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However, the combination of a resistor and a capacitor (an RC circuit, a common low-pass filter) has what is called kTC noise. The noise bandwidth of an RC circuit is =. [7] When this is substituted into the thermal noise equation, the result has an unusually simple form as the value of the resistance (R) drops out of the equation.
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.
Noise reduction, the recovery of the original signal from the noise-corrupted one, is a very common goal in the design of signal processing systems, especially filters. The mathematical limits for noise removal are set by information theory .
Taking into account both noise and bandwidth limitations, however, there is a limit to the amount of information that can be transferred by a signal of a bounded power, even when sophisticated multi-level encoding techniques are used. In the channel considered by the Shannon–Hartley theorem, noise and signal are combined by addition.
If one desired to sample an FM radio broadcast centered at 87.9 MHz and bandlimited to a 200 kHz band, then an appropriate anti-alias filter would be centered on 87.9 MHz with 200 kHz bandwidth (or passband of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz, but should also satisfy other constraints to prevent aliasing.
The noise equivalent bandwidth (or equivalent noise bandwidth (enbw)) of a system of frequency response is the bandwidth of an ideal filter with rectangular frequency response centered on the system's central frequency that produces the same average power outgoing () when both systems are excited with a white noise source. The value of the ...
To derive the criterion, we first express the received signal in terms of the transmitted symbol and the channel response. Let the function h(t) be the channel impulse response, x[n] the symbols to be sent, with a symbol period of T s; the received signal y(t) will be in the form (where noise has been ignored for simplicity):
Research has mostly focused on studying additive noise channels under certain power constraints and noise distributions, as analytical methods are not feasible in the majority of other scenarios. Hence, alternative approaches such as, investigation on the input support, [ 6 ] relaxations [ 7 ] and capacity bounds, [ 8 ] have been proposed in ...