| Nyquist Frequency |
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In principle, a Nyquist frequency just larger than the signal bandwidth is sufficient to allow perfect reconstruction of the signal from the samples. However, this reconstruction requires an unrealizable filter that passes some frequencies unchanged while suppressing all others completely (commonly called a Brickwall Filter ). When realizable filters are used, some degree of Oversampling is necessary to accommodate the practical constraints on Anti-aliasing Filter s. Even with oversampling, the Nyquist frequency is half the sampling frequency, however some textbooks have defined the Nyquist freqency as the upper bound of frequencies with non-zero amplitude (or the bandwidth) independent of the sampling rate, but this alternative (and substantively different) definition is not as common. For example, audio CDs have a sampling frequency of 44,100 Hz . The Nyquist frequency is therefore 22,050 Hz, which is just larger than the highest frequency the data can accurately produce (again if the anti-aliasing filter is perfect). For example, if the chosen anti-aliasing filter (a Low-pass Filter in this case) has a Transition Band of 2,000 Hz then the Cut-off Frequency should be no higher than 20,050 Hz to yield a signal with negligible power at frequencies of 22,050 Hz and greater. It should be noted that the Nyquist frequency must be strictly ''greater'' than the maximum frequency component within the signal. If the signal contains a frequency component at precisely the Nyquist frequency then the corresponding component of the sample values can not have sufficient information to reconstruct the Nyquist component in the Continuous-time signal because of phase ambiguity. In such a case, there would be an infinite number of possible and ''different'' sinusoids (of varying amplitude and phase) of the Nyquist frequency component that are represented by the discrete samples. This is because : all have samples of alternating -1 and +1 for any θ and there is no way to determine both the amplitude and the phase of the continuous-time sinusoid that ''x'' {Link without Title} was sampled from. SEE ALSO |
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