Spectrum is the abbreviation of frequency spectral density, which is the distribution curve of frequency.Complex oscillations are decomposed into harmonic oscillations with different amplitudes and frequencies. The graph of the amplitude of these harmonic oscillations arranged by frequency is called spectrum.Spectrum is widely used in optics and radio technology.Spectrum introduces the research of signal from time domain to frequency domain, which brings more intuitive understanding.The spectrum decomposed from complex mechanical vibration is called mechanical vibration spectrum, the spectrum decomposed from acoustic vibration is called acoustic spectrum, the spectrum decomposed from optical vibration is called spectrum, and the spectrum decomposed from electromagnetic vibration is called electromagnetic spectrum. Generally, the spectrum is included in the scope of electromagnetic spectrum.Many basic properties of the complex vibration can be understood by analyzing the spectrum of various vibrations, so spectrum analysis has become a basic method for analyzing various complex vibrations.
Spectrum, also called vibration spectrum[1]。The most basic physical quantity reflecting vibration phenomenon isfrequencySimple periodic vibration has only one frequency.Complex motion can not be described with a frequency, as shown in the left figure in Figure 1 and Figure 2 below. Moreover, we can not quantitatively describe their characteristics from the vibration graph. Usually, spectrum is used to describe a complex vibration.Any complex vibration can be decomposed into many different amplitudes and frequenciesSimple harmonic vibrationThe sum of.In order to analyze the nature of the actual vibration, the image formed by arranging the amplitude of the component vibration according to its frequency is called the spectrum of the complex vibration.In the vibration spectrum, abscissa represents fractional vibrationCircular frequency, the ordinate represents the partial vibrationamplitude。For periodic complex vibration, its frequency isf, then followFourier Theorem, the frequency of each simple harmonic vibration decomposed by it is an integral multiple of f, that isf，2f，3f，4f,..., whose vibration spectrum is discrete linear spectrum, and each line in the figure is calledSpectral line。For non periodic vibration (e.gDamped vibrationOr short shock), as perFourier integralIt can be decomposed into the sum of infinitely many simple harmonic vibrations with continuous frequency distribution.As the spectral lines become infinite, the vibration spectrum is no longer a discrete linear spectrum, and each spectral line is dense to form a continuous curve at the top, that is, to form the so-calledContinuous spectrum, the continuous spectral curve is theEnvelope;It may also be decomposed into frequencyConcordanceMany simple harmonic vibrations form discrete spectra.[1]
Figure 1 and Figure 2
Figure 1 shows the zigzag vibration and vibration spectrum.Figure 2 shows the damped vibration and vibration spectrum.[1]
Video explanation
Video for explaining the concept of signal spectrum in micro class.[2]
The concept of signal spectrum includes strong mathematical theories (Fourier transformFourier series Etc.);It also has a clear physical meaning (including harmonic composition, amplitude frequency, phase frequency, etc.).This video (less than 20 minutes) covers the origin, development, theoretical basis and practical application of the signal spectrum, which can be integrated by itself.This video is suitable for all kinds of practitioners with different backgrounds to help them appreciate the essence of signal spectrum in a short time.
How many pairs of users can make calls at the same time per cell per MHz;For data services, it is defined as the maximum transmission rate per cell per MHz.Here, the frequency reuse coefficient of the cellfVery important: The lower the f, the greater the degree of freedom of the frequency available for each cell.stayCDMA systemEach cell can reuse the samefrequency band(f=1)。The total interference to each mobile station in a cell is the interference from other mobile stations in the same cell plus all mobile stations in the adjacent cellSum of interferences。
Electromagnetic wave spectrum
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Optical spectrum
Fig. 4 Spectrum diagram of output signal
Simulated natural light spectrum pattern spectrum, fully called optical spectrum, isPolychromatic lightThrough dispersion system (such as gratingPrism）The pattern formed after light splitting is arranged in order according to the frequency (or wavelength) of light.The largest part of the spectrumvisible lightSpectrum isElectromagnetic spectrumThe part visible to the human eye in this frequency rangeelectromagnetic radiationIt is called visible light.The spectrum does not contain all the colors that human brain vision can distinguish, such as brown and gray.
principle
The polychromatic light has various frequencies (or wavelengths) of light, which have different refractive indexes in the medium.Therefore, when polychromatic light passes through a medium with a certain geometric shape (such as a prism), light with different frequencies will have dispersion due to different exit angles, projecting continuous or discontinuous color bands.
The principle that sunlight is separated by a prism is also used in the famous dispersion experiment of sunlight.The sunlight appears white when it passes throughprismAfter refraction, a color spectrum consisting of red, orange, yellow, green, blue, indigo and purple will be formed, covering the visible light area of about 300~750THz.Historically, this experiment was conducted by British scientistsIsaac NewtonJazz was completed in 1665, making people first contact withlightThe objective and quantitative characteristics of.
Spectral classification
1. By frequency area
Figure 5 Spread spectrum mode (ssm)
Outside the red end of some visible spectra, there are infrared rays with lower frequency;Similarly, outside the ultraviolet end, there is a higher frequency of ultraviolet rays.For infrared and ultraviolet rays, the resonance frequency of our optic nerve cannot reach these two limits, so both infrared and ultraviolet rays cannot be detected by the naked eye, but can be recorded by instruments.Therefore, exceptVisible spectrumThe spectrum also includes infrared spectrum and ultraviolet spectrum.
Some objects can emit light on their own. The spectrum formed by the light directly generated by them is called emission spectrum.
The emission spectrum can be divided into three different categories:Linear spectrum、Banded spectrumandContinuous spectrum。Linear spectrum is mainly generated fromatom, composed of some discontinuous bright lines;Banded spectrum is mainly produced by the fact that molecules are composed of some dense light within a certain frequency range;Continuous spectrum is mainly generated fromIncandescenceThe excited solid, liquid or high-pressure gas emits electromagnetic radiation, which is composed of light of all frequencies distributed continuously.
Fig. 6 Spread spectrum+ael
The solar spectrum is a typical absorption spectrum.Because when the strong light emitted from the inside of the sun passes through the lower temperature solar atmosphere, various atoms in the solar atmosphere will absorb light of certain frequencies, resulting in dark lines in the generated spectrum.As white light passes through the gas, the gas will absorb itsCharacteristic spectral lineLight with the same frequency, which makes white light formContinuous spectrumA dark line appears in the.At this time, the spectrum generated after the light of certain frequencies in the continuous spectrum is absorbed by the material is called the absorption spectrum.Normally, whenabsorption spectrumThe characteristic spectrum lines seen in will be less than the linear spectrum.
When light strikes a substanceInelastic scattering, except excitation in scattered lightlightIn addition to the elastic components (Rayleigh scattering) with the same frequency, there are components with higher and lower frequencies than the excitation light. The latter phenomenon is collectively called Raman effect.This phenomenon was discovered by Indian scientist Raman in 1928, so this kind ofLight scatteringgo by the name ofRaman scatteringThe resulting spectrum is calledRaman spectraOr Raman scattering spectrum.
3. According to the nature of production
Figure 7 ofdm spectrum
According to the nature of production, spectrum can be divided into molecular spectrum andAtomic spectrum。
In the molecule, the energy of the electronic state is 50-100 times greater than that of the vibrational state, and the energy of the vibrational state is 50-100 times greater than that of the rotational state.Therefore, the transition between the electronic states of molecules is always accompanied by vibration transition and rotation transition, so manySpectral lineThey are clustered together to form a molecular spectrum.Therefore, molecular spectrum is also called band spectrum.
In an atom, when the atom rises from the ground state to a higher energy state in some way, the energy inside the atom increases, and these excess energy will be emitted in the form of light, thus generating the atomic emission spectrum, that is, atomic spectrum.Because the change of atomic energy state is discontinuousQuantum propertyThe resulting spectrum is also composed of some discontinuous bright lines, so the atomic spectrum is also called linear spectrum.
Radio spectrum
Figure 8 Bioimpedance Spectrum Measurement System
The spectrum resource of radio is also calledFrequency resources, usually refers to long wave, medium waveshortwave, ultrashort wave and microwave.Generally, it refers to the transmission within the frequency range of 9KHz-3000GHzradio wavesThe general term for radio frequencies of.radioFrequency inHz(Hz), expressed as:
―― Above 3MHz to 3000MHz (including 3000MHz), expressed in MHz (megahertz);
―― Above 3GHz to 3000GHz (including 3000GHz), expressed in GHz (Gigahertz).
Radio spectrum division
Figure 9 Radio spectrum and band division
Mechanical wave (sound) spectrum
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frequency range
Short wave band
The amplitude of this band affects the expressiveness of voice.If the amplitude of this frequency band is relatively large, the resolution is good.The amplitude of this frequency band is not very large, that is, the intensity is not very large, but it has a great impact on voice color, so it is valuable and important.
Medium short band
It affects the coolness (coldness) of the voice.If there are too few components in this band, the timbre will become warm;If the frequency band composition is too high, the timbre will become cold.
Medium and long band
This frequency band is more sensitive to human hearing.If there are many bands, the timbre will be mellow and warm.The performance is strong and the intensity is strong.If this band is lacking, its timbre will become cold and empty;If the frequency is too strong, the timbre will become stiff and unnatural.Because this component is too strong, the relative strength of other components becomes weak, so the timbre lacks lubricity.
Long wave band
If there are more long wave bands, the timbre will become hot and have a sense of space, because the whole room has wavelength, and all are long wave areas;If there are more frequency components, people will naturally associate with the space propagation state of the room.If this frequency component is lacking, the timbre will appear pale and cold;If there are too many components in this frequency, the monophonic sound will appear too hot.
