EE5410 Signal Processing sampling - Reconstructing x(t)

EE5410 Signal Processing sampling - Reconstructing x(t)

1. Given these samples, we can reconstruct x9t) by generating a periodic impulse train p(t) in which successive impulses have amplitudes that are successive values.

2. This impulse train is then processed through an ideal lowpass filter with gain T and cutoff frequency greater that wm and LESS than (ws - wm).

3. The resulting output signal will be exactly equal x(t).

4. Based on the use of Fourier Series, that 2TW numbers are sufficient to represent a function of duration T and highest frequency W.

5. The frequency 2wm, which, under the sampling theorem, MUST be exceeded by the sampling frequency ws, is commonly referred to as the Nyquist rate.

6. The frequency wm corresponding to one-half the Nyquist rate is often referred to as the Nyquist frequency.

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