Formula Of Sampling Theorem. For simplicity specialize to a sinusoid where NOTE. If f t contains no frequencies of W hertz or higher then it can be recovered from its samples by the Nyquist-Shannon interpolation formula.
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If the sampling criterion holds then the input waveform can be exactly. We call the formula 19 the sampling formula S-formula for the function I l x. Shannon in 1949 places re-strictions on the frequency content of the time function sig-nal ft and can be simply stated as follows.
The formula 5 for f x and the corresponding S-formulas for f x f x and f x are obtained by using c n l a and I l x for l 1 2 3 and 4 respectively of Table 1 in 19 where we put a x y.
Sampling and the Nyquist Theorem Nyquist sampling f d2 where dthe smallest object or highest frequency you wish to record. The sampling rate of 2 W samples per second is called the Nyquist rate. δ t a 0 Σ n 1. However notice that we can still clearly identify the frequency of the discrete-time waveform.
