Signal bandwidth and channel bandwidth
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 composed of several sine waves, the lowest frequency component is its fundamental frequency, which is assumed to be f = 2kHz, 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 frequency and upper frequency of the signal allowed to pass through the channel, that is, a frequency pass band. For example, the allowable passband of a channel is 1.5kHz to 15kHz, and its bandwidth is 13.5kHz. Of course, all the frequency components of the above square wave signal can pass through the channel. If attenuation, delay, noise and other factors are not considered, pass this channel The signal will be undistorted. However, if a square wave with a fundamental frequency of 1 kHz, the distortion will definitely be severe through this channel; if the fundamental frequency of a square wave signal is 2 kHz, but the highest harmonic frequency is 18 kHz, the bandwidth exceeds the channel bandwidth, and its higher harmonics will Filtered by the channel, the quality of the square wave received through this channel is not good; then, if the fundamental frequency of the square wave signal is 500Hz, the highest frequency component is the 11th harmonic frequency is 5.5kHz, and its bandwidth only needs 5kHz, It is much smaller 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 the harmonics can pass, and the signal waveform must be unsightly.
Through the above analysis and further inference, some results can be obtained:
(1) If the signal and channel bandwidth are the same and the frequency range is consistent, the signal can pass through the channel without losing frequency components;
(2) If the bandwidth is the same but the frequency range is inconsistent, the frequency component of the signal must not completely pass through the channel (it can be considered to be realized by spectrum shift, that is, modulation);
(3) If the bandwidth is different and the signal bandwidth is less than the channel bandwidth, but all the frequency components of the signal are included in the passband of the channel, the signal can pass without losing the frequency component;
(4) If the bandwidth is different and the signal bandwidth is greater than the channel bandwidth, but the main frequency component that contains most of the energy of the signal is included in the passband of the channel, the signal passing through the channel will lose part of the frequency component, but it may still be recognized, as The baseband transmission of digital signals and the transmission of voice signals over the telephone channel;
(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 of the channel, these signal frequency components will be filtered out, and the signal distortion or even severe distortion;
(6) Regardless of whether the bandwidth is the same, if all frequency components of the signal are not within the passband of the channel, the signal cannot pass through;
(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 component passes, the signal is distorted.
In addition, when we analyze the signal transmitted on the channel, we cannot always think that its bandwidth must occupy the entire channel, such as frequency band transmission; even if the signal occupies the entire channel, it may not always be imagined as a square wave. It may be other waveforms, such as a composite waveform formed by carrying other analog signals or digital signals on a single frequency sine wave. Let us give some more examples to further clarify the signal and channel bandwidth issues.
The first example is still the baseband transmission of a digital square wave signal (the signal may or may not start at zero frequency until a certain higher frequency component occupies the entire channel bandwidth, which is usually determined by the upper limit of the channel Frequency determination), we know that the digital square wave signal bandwidth can be unlimited, but the channel bandwidth is always limited, so the channel bandwidth defines the signal bandwidth through the channel. If the fundamental frequency and some harmonics of the signal can pass through the channel, generally speaking, the received signal can be identified; if the lower frequency of the channel is higher than the fundamental frequency of the signal, then the fundamental frequency and even some harmonics are filtered out, Since the fundamental frequency contains most of the energy of the signal (which is reflected in the time-domain diagram as the waveform with the largest amplitude of all superimposed signal waveforms), the received signal is difficult to identify. Therefore, the channel transmitting the square wave requires that the lower limit frequency is lower than the fundamental frequency of the signal.
The second example is the telephone channel, assuming a frequency range from 300 to 3300 Hz and a bandwidth of 3 kHz, while the voice signal spectrum is generally in the range of 100 Hz to 7 kHz. The telephone channel truncates the speech signal spectrum. Because the main energy of the speech signal is concentrated near some frequency components in the center, the speech signal transmitted through the telephone channel can be distinguished although it is distorted.
The third example is a telephone line digital carrier, which modulates a digital signal onto an audio carrier signal, which is a sine wave. Telephone line data transmission does not occupy the entire bandwidth, but takes the middle part of the frequency band, that is 600 ~ 3000Hz, bandwidth 2400Hz. Assuming that amplitude modulation is used (the simplest way is to represent the two values ​​of binary by retaining the carrier or removing the carrier in each signal unit), if the full-duplex communication method is used, the telephone line data channel needs to be divided into two , Each sub-channel occupies a bandwidth of 1200Hz, one 600 ~ 1800Hz, the other 1800 ~ 3000Hz; the carrier frequency of the two sub-channels is the center frequency in each sub-channel, namely 1200Hz and 2400Hz, in other words, each center frequency There is a 600 Hz sideband on each side.
Digital frequency modulation and phase modulation techniques are more complicated. In the time domain, the cycle time of each signal unit can be the same as the amplitude modulation; but from the frequency domain, the carrier frequency and phase in each cycle are expressed as The value of the signal changes and the signal phase changes actually appear as a frequency change on the amplitude-frequency domain diagram. Especially when each signal unit contains multiple bits, multiple frequency components are generated. For the case where each signal unit contains 1 bit, each subchannel of digital frequency modulation requires two different frequencies to represent binary digits, that is, there are four center frequencies and their sidebands on a 2400 Hz bandwidth data channel. That is to say, it is divided into four frequency bands, 600 ~ 1200Hz, 1200 ~ 1800Hz, 1800 ~ 2400Hz, 2400 ~ 3000Hz; the center frequency is 900Hz, 1500Hz, 2100Hz and 2700Hz respectively.
The fourth example is the analog carrier of wireless AM broadcasting, that is, the original electrical signal generated by audio data such as voice and music is modulated onto a carrier with a certain broadcast frequency (actually, the spectrum is shifted, and the relatively low 20Hz ~ 20kHz spectrum Relocated to the higher 300kHz ~ 3MHz spectrum). The wireless channel uses free space, and the bandwidth seems to reach the entire frequency spectrum, but in fact it is not the case. First, different frequency bands require different propagation methods (surface-guided waves, tropospheric scattering, ionospheric reflection, line-of-sight, space forwarding) In order to achieve the best efficiency, it is impossible to use such a wide frequency band with only one propagation method; secondly, the frequency band span is too large, and the propagation delay of different frequency components differs greatly, which is not conducive to the correct identification and restoration of the signal, and the data rate is also It is limited due to the difficulty of taking into consideration the height; furthermore, the wireless channel is a shared public broadcast channel. In order to avoid the mutual interference of different sources, channel division and allocation must be performed in the global or local scope, and each channel divided According to different uses, its bandwidth is very large, but no matter how wide, it is very limited; no matter what kind of signal (even a theoretically unlimited bandwidth signal) does not have to be very wide in actual transmission, it is also allowed for loss Certain frequency components. The wireless AM broadcast takes the carrier frequency as the center frequency, and the original signal is carried on the carrier as two sidebands (upper and lower sidebands) of the same bandwidth. The total bandwidth of the modulated AM signal is twice that of the original signal.
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