(New page: == Nyquist Rates == In order to find the Nyquist rate of a signal given x(t): We will first find the fourrier transform X(w) and plot out its signal over a period of frequency Wm. Once...) |
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In order to find the Nyquist rate of a signal given x(t): | In order to find the Nyquist rate of a signal given x(t): | ||
| − | We will first find the fourrier transform X( | + | We will first find the fourrier transform X(W) and plot out its signal over a period of frequency Wm. |
Once the Wm is found, then it is to be multiplied by two and that is the total given nyquist rate. | Once the Wm is found, then it is to be multiplied by two and that is the total given nyquist rate. | ||
| − | + | ||
| + | 2Wm is known as the total Nyquist rate. | ||
| + | Using the sampling theorem we know that if we let x(t) be a band limited signal with X(jW) = 0 for |W| > Wm, then x(t) is uniquely determined to be from X(nT): n=0,1,-1,2,-2...etc. as long as Ws > 2Wm | ||
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| + | and Ws = <math> \frac{2* \pi}{T} </math> | ||
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| + | Since we have the Wm and the original signal to be recovered we know that the cutoff frequency is greater than Wm and less than Ws - Wm. We process this signal through a lowpass filter and receive the output signal that is exactly x(t). | ||
Latest revision as of 19:06, 17 November 2008
Nyquist Rates
In order to find the Nyquist rate of a signal given x(t):
We will first find the fourrier transform X(W) and plot out its signal over a period of frequency Wm.
Once the Wm is found, then it is to be multiplied by two and that is the total given nyquist rate.
2Wm is known as the total Nyquist rate.
Using the sampling theorem we know that if we let x(t) be a band limited signal with X(jW) = 0 for |W| > Wm, then x(t) is uniquely determined to be from X(nT): n=0,1,-1,2,-2...etc. as long as Ws > 2Wm
and Ws = $ \frac{2* \pi}{T} $
Since we have the Wm and the original signal to be recovered we know that the cutoff frequency is greater than Wm and less than Ws - Wm. We process this signal through a lowpass filter and receive the output signal that is exactly x(t).
