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## Nyquist's Sampling Theorem

• Suppose we are sampling a sine wave (Fig 6.3. How often do we need to sample it to figure out its frequency? A Sine Wave

• If we sample at 1 time per cycle, we can think it's a constant (Fig 6.4) Sampling at 1 time per cycle

• If we sample at 1.5 times per cycle, we can think it's a lower frequency sine wave (Fig. 6.6) Sampling at 1.5 times per cycle

• Now if we sample at twice the sample frequency, i.e Nyquist Rate, we start to make some progress. An alternative way of viewing thr waveform (re)genereation is to think of straight lines joining up the peaks of the samples. In this case (at these sample points) we see we get a sawtooth wave that begins to start crudely approximating a sine wave Sampling at 2 times per cycle

• Nyquist rate -- For lossless digitization, the sampling rate should be at least twice the maximum frequency responses. Indeed many times more the better. Sampling at many times per cycle

Dave Marshall
10/4/2001