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_Signal_FAQ18_Sampling_Frequency_&amp;_Nyquist_Rule

# _Signal_FAQ18_Sampling_Frequency_&amp;_Nyquist_Rule -...

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Must the Nyquist rule be always obeyed? The Nyquist rule is a simple one and is formulated for signal which is low pass in nature. Consider a signal with spectrum as shown below. The signal occupies a band from 20 - to 20 kHz, and has an absolute one-sided bandwidth of 20 kHz. Thus, using Nyquist rule, the signal must be sampled at a minimum of 40 kHz in order that the resulting sampled digital signal can be used to re-construct the original analog signal perfectly. This simple Nyquist rule, however, is not appropriate if the signal is, for example, band pass in nature Consider, say, a signal with the following spectrum. If this signal is treated in the same way as the previous low pass example and the simple Nyquist rule is used, we will need a sampling frequency of at least 80 kHz. This is much more than two times the absolute one-sided bandwidth of 10 kHz. In fact, sampling at 20 kHz will be good enough for this case. To prove this, sketch the spectrum after digitization at 20 kHz and see that there is no aliasing and so re-

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_Signal_FAQ18_Sampling_Frequency_&amp;_Nyquist_Rule -...

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