BAND WIDTH
Bandwidth is a measure of frequency range and is typically measured in hertz. Bandwidth is a central concept in many fields, including information theory, radio communications, signal processing, and spectroscopy. Bandwidth is related to channel capacity for information transmission and often the two can be confused. In particular, in common usage "bandwidth" also refers to data (information) transmission rates when communicating over certain media or devices.
[edit] Overview
Bandwidth is a key concept in many applications. In radio communications, for example, bandwidth is the range of frequencies occupied by a modulated carrier wave, whereas in optics it is the width of an individual spectral line or the entire spectral range.
There is no single universal precise definition of bandwidth, as it is vaguely understood to be a measure of how wide a function is in the frequency domain.
For different applications there are different precise definitions. For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero. This would correspond to the mathematical notion of the support of a function (i.e., the total "length" of values for which the function is nonzero). Another definition might not be so strict and ignore the frequencies where the frequency function is small. Small could mean less than 3 dB below (i.e., less than half of) the maximum value, or it could mean below a certain absolute value. As with any definition of the width of a function, there are many definitions available, which are suitable for different applications.
According to the Shannon–Hartley theorem, the data rate of reliable communication is directly proportional to the frequency range of the signal used for the communication. In this context, the word bandwidth can refer to either the data rate or the frequency range of the communication system (or both).
[edit] Analog systems
A graph of a power spectral density, illustrating the concept of 3-dB (or half-power) bandwidth. The vertical axis here is proportional to power (square of Fourier magnitude); the frequency axis of this symbolic diagram can be linear or logarithmically scaled.
For analog signals, which can be mathematically viewed as functions of time, bandwidth Δf is the width, measured in hertz, of the frequency range in which the signal's Fourier transform is nonzero. Because this range of non-zero amplitude may be very broad, this definition is often relaxed so that the bandwidth is defined as the range of frequencies where the signal's Fourier transform has a power above a certain amplitude threshold, commonly half the maximum value (half power -3 dB). Bandwidth of a signal is a measure of how rapidly its parameters (e.g. amplitude and phase) fluctuate with respect to time. Hence, the greater the bandwidth, the faster the variation in the signal parameters may be. The word bandwidth applies to signals as described above, but it could also apply to systems. In the latter case, to say that a system has a certain bandwidth means that the system can process signals of that bandwidth.
A baseband bandwidth is a specification of only the highest frequency limit of a signal. A non-baseband bandwidth is a difference between highest and lowest frequencies.
As an example, the (non-baseband) 3-dB bandwidth of the function depicted in the figure is Δf = f2 − f1, whereas other definitions of bandwidth would yield a different answer.
A commonly used quantity is fractional bandwidth. This is the bandwidth of a device divided by its center frequency. E.g., a device that has a bandwidth of 2 MHz with center frequency 10 MHz will have a fractional bandwidth of 2/10, or 20%.
The fact that real baseband systems have both negative and positive frequencies can lead to confusion about bandwidth, since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as B = 2W, where B is the total bandwidth, and W is the positive bandwidth. For instance, this signal would require a lowpass filter with cutoff frequency of at least W to stay intact.
The 3-dB bandwidth of an electronic filter is the part of the filter's frequency response that lies within 3 dB of the response at its peak, which is typically at or near its center frequency.
In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops to −3 dB.
In basic electric circuit theory when studying Band-pass and Band-reject filters the bandwidth represents the distance between the two points in the frequency domain where the signal is of the maximum signal amplitude (half power).
In photonics, the term bandwidth occurs in a variety of meanings:
the bandwidth of the output of some light source, e.g., an ASE source or a laser; the bandwidth of ultrashort optical pulses can be particularly large
the width of the frequency range that can be transmitted by some element, e.g. an optical fiber
the gain bandwidth of an optical amplifier
the width of the range of some other phenomenon (e.g., a reflection, the phase matching of a nonlinear process, or some resonance)
the maximum modulation frequency (or range of modulation frequencies) of an optical modulator
the range of frequencies in which some measurement apparatus (e.g., a powermeter) can operate
the data rate (e.g., in Gbit/s) achieved in an optical communication system
[edit] Digital systems
In a digital communication system, bandwidth has a dual meaning. In the technical sense, it is slang for baud, the rate at which symbols may be transmitted through the system. It is also used in the colloquial sense to describe channel capacity, the rate at which bits may be transmitted through the system (see Shannon Limit). Hence, a 66 MHz digital data bus with 32 separate data lines may properly be said to have a bandwidth of 66 MHz and a capacity of 2.1 Gbit/s — but it would not be surprising to hear such a bus described as having a "bandwidth of 2.1 Gbit/s." Similar confusion exists for analog modems, where each symbol carries multiple bits of information so that a modem may transmit 56 kbit/s of information over a phone line with a bandwidth of only 12 kHz. A related metric which is used to measure the aggregated bandwidth of a whole network is bisection bandwidth.
In discrete time systems and digital signal processing, bandwidth is related to sampling rate according to the Nyquist-Shannon sampling theorem.
Bandwidth is also used in the sense of commodity, referring to something limited or something costing money. Thus, communication costs bandwidth, and improper use of someone else's bandwidth may be called bandwidth theft.
When Additive white Gaussian noise is present in a digital communication channel, the Shannon–Hartley theorem gives the relationship between the channel's bandwidth, the channel's capacity, and the Signal-to-noise ratio (SNR) ratio of the system.
[edit] Meaning of bandwidth in web hosting
In website hosting, bandwidth is the amount of data that can be transferred to or from the website, measured in bytes transfered over a prescribed period of time. Web hosting companies often quote a monthly bandwidth limit for a website, for example 100 gigabytes per month. If visitors to the website download a total greater than 100 gigabytes in one month, the bandwidth limit will have been exceeded.
NARROW BAND
Narrowband (narrow bandwidth) refers to a signal which occupies only a small amount of space on the radio spectrum — the opposite of broadband or wideband.
This is entirely relative to what is being described; for example, an FM broadcast station takes up 150–200 kHz on the FM band, whereas a TV station's audio is narrowband, taking up only 25 kHz, and weatheradio broadcasts are even narrower than that. It is also very often used to describe radio antennas, called narrowband when they are designed specifically for one frequency or channel only instead of a wide range.
Narrowband can also be used with the audio spectrum to describe sounds which occupy a narrow range of frequencies. In telephony narrowband is usually considered to cover frequencies 300–3400 Hz.
In the study of wireless channels, narrowband implies that the channel under consideration is sufficiently narrow that the fading across it is flat (i.e. constant). It is usually used as an idealizing assumption; no channel has perfectly flat fading, but the analysis of many aspects of wireless systems is greatly simplified if flat fading can be assumed.
WIDE BAND OR BROAD BAND
Broadband in telecommunications is a term which refers to a signaling method which includes or handles a relatively wide range of frequencies which may be divided into channels or frequency bins. Broadband is always a relative term, understood according to its context. The wider the bandwidth, the more information can be carried. In radio, for example, a very narrowband signal will carry Morse code; a broader band will carry speech; a yet broader band is required to carry music without losing the high audio frequencies required for realistic sound reproduction. A television antenna described as "normal" may be capable of receiving a certain range of channels; one described as "broadband" will receive more channels. In data communications a modem will transmit a bandwidth of 64 kilobits per seconds (kbit/s) over a telephone line; over the same telephone line a bandwidth of several megabits per second can be handled by ADSL, which is described as broadband (relative to a modem over a telephone line, although much less than can be achieved over a fibre optic circuit, for example).
edit] Introduction
Broadband in data communications may have the same meaning as above, so that data transmission over a fibre optic cable would be referred to as broadband as compared to a telephone modem operating at 600 bits per second.
However, broadband in data communications is frequently used in a more technical sense to refer to data transmission where multiple pieces of data are sent simultaneously to increase the effective rate of transmission, regardless of actual data rate. In network engineering this term is used for methods where two or more signals share a medium.
Various forms of Digital Subscriber Line service are broadband in the sense that digital information is sent over one channel and voice over another channel sharing a single pair of wires. Analog modems operating at speeds greater than 600 bit/s are technically broadband. They obtain higher effective transmission rates by using multiple channels with the rate on each channel limited to 600 baud. For example, a 2400 bit/s modem uses four 600 baud channels (see baud). This is in contrast to a baseband transmission where one type of signal uses a medium's full bandwidth such as 100BASE-T Ethernet. Fibre optic cables are of no use
[edit] Multiplexing
Communications may utilize a number of distinct physical channels simultaneously; this is multiplexing for multiple access. Such channels may be distinguished by being separated from each other in time (time division multiplexing or TDMA), in carrier frequency (frequency division multiplexing (FDMA) or wavelength division multiplexing (WDM)), or in access method (code division multiplexing or CDM). Each channel that takes part in such a multiplexing exercise is by definition narrowband (because it is not utilising the whole bandwidth of the medium), whereas the whole set of channels taken together and utilized for the same communication could be described as broadband.
BASE BAND SIGNALS
Baseband
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Baseband is an adjective that describes signals and systems whose range of frequencies is measured from 0 to a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies starting at 0. It can often be considered as synonym to lowpass, and antonym to passband.
A baseband bandwidth is equal to a highest frequency of a signal or system, or an upper bound on such frequencies. By contrast, a non-baseband (passband) bandwidth is the difference between a highest frequency and a nonzero lowest frequency.
A baseband signal or lowpass signal is a signal that can include frequencies that are equal to or very near zero, by comparison with its highest frequency (for example, a sound waveform can be considered as a baseband signal, whereas a radio signal is not).
A baseband channel or lowpass channel (or system, or network) is a channel (e.g. a telecommunications system) that can transfer frequencies that are equal to or very near zero. Examples are serial cables and local area networks (LANs).
Baseband modulation, also known as line coding, aims at transferring a digital bit stream over an analog baseband channel.
An equivalent baseband signal or equivalent lowpass signal is – in analog and digital modulation methods with constant carrier frequency (for example ASK, PSK and QAM but not FSK) – a complex valued representation of the modulated physical signal (the so called passband signal or RF signal). The equivalent baseband signal is
Z(t) = I(t) + jQ(t),where I(t) is the inphase signal, Q(t) the quadrature phase signal, and j the imaginary unit. In a digital modulation method, the I(t) and Q(t) signals of each modulation symbol are evident from the constellation diagram. The physical passband signal corresponds to
I(t)cos(ωt) + Q(t)sin(ωt) = real(Z(t)ejωt),where ω is the carrier angular frequency in rad/s.
A signal "at baseband" is usually considered to include frequencies from near 0 Hz up to the highest frequency in the signal with significant power.
In general, signals can be described as including a whole range of different frequencies added together. In telecommunications in particular, it is often the case that those parts of the signal which are at low frequencies are 'copied' up to higher frequencies for transmission purposes, since there are few communications media that will pass low frequencies without distortion. Then, the original, low frequency components, are referred to as the baseband signal. Typically, the new, high-frequency copy is referred to as the 'RF' (radio-frequency) signal.
The concept of baseband signals is most often applied to real-valued signals, and systems that handle real-value signals. Fourier analysis of such signals includes a negative-frequency band, but the negative-frequency information is just a mirror of the positive-frequency information, not new information. For complex-valued signals, on the other hand, the negative frequencies carry new information. In that case, the full two-sided bandwidth is generally quoted, rather than just the half measured from zero; the concept of baseband can be applied by treating the real and imaginary parts of the complex-valued signal as two different real signals.
A signal at baseband is often modulated in order that it may be transmitted. Modulation results in shifting the signal up to much higher (RF) frequencies than it originally spanned. A key consequence of the usual double-sideband amplitude modulation (AM) is that, usually, the range of frequencies the signal spans (its spectral bandwidth) is doubled. Thus, the RF bandwidth of a signal (measured from the lowest frequency as opposed to 0 Hz) is usually twice its baseband bandwidth. Steps may be taken to reduce this effect, such as single-sideband modulation; the highest frequency of such signals greatly exceeds the baseband bandwidth.
Some signals can be treated as baseband or not, depending on the situation. For example, a switched analog connection in the telephone network has energy below 300 hertz and 3400 hertz removed by bandpass filtering; since the signal has no energy very close to zero frequency, it may not be considered a baseband signal, but in the telephone systems frequency-division multiplexing hierarchy, it is usually treated as a baseband signal, by comparison with the modulated signals used for long-distance transmission. The 300 Hz lower band edge is this case is treated as "near zero", being a small fraction of the upper band edge.
The figure shows what happens with AM modulation:
Comparison of the baseband version of a signal and its RF version, showing the typical doubling of the occupied bandwidth.
The simplest definition is that a signal's baseband bandwidth is its bandwidth before modulation and multiplexing, or after demultiplexing and demodulation.
The composite video signal created by devices such as most newer VCRs, game consoles and DVD players is a commonly used baseband signal.
Friday, November 23, 2007
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