nyquist rate of sin(200πt)


What is the Nyquist rate?

    The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called the Nyquist rate. Determine the Nyquist rate corresponding to each of the following signals: x(t) = 1 + cos(3,000?t) + sin(6,500?t) 4S. Let x(t) be a signal with Nyquist rate wo. Determine the Nyquist rate for each of the following signals:

Can x(t) be a sinusoid at a lower frequency?

    After sampling at frequency There are no other sinusoidal signals with fundamental frequencies less than 1KHz that have exactly the same samples as those in previous two examples. Thus, for these sampling rates any fundamental frequencycan be uniquely identified With only 2 samples/cycle we may confuse x(t) with a sinusoid at lower frequency (0Hz).

What is the sampling rate of x(t)?

    This implies that if x(t) has a spectrum as indicated in figure (a) then x(t) must be samples at a rate greater than 2w2. However, since the signal has most of its energy concentrated in a narrow band, it would seem reasonable to expect that a sampling rate lower than twice the highest frequency could be used.
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