Periodic signals have their corresponding frequencies and can pass throughFourier series Convert to different frequenciesSine waveAnd.Most signals (periodic or aperiodic) can be usedFourier transformIt is converted into amplitude and phase corresponding to different frequencies. This analysis method considering signal or system frequency related parts is calledfrequency domain。
The characteristics of many physical components will change with the frequency of the input signal. For example, the impedance of the capacitor becomes larger at low frequencies, and smaller at high frequencies. On the contrary, the impedance of the inductance becomes larger at high frequencies, and smaller at low frequencies.OneLinear time invariant systemIts characteristics also change with frequency, so it also has its characteristics in frequency domain,frequency responseIt refers to chord waves with the same input amplitude and different frequencies. The amplitude and phase relative frequency of each frequency output can be plotted to show the characteristics of a system in the frequency domain.
Some systems are defined in frequency domain, for examplelow pass filter Only signals below a certain frequency are allowed to pass.
In electromagnetic field, frequency characteristic refers to the relationship between the secondary field of conductor and the frequency of primary field when other conditions remain unchanged.Using the measured frequency characteristic curve on the abnormal body, the optimal frequency of the abnormal body can be determined;Comparing the measured and theoretical frequency characteristic curves, the obtained data can be semi quantitatively interpreted.In RLC series circuit, inductive reactance and capacitive reactance will change with the change of voltage and frequency, so the mode, impedance angle, current, voltage and other quantities of circuit impedance will change with the change of frequency, which is called frequency characteristic.
Signal bandwidth
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Is the width of the signal spectrum, that is, the difference between the highest frequency component and the lowest frequency component of the signal. For example, for a square wave signal composed of several sine waves, the lowest frequency component is its fundamental frequency, assuming that f=2kHz, and its highest frequency component is its 7th harmonic frequency, that is, 7f=7 × 2=14kHz, so the signal bandwidth is 7f - f=14-2=12kHz.
The signal bandwidth defines the lower limit frequency and upper limit frequency of the signal allowed to pass through the channel, that is, a frequency passband.For example, the allowable passband of a channel is 1.5kHz to 15kHz, and its bandwidth is 13.5kHz. Of course, all frequency components of the above square wave signal can pass through the channel. If attenuation, delay, noise and other factors are not considered, the signal passing through the channel will not be distorted.However, if a square wave with a fundamental frequency of 1kHz passes through this channel, the distortion will be very serious;If the fundamental frequency of the square wave signal is 2kHz, but the highest harmonic frequency is 18kHz, and the bandwidth exceeds the channel bandwidth, its higher harmonics will be filtered out by the channel, and the square wave received through the channel is not of good transmission quality;So, if the fundamental frequency of the square wave signal is 500Hz, the highest frequency component is the 11th harmonic, and the frequency is 5.5kHz, its bandwidth only needs 5kHz, which is far less than the channel bandwidth, can it pass through the channel well?In fact, when the signal is transmitted on the channel, the fundamental frequency is filtered out, and only harmonics can pass through, so the signal waveform must be unsightly.[1]
Through the above analysis and further deduction, we can get some results as follows:
(1) If the signal has the same bandwidth as the channel and the same frequency range, the signal can pass through the channel without losing frequency components;
(2) If the bandwidth is the same but the frequency range is not the same, the frequency component of the signal must not completely pass through the channel (it can be realized by spectrum shifting, that is, modulation);
(3) If the bandwidth is different and the signal bandwidth is less than the channel bandwidth, but all frequency components of the signal are included in the passband range of the channel, the signal can pass through without losing frequency components;
(4) If the bandwidth is different and the signal bandwidth is greater than the channel bandwidth, but the main frequency component containing most of the energy of the signal is included in the passband range of the channel, the signal passing through the channel will lose part of the frequency component, but it may still be recognized, just like the baseband transmission of digital signals and voice signals in the telephone channel transmission;
(5) If the bandwidth is different and the signal bandwidth is greater than the channel bandwidth, and the frequency components containing considerable energy of the signal are not within the passband range of the channel, these signal frequency components will be filtered out, and the signal will be distorted or even severely distorted;
(6) Regardless of whether the bandwidth is the same, if all frequency components of the signal are not within the passband range of the channel, the signal cannot pass;
(7) Regardless of whether the bandwidth is the same, if the signal spectrum is interleaved with the channel passband, and only part of the frequency components pass through, the signal will be distorted.
In addition, when we analyze the signals transmitted on the channel, we cannot always consider them asbandwidthIt must occupy the whole channel, such as frequency band transmission;Even if the signal occupies the whole channel, it may not always be imagined as a square wave, but it may also be other waveforms, such as sending others on a single frequency sine waveanalog signalOr digital signal.Let's give some examples to further clarify the bandwidth of signals and channels.
Scope area
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The first example is still the baseband transmission of digital square wave signals (signals may or may not start from zero until a higher frequency component occupies the entire channel bandwidth, which is usually determined by the upper limit frequency of the channel). We know that the bandwidth of digital square wave signals can be unlimited, but the channel bandwidth is always limited,Therefore, the channel bandwidth defines the signal bandwidth passing through the channel.If the fundamental frequency and partial harmonics of the signal can pass through the channel, generally speaking, the received signal can be identified;If the lower limit frequency of the channel is higher than the fundamental frequency of the signal, the fundamental frequency and even some harmonics will be filtered out. Since the fundamental frequency contains most of the energy of the signal (reflected on the time domain diagram as the waveform with the largest amplitude in all superimposed signal waveforms), the received signal is difficult to identify.Therefore, the channel transmitting square wave requires its lower limit frequency to be lower than the fundamental frequency of the signal.
The second example is the telephone channel. Assume that the frequency range is 300~3300Hz, the bandwidth is 3kHz, and the speech signal spectrum is generally 100Hz~7kHz.The telephone channel pinches the spectrum of the voice signal. Because the main energy of the voice signal is concentrated near some frequency components in the center, the voice signal transmitted through the telephone channel, although distorted, can still be distinguished.
The third example is the telephone line digital carrier, that is, the digital signal is modulated onto the audio frequency carrier signal, which is a sine wave.Telephone line data transmission does not occupy the wholebandwidth, but the middle part of the frequency band, that is, 600~3000Hz, and the bandwidth is 2400Hz.Assumedamplitude modulation (The simplest way is to retain the carrier or remove the carrier in each signal unit to represent the two binary values). If the full duplex communication mode is adopted, the data channel of the telephone line needs to be divided into two parts. Each sub channel occupies 1200Hz bandwidth, one is 600~1800Hz, and the other is 1800~3000Hz;The carrier frequency of the two subchannels is the center frequency of each subchannel, that is, 1200Hz and 2400Hz respectively. In other words, there is a 600Hz sideband on both sides of each center frequency.
Digital frequency modulation and phase modulation technology are more complex. In time domain, the cycle time of each signal unit can be the same as that of amplitude modulation;However, in the frequency domain, the carrier frequency and phase change with the numerical value in each cycle, and the change of signal phase is actually a change of frequency in the amplitude frequency domain diagram.Especially when each signal unit contains multiple bits, multiple frequency components will be generated.When each signal unit contains one bit, each subchannel of digital FM needs two different frequencies to represent binary digits, that is, at 2400HzbandwidthThere are four center frequencies and their sidebands on the data channel of.That is to say, it is divided into four bands, 600~1200Hz, 1200~1800Hz, 1800~2400Hz, 2400~3000Hz;The center frequencies are 900Hz, 1500Hz, 2100Hz and 2700Hz respectively.
The fourth example is the analog carrier of radio amplitude modulation broadcasting, that is, to modulate the original electrical signal generated by audio data such as voice and music to the carrier with a certain broadcasting frequency (actually, the spectrum is shifted from the relatively low 20Hz~20kHz spectrum to the higher 300kHz~3MHz spectrum).The wireless channel uses free space, and the bandwidth seems to be able to reach the entire spectrum, but in fact it is not. First of all, the frequencies of different bands need different propagation modes (surface guided waves, tropospheric scattering, ionospheric reflection, line of sight orientation, spatial forwarding) to achieve the best efficiency, and it is impossible to use such a wide band only in one propagation mode;Secondly, the frequency band span is too large, and the propagation delay of different frequency components is far different, which is not conducive to the correct identification and restoration of signals, and the data rate is also limited because it is difficult to consider both high and low;Moreover, the wireless channel is a shared public broadcast channel. In order to avoid mutual interference between different sources, channel division and allocation must be carried out globally or locally. Each channel divided is widely separated in bandwidth according to different purposes, but no matter how wide, it is very limited;No matter what kind of signal (even the signal with unlimited bandwidth in theory), it does not have to be very wide in actual transmission, but also allows the loss of certain frequency components.The radio AM broadcasting takes the carrier frequency as the center frequency, and regards the original signal as two identicalbandwidthThe sideband (upper and lower sidebands) of is sent to the carrier.[2]
"Bandwidth" indicates the data transmission rate of the channel
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Therefore, the maximum transmission rate of the communication channel and the channelbandwidthThere is a clear relationship between them, so people can replace "speed" with "bandwidth".For example, people often describe the "high data transmission rate" of the network as the "high bandwidth" of the network.So "bandwidth" and "rate" arenetwork techniqueHas become almost synonymous in our discussion.
Related differences
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The signal bandwidth is the width of the signal spectrum, that is, the difference between the highest frequency component and the lowest frequency component of the signal. For example, for a square wave signal superimposed by several sine waves, the lowest frequency component is its fundamental frequency, assuming that f=2kHz, and its highest frequency component is its 7th harmonic frequency, that is, 7f=7 × 2=14kHz, so the signal bandwidth is 7f - f=14-2=12kHz.The channel bandwidth defines the lower limit frequency and upper limit frequency of the signal allowed to pass through the channel, that is, a frequency passband.For example, the allowable passband of a channel is 1.5kHz to 15kHz, and its bandwidth is 13.5kHz. Of course, all frequency components of the above square wave signal can pass through the channel. If attenuation, delay, noise and other factors are not considered, the signal passing through the channel will not be distorted.However, if a square wave with a fundamental frequency of 1kHz passes through this channel, the distortion will be very serious;If the fundamental frequency of the square wave signal is 2kHz, but the highest harmonic frequency is 18kHz, and the bandwidth exceeds the channel bandwidth, its higher harmonics will be filtered out by the channel, and the square wave received through the channel is not of good transmission quality;So, if the fundamental frequency of the square wave signal is 500Hz, the highest frequency component is the 11th harmonic, and the frequency is 5.5kHz, its bandwidth only needs 5kHz, which is far less than the channel bandwidth, can it pass through the channel well?In fact, when the signal is transmitted on the channel, the fundamental frequency is filtered out. Only harmonics can pass through, and the signal waveform is distorted.
