What is the Nyquist criterion
Nyquist criterion is to eliminate the code crosstalk, and the baseband transmission system impact response H (t) has the maximum value only in the sample element sampling, and is 0 in the sample time of other symbols, that is, according to H (T The correspondence between ← → H (JW), which will be brought to the frequency domain, and the system function is transmitted when there is no code crosstalk.
Three Nyquist criterion
Nyquist first criterion: no distortion criterion sampling points, or no intersymbol interference (ISIFree) Guidelines
The second Nyquist criterion: no distortion criterion transition point or no jitter (JitterFree) Guidelines
The third Nyquist criterion: the waveform area without distortion criterion.
The first criterion: the sample values without distortion
That is, if the entire transmission signal waveform changes, as long as the value of its specific sampling points remains the same, then the re-sampling method may still accurately recover the original letter code. Nyquist first criterion of a predetermined threshold over a channel with a low cut-off frequency channel is fH, without interference between the maximum limit of the transmission rate of 2fH. For example, the channel bandwidth is 2000Hz, you can transmit up to 4000 binary symbols per second. One digital telephone rate of 64kbit / s, channel bandwidth no inter-code interference is 32kHz.
The second criterion: lossless conversion point
In certain controllably symbol sampling time introduced intersymbol interference, whereas in the remaining symbol sampling time point without inter-symbol interference, can make the theoretical maximum bandwidth efficiency, while at the same timing accuracy requirements for reducing . Usually satisfies the Nyquist criterion a second wave called a partial response waveform. Utilizing partial response waveform transmitted baseband transmission system, referred to as partial response system.
The third criterion: the pulse waveform area remains unchanged
That is, if one symbol interval of the received waveform transmission area is proportional to the amplitude of the rectangular pulses, other pulses transmitted symbol interval area within this symbol interval is zero, the receiver can recover the original signal without distortion code.
Relationship with Shannon theorem
Nyquist criterion: for a bandwidth W (Hz) of the low-noise-free communication channel, the maximum transmission rate Bmax of the symbols:
Bmax = 2W (band)
If the symbol number of states of the coding scheme is M, obtain transmission rate limit information (channel capacity) Cmax:
Cmax = 2Wlog2M (b / s)
Since the channel is always noisy, and therefore the Nyquist criterion given theoretical limit.
Shannon's theorem Profile
Cmax = Wlog2 (1 + S / N) (b / s) S is the average power of the channel signal to be transmitted, N is the Gaussian noise power inside the channel
Shannon's theorem described with limited bandwidth, maximum transmission rate of the channel bandwidth and random thermal noise of the channel, the relationship between the signal to noise power ratio.
When a data signal transmitted over a channel random thermal noise, and data rate Rmax channel bandwidth B, S / N ratio relationship: Rmax = B * log2 (1 + S / N). Note here log2 is logarithm of 2, the same below.
In the relevant fields of signal processing and information theory, the How to decay after a certain distance by studying how much data signal and a reference signal can be loaded to get a well-known formula called Shannon (Shannon) theorem. It gives a speed link in the form of bits per second (bps) the upper limit is expressed as a function of signal to noise ratio of the link, the link signal to noise ratio in decibels (dB) measured. Therefore, we can use Shannon detected data rate telephone lines.
Shannon given reasons given by the following equation: C = B * log2 * (1 + S / N) where C is the available link speed, B is the link bandwidth, S is the average signal power, N is the average noise power , signal to noise ratio (S / N) is usually expressed in decibels (dB), the number of dB = 10 × log10 (S / N).
Audio telephone connection typically supported frequency range is 300Hz to 3300Hz, then B = 3300Hz-300Hz = 3000Hz, and general link signal to noise ratio is typically 30dB, i.e., S / N = 1000, we have C = 3000 × log2 ( 1+ 1000), is approximately equal to 30Kbps, 28.8Kbps modem is the limit, so the telephone network if the SNR is not improved or not using a compression method, the modem will not reach the higher rate. Read more
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