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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.
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.
is the noise spectral density, the noise power in a 1 Hz bandwidth, measured in watts per hertz or joules. These are the same units as E b {\displaystyle E_{b}} so the ratio E b / N 0 {\displaystyle E_{b}/N_{0}} is dimensionless ; it is frequently expressed in decibels .
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.
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.
But they also tend to be highly correlated with the total leakage, which is quantifiable. It is usually expressed as an equivalent bandwidth, B. It can be thought of as redistributing the DTFT into a rectangular shape with height equal to the spectral maximum and width B. [A] [3] The more the leakage, the greater the bandwidth.
OVER: noise interpreted as speech due to the VAD flag remaining active in passing from speech activity to noise; NDS (Noise Detected as Speech): noise interpreted as speech within a silence period. Although the method described above provides useful objective information concerning the performance of a VAD, it is only an approximate measure of ...
Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction and sample-rate reduction. [ 1 ] [ 2 ] When the process is performed on a sequence of samples of a signal or a continuous function, it produces an approximation of the sequence that would have been obtained by ...