16-4700 Hz) of people are adjusted can distinguish about 1500 various sounds!
The range of 16-4700 Hz can surprise a communications operator. It is known that sound broadcasting l-ro a class the upper frequency of the range is set aimost equal 15000 Hz. Why, if tools are set up in much narrower range? The matter is that if the string is set up on the frequency of 4700 Hz, then the radiated by it, third harmonica makes 4700 x 3 — 14100 Hz. On this frequency it isn't necessary to set up anything, it is formed automatically. And it is necessaty to transfer her as it sounds in the hall, and the listener perceives it.
So, in the range of 16-4700 Hz of person it is capable to distinguish about 1500 various sounds. And how many sounds are expedient to use at creation of musical instruments? It is natural that the musical instrument has to have perhaps smaller quantity of the adjusted elements. The violin having four strings can be an example. However it can't be taken as a basis. The matter is that smoothly changing position of the finger pressing a string to a signature stamp the violinist also smoothly changes sound frequency. In other words it "sets up" the tool on a certain frequency of a sound during work execution. Otherwise the performer on a harp or a piano carries out the task. It can arrange and change nothing during performance. The instrument is adjusted before a concert and allows to reproduce a certain set of the fixed frequencies. A similar situation at performers on wind instruments.
What quantity of the sounds fixed on frequency is used in practice? The response to this question ean be reeeived having counted quantity of white and black keys at a grand piano. Their only 88 pieces. And the grand piano envelops practically all frequency range! And violin? Though the violinist can derive about 400 frequencies in practice he uses only an order 50 even appearing solo and executing difficult work. To depart from this rule, he can't, playing in ensemble with other tools.
So, the number of the reproduced frequencies is seleeted an order 88. We will mark that there was a process of quantization of frequencies. How in practice the choice of the discrete values of frequencies is carried out? For this purpose we will address history. Musicians, and they were already professionals in ancient Egypt, have by practical consideration come to need of changc of a natural system. The matter is that developing technology of game, they have begun to use chords. As it is known a chord call simultaneous use not less than three sounds.
Practice showed that pleasant sounding of a chord turns out if frequencies correspond as 4:5:6. In a natural scale as it is obvious from table I. there is only one such combination, it is 192:240:288.
And musicians wanted that such combination could be reeeived, since any frequency of a sound row . For this purpose a natural sound row was "upgraded". Upgrade was reduced to change of numerical values of two frequencies and deleting one frequency. For this purpose a natural sound row was "upgraded". Upgrade was reduced to change of numerical values of two frequencies and deleting [4-5].
To solve this problem, it was decided to impose additional sounds, the frequency of which would share the intervals as much as halftones. For this purpose, five additional frequencies were introduced. Recall that at the piano, each octave contains five black keys that reflect this idea. For determination of frequency of the additional sounds reproduced by a musical instrument Pythagoras offered the row presented in the first line of table 2.
Table 2
(2/3)' mr (2/3) (2/3): 2/3 1 3/2 (3/2) (3/2) (3/2 )J (3/2) (3/2)"
46.4 69.6 103.4 155.13 232.7 349 523.5 785 1176 1764 2646 3969
Hz Hz Hz Hz H Z Hz Hz Hz Hz Hz Hz Hz
sol lint re la mi si fa do sol re 1» mi si
couiuer flat flat Dal Hat t 1 2 3 3 4 4
octave most most small small octave octave octave octave octave octave octave
octavc octave octavc octave
You can see in the middle of the first is the number 1. It correspond to a particular source frequency soond which ean be chosen arbitrarily. The digits located on the right and to the leil of initial 1 show in how many time it is necessary to increase (or to reduce) the initial frequency for receiving a sound row.
As on the right are fractions 3/2 large 1, built in varying degree of frequencies located on the light form a monotone sequence, On the contrary, to the left of unit the fractions 2/3 built in the same degrees are located. As 2/3 less units, the sequence located at the left are decreasing.
The result of computation is given as an example on the second line of table 2. The frequency of 349 I Iz is taken for unit. As a result the sequence of the discrete frequencies from 46.4 to 2646 Hz turned out. The initial frequency of 349 Hz is selected not accidental.
Communications operators got used that many frequency parameters are standardized. In musical acoustics the same there are standards including on values of those 88 frcqoencies on which set up grand piano strings. On it the frequency of 349.23 Hz confonns to the standard (a piano of the L-120 model) to a note "fa" of the first octave. It is also designated under I, in the second line of the table. Pay attention that strings are adjusted with high precision (to the tenth beats of Hz). In calculations value of the initial frequency is rounded. The following frequency 523.5, is calculated by means of Pythagoras's row.
We will address the above-mentioned standard again. Whether there is this in it this figure? Yes is available. It is equal to 523.25 Hz, According to the standard this figure corresponds to a note C, but already the second octave.
Further it is possible to find all frequencies in the standard the tables calculated on Pythagoras's row and provided in the second
line. Frequency of 1176 Hz, according lo the standard, corresponds to a note of "re" of the third octave, the frequency of 1764 Hz, corresponds to a note oT "la" of the third octavc, the frequency of 2646 Hz, corresponds lo a note of "mi" already of the fourth octave, the frequency of 3969 Hz a note of "si".
Thus, Pythagoras's row allowed us to calculate the standard frequencies reproduced by seven while keys of a grand piano: «do-re-mi-fa-sol-la-si». The truth belong these frequencies to different octaves, but it has no essential value. We will remind that at the time of Pythagoras there were yet no frequency meters therefore Pythagoras invented the row for implementation of control of musical instruments by practical consideration relying on string length.
However comparing figures of the second row of table 2 to designations of keys of a modern grand piano in the third row it is possible to draw a conclusion that the modern standard of control of a grand piano is based on Pythagoras's invention.
The main difference of musicians from the ordinary engineers-operators who are carrying out control of frequency of the generator by means of an electronic frequency meter is existence of the developed ear for music allowing having adjusted one string, for example on a note "fa" of the I octave, to adjust the second string on the doubled frequency that will correspond to a note "fa" of the 2nd octave.
In other words, speaking to the modern language, Pythagoras in addition to mathematical reasons for a sound row invented the algorithm which is allowing to realize setup of music instruments, didn't lose value till our time as in addition to frequencies of setup of the strings of a grand piano "serviced" by while keys allows to set up also the strings "serviced" by five black keys which frequencies are specified in the second Sine of table 2, to the left of basic frequency of 349 Hz. These are notes "sol flat", "re, mi, la, the si llat".
The term a llat is entered not to give separate names for black keys. The so! flat key is between the next keys reproducing "fa" and "sol", and "so!" is slightly more left. If to take "fa" for an initial key, then the same black key is more to the right and will be called "fa sharp".
Thus Pythagoras "took care" of control of all strings of a grand piano which was invented later approximately 1300.
Summing up the results, it is necessary to mark that in musical acoustics quantization of the reproduced frequencies is used. Division of the general range of frequencies into octaves is the basis. The provision of the beginning and end of an octave in the frequency range submits logarithmie to the law with the base 2 as the finite frequency of each octave exceeds initial frequency twice. The octave in an equal temperament is divided into 12 equal parts. We will add that quantity of octaves in the frequency range used in music - 9, at a grand piano of full octaves only 7.
Returning to a question of a range, it is necessary to mark that values of frequencies in table 2 it not that other as, values of frequencies on a horizontal axis of the spectral chart of a sound musical signal. Feature of this range is its discretization. In case of execution of the musical piece volume of sounding of strings changes and changes amplitudes of different frequency spectrum components, some components can disappear, others to arise, but
all values of frequencies on a horizontal axis remain in an invariable look.
After consideration of spectral features of musical instruments the question of features of a range of acoustic vibrations of the concrete piece of music arising at performance is of interest. The question at first sight seems strange.
Really during one concert the pianist executes different works, different composers using only one in advance adjusted grand piano. Whence can take the difference in the spectra of acoustic oscillations? I lowever it occurs, and it is connceted with the notion of tonality
It is known that all pieces of music are created in two keys: major and minor. Application of a certain key results in need of use at the composition only 7 notes of each octave, instead of available 12.
So for example, when writing work in "To - major" tonalities are used the following notes: do, re, mi, fa, sal, la, si. The pianist at execution of such work will use only white keys of a grand piano. All seven black keys can't be used.
Familiar names of each musical range — from «do» lo «si» — in the XI cenlury were entered into use by the monk-Benedictine Guido D'Arezzo and designated the first syllables of words of a prayer to John the Baplist.
In Latin the first letters looked as "ut, re, mi, fa, sol, la". Then notes was only six, and the first of them sounded differently. Subsequently the note of "ut" has been replaced on "do" because the open sound was inconvenient to be sung. The name to a new note was given by a certain Dhoni — whether in honor of himself favourite, whether in honor of the Lord (Dominus). The 7-th note of "si" has appeared much later, upon transition to present octava system.
There is a question: "And why notes there have to be only seven and who has defined it"? At the moment it is hardly possible to clearly answer the question. However the statement doesn't raise doubts that it is connected with feature of perception of music the person. Process of processing of musical sounds in a brain of the person process very difficult.
However some data on where and how there is a processing of musical information have begun lo appear in recent years. The study of patients with brain injuries and a study of healthy people with modem n euro imaging techniques have led scientists to an unexpected conclusion: the human brain is not a specialized center of music. The numerous areas dispersed on all brain including those that are usually involved in other forms of cognitive activity participate in her processing. The sizes of active zones vary depending on individual experience and musical training of the person.
The auditory system, like all other sensory systems of the body, has a hierarchical organization. !t consists of a chain of centers that process nerve signals traveling from the ear to the highest acoustic analyzer department - auditory cortex. Processing of sounds (such as musical tones) begins in the inner ear (cochlea), sorts complex sounds (published, for example, the violin) to constitute the basic frequency. Then, the auditory nerve fibers, tuned lo different frequencies, snail sends information as a sequence of neural bits (pulses) in the brain.
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In the end, they reach the auditory cortex in the temporal lobes of the brain, where each cell responds to a certain frequency sounds. Frequency adjustment curves of adjacent cells overlap, those there are no gaps between them, and the frequency of sound card is formed on the surface of the auditory cortex.
Thus, we can assume that the spectral separation is carried oot sound components into separate frequency components of the human ear (cochlea). In communication engineering such a separation is carried out in a device called a "spectrum analyzer".
However, if such a separation device is carried out sequentially by sequentially tuning a narrowband filter in the human inner ear, this process occurs simultaneously, as it is 3.5 thousand. Hair cells having frequency selectivity. With their participation is performed in the signal conversion range, at which the fibers oflhe auditory nerve to the brain.
Although studies of the human hearing system at the cellular level that are written above, only recently made, but the idea of its spectral structure outlined for the first time a famous scientist Om. Om is known as the author of the "Ohm's law" and the name of the resistance unit.
However in 1839 a number of the works on acoustics which have led to results of great importance has followed. In the article Über die Definition des Tones nebst daran geknüpfter Theorie der Sirene und ähnlicher tonbildender Vorrichtungen» (1843) the law (too called by "the law of Ohm") is stated that the human ear learns only simple harmonic oscillations and that any difficult tone decays an ear on compound (under Fourier's law) and it is learned only as their amount. And this law has not been adopted by contemporaries of Ohm, and only Ilelmholtz, in eight years after death of Ohm, has proved its complete justice.
The fact that in a brain sound information arrives in the form of a range demonstrates very difficult process of its con version.They can change even under the influence of short-term training. So, for example, 10 years ago scientists considered that each cell of acoustical bark is once and for all configured to certain characteristics of a sound. However it has turned out that control of cages can change: some neurons become supersensitive to the sounds drawing attention of animals and which are Stored at them in memory, in communication to explained there is clear a value of a pattern of a tunc: processing of information in the hearing system significantly differs from simple relaying of sounds in phone or a stereosystem.
In developing the musical frets in the old days we are certainly taken into account sound intervals and chords. Already at the time of Pythagoras it was aware that a pleasant harmonies (consonance) include such musical intervals or chords, which are characterized by a simple ratio of frequencies of their constituent sounds.
As an example, «do» the first octave (frequency of about 260 Hz) and «sal» of the same octave (near 390 Flz frequency). The tone ratio is 2: 3, that while their playing generates pleasant to the ear consonance. On the contrary, «do» the first octave and the neighboring «do» Sharp (frequency 277 Hz) produce a complex ratio of frequencies, constituting 8: 9, and while the sound perceived as an unpleasant chord. With the help of modern imaging, scientists have proved that the development of emotional reac-
dons while listening subjects harmonies, consonance and dissonance involving different areas of the brain.
From considered obvious that the main components of a musical number to be chosen in a certain way, but the question remains why only seven notes should be applied in each pitch?
Most likely this is due to the peculiarities of the human brain in the conversion of the spectrum in the perception of music. Apparently the use of a greater number of notes in the perception of a musical work is a violation of its melody. This property of the human brain to the maximum seven influences perception is confirmed by the fact that now clarified the ability of air traffic controllers at the same lime comfortable to serve no more than seven aircraft. May be even for this reason, the number 7 is often used by man: 7 colors of the rainbow, 7 days a week?
We consider the characteristics of early music in different countries, it is possible to find, use, and 5 notes. On the so-called built pentatonic Chinese, Mongolian, as well as Scottish, Irish music. 5 Application of the music does not cause problems, and the use of 10 music shows that this perception of music (at least in this country) does not stop, but does not cause positive emotions among Europeans.
The Sound of Music is always organized in a certain sound Systems. In a single sound system used in Western Europe and Russia. Works by Bach, Mozart. Beethoven, Shostakovich, written under the sound system. It is also widely used in various genres currently.
The scale adopted in the European music system consists of seven stages. Of these stable (reference) are 1, III and V stage, and, respectively, II, IV, VI and VII - unstable. Any work can not end on an unstable stage. His last sounds should be stable (I, 111 and V stages) and to create the listener a feeling of completeness.
The two most important oflhe mode adopted in classical music — major and minor. The color of the sound, they are very different from each other. Lad - the relationship of musical sounds of different heights, some of which are perceived by the ear as a stable, and the other- as unsustainable.
Different historical periods and national musical culture gave rise to a kind of frets. Each way has a certain range of emotional expression. Determinant of major and minor chord is formed by stable steps fret.
The Major between 1 and III stage comprises two tones, and in a minor key - a half tone. Major or minor scale, you can choose from any of the twelve steps of the scale. This range will be the sound of a well-defined key, which determines the degree of the scale 1 - tonic. Major scale, performed by the sound to be called in do Major and minor scales on the same note - do Minor. The tone re Heels the specific height of a series of sounds.
Each classical piece of music written by the composer in a certain tonality that to some extent determines the nature of the work. For example, many lyrical bardic songs are written in the key of la minor. In total there are 24 tones. All of them are now widely used by composers. The first outstanding composer, has composed a cycle of works in all keys, was Johann Sebastian Bach. They were created by the deepest in content, diverse in mood works in those keys that were previously never used.
Musicians and music lovers were able to feel some unknown images arise before using them. Nowadays all 24 tones used in their works Shostakovich.]
When the entire system of 24 tones included in musical practice, we found that some composers individual tone associated with a particular shaped area, and even color. Beethoven, for example, called the Si Minor "black" tone. Rimsky-Korsakov seen in all color tone.
So 24 tones, each of which contains a different set of sounds to form 24 of the spectrum of sound vibrations. These spectra are different from the spectrum of sound radiation, such as the piano, the absence of a specific set of frequencies. As previously stated by the piano 88 keys.
As in any key is used only 7 of 12 each octavc key total maximum number of keys that can be used in the execution of any works will be equal to 7/12 x 88 = 49. This number determines the number of keys used, not the number of reproduced frequencies. The fact that the strings generated not only the basic frequency but also harmonic. High string harmonics (ills the frequency range up to 15 kHz while maintaining the structure, typical of the lone used.
Concluding its consideration of the spectrum of musical sounds, it should be noted that a fixed set of frequencies in the performance of the product is accompanied by changes in the amplitude of oscillations, so the value is plotted on the vertical axis of the graph of the spectrum are of a continuous nature.
After finishing a historical overview of the formation of musical acoustics can be considered a problem that since the end of the 19th century had to deal with professionals in the field of communication. The first problem was the telephony, the second broadcast. Their difference is that the telephony and speech recognition are important economical and for broadcasting sound quality. To solve these problems various methods have been used, including methods for spectral analysis.
The previous sections dealt with harmonic signals. In technology, communication had to deal with different types of signals. With respect to the music, the following terms are used in communications technology. A simple tone - is sound vibrations occurring harmonically. Its main characteristic is the frequency. If the tone is a non-harmonic oscillation, it is called complex. Simple tone gives a tuning fork, a complex - musical instruments or voice box.
Next term, widely used in communications technology -noise. Noises superimposed on the transmitted signal and degrade the sound quality. They have their spectral composition, which must take into account when solving technical problems.
With the development of broadcasting and recording had to develop another type of signal - sonic booms. They are widely used in the orchestral performance of music.
Solution of technical problems associated with the sound led to serious research in the field of psycho-physical characteristics of human hearing. These studies were made possible due to the development of various types of measuring instruments, allowing to make measurements with minimal time and averaging the results obtained for a large number of subjects.
For example, the scale of volume levels was created. It is based on the psychophysical law of Weber-Fechner. According to this law with increasing irritation exponentially increases the feeling of irritation in ail arithmetic progression. This law implies that the volume is proportional to the logarithm of the ratio of the intensities of sounds: At the heart of the creation of the scale
E-klgd/Ig), (1)
where I - intensity of sound; Iq - intensity of sound at the threshold of audibility; k - a certain proportionality coefficient that depends on the frequency and intensity. Volume is expressed in backgrounds (background). It is believed that at a frequency of 1 kHz, the volume scale and intensity of the same level. In this case k = I.
The normal human car perceives a fairly wide range of sound intensities: for example, at a frequency of 1 kHz from I0 = = 10*li W/nr (hearing threshold) to ImaJl = 10 W/nr (threshold of pain).
To find the correspondence between the volume and intensity of sound at different frequencies are equal loudness curves (Figure 2). They build on the basis of secondary data obtained from people with normal hearing. The lower curve corresponds to the intensity of the weakest audible sounds — the threshold of audibility. For all frequencies of this curve E = (J; for the frequency of ! kHz sound intensity 1<> = 10 " W / nr. The upper curve corresponds to the threshold of pain.
Almost all of the electrical signals representing the real message contains an infinite spectrum of frequencies. For the undis-torted transmission of such signals would require a channel of infinite bandwidth. On the other hand, the loss at the reception of at least one spectral component results in distortion of the waveform time.
Therefore, the task of transmitting the signal to a limited bandwidth of the channel so as to meet the requirements of signal distortion and quality of information transmission. Thus, the frequency band - is limited {in terms of technical and economic considerations and requirements for transmission quality) signal spectrum.
Primary telephone signal (voice message), also called subscriber is a non-stationary random process with a bandwidth of 80 to 12000 Hz. Speech intelligibility is determined formants (enhanced frequency region of the spectrum), the majority of which are located in the band of 300...3400 Hz (Figure 2). The graphs show that it was in this band has a minimum threshold of audibility, ie, signals in this band are most susceptible to human hearing.
Therefore, on the recommendation of the International Advisory Committee for Telephony and Telegraphy (CCITT) for telephone transmission adopted efficiently transmitted frequency band 300 ... 3400 Hz. Such a signal is called a tone signal (PM). The quality of the transmitted signals obtained high enough -syllabic intelligibility is about 90%, and the intelligibility of sentences - 99%.
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ИСТОРИЯ СПЕКТРА В ТЕХНИКЕ СВЯЗИ
Хромой Борис Петрович,
Московский технический университет связи и информатики (МТУСИ), Москва, Россия, mtuci@mtuci.ru
Аннотация
Термин "спектр" произошел от слова "spectrum", которое в переводе с латинского означает "виде?ние". В научный обиход термин спектр ввёл Ньютон в 1671-1672 годах для обозначения многоцветной полосы, похожей на радугу, которая получается при прохождении солнечного луча через треугольную стеклянную призму. В настоящее время в физике под спектром понимается распределение физической величины: энергии, массы, частоты. Графическое представление такого распределения называется спектральной диаграммой. В технике связи под спектром подразумевается электромагнитный спектр - спектр частот электромагнитного излучения. С середины XX века, с развитием радиотехники, получило развитие другое направление спектральных исследований, связанное с обработкой и анализом первоначально звуковых, а потом и любых произвольных сигналов. Исследования в этом направлении показали, что по характеру распределения значений физической величины спектры могут быть дискретными (линейчатыми), непрерывными (сплошными), а также представлять комбинацию (наложение) дискретных и непрерывных спектров. Если на первоначальном этапе в оптике и в других областях спектры изучались экспериментальными методами, то в технике связи начали исследоваться спектры теоретически. Это произошло в связи с тем, что функции, описывающие электрические сигналы заданы во временной области и могут быть описаны математически. Преобразование Фурье, рождение которого связано с 1822 годом, наконец, благодаря развитию связи получило весьма эффективное применение.
Совершенно очевидно, что различные преобразования речевого сигнала могли появиться лишь после того, как человек научился преобразовывать речевой акустический сигнал в сигнал электрический, а это произошло сравнительно недавно. После рассмотрения спектральных особенностей музыкальных инструментов представляет интерес вопрос об особенностях спектра акустических колебаний возникающего при исполнении конкретного музыкального произведения. Вопрос на первый взгляд кажется странным. Действительно в течение одного концерта пианист исполняет разные произведения, разных композиторов используя всего лишь один заранее настроенный рояль. Откуда же может взяться различие в спектрах акустических колебаний? Однако оно возникает и связано это с понятием тональности. Однако в последние годы начали появляться некоторые данные о том, где и каким образом происходит переработка музыкальной информации. Изучение пациентов с черепно-мозговыми травмами и исследование здоровых людей современными методами нейровизуализации привели учёных к неожиданному выводу: в головном мозге человека нет специализированного центра музыки. В её переработке участвуют многочисленные области, рассредоточенные по всему мозгу, в том числе и те, что обычно задействованы в других формах познавательной деятельности. Размеры активных зон варьируют в зависимости от индивидуального опыта и музыкальной подготовки человека. Автор также лдает ответ на вопрос: "Зачем удаляется несущая частота в спектре передаваемого сигнала?". Удаление боковой полосы АМ сигнала обеспечивает экономное использование пропускной способности линии передачи, а удаление несущей такой экономии не дает, и приводит к необходимости её восстановления на приёмном конце. Объяснение достаточно простое. Усилители кабельной линии должны обеспечить одновременное усиление суммы всех телефонных сигналов. При суммировании значительная часть энергии приходится на несущие частоты. Превышение уровня суммарного сигнала приводит к нелинейным искажениям и взаимным помехам в индивидуальных телефонных каналах.
Таким образом, при построении аналоговых кабельных сетей широко использовался спектральный анализ сигналов, который позволял осуществить оптимальное проектирование.
Ключевые слова: cпектр, оптика, частота,музыка, дискретизация, шум, сигналы..
Литература
1. Уэйнбергер Н. "Музыка и мозг. В чем секрет завораживающей власти музыки?" // В Мире науки, №2, 2006.
2. Ремизов А.Н. Медицинская и биологическая физика. М., 1999, Гл. 8.
3. Газарян С.С. В мире музыкальных инструментов. М. Просвещение, 1989.
4. Аджемов А.С., Хромой Б.П. История развития связи и кибернетики. 2015. № 11. С 68-72.
5. Аджемов А.С., Хромой Б.П. Исторические аспекты аналого-цифрового преобразования. 2015. № 4. С 83-87.
T-Comm Vol.10. #11-2016
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