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Here is a signal, x(t) with X(w) = 0 when |W| > Wm.

With sampling period, T, samples of x(t),x(nT), can be obtained from x(t), where n = 0 +-1, +-2, ....

The sampling frequency is $ frac{2*/pi}{T} $. It is called Ws.

If Ws is greater than 2Wm, x(t) can be recovered from its samples.

Here, 2Wm is called the "Nyquist rate".

To recover, first we need a filter with amplited T when |W| < Wc.

Wc has to exist between Wm and Ws-Wm.

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

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