DAC and Sampling Rates

[first7movie]

Hi ,
According to nyquist theorm output frequency < 2 X Sampling Rate
If i am to generate a sine wave at 1 Hz . Sample Rate = 2 Hz (2 point per cycle).
However using just 2 point or even 3 is insufficient to generate a sine wave using lookup table .

Is there something i mistaken ?
Is there a minimum points required for sine wave generation?

This have been bothering me for days .Thanks for all help.

 

[flipcity]

Recall that the Nyquist sampling theorem implies the use of an analog reconstruction filter to recover the original signal and you haven't mentioned what you are using for that. If you sample at min rate (2x) then you need a perfect "brickwall" reconstruction filter which is unachievable in practice. So in practice you must sample greater than 2x so that your reconstruction filter can be practical. 3x should be adequate depending on the fidelity of the sine wave that you are trying to generate.

 

[first7movie]

i am using it to woking like a sine wave generator. Is 3 point sufficient as from what i know 3 point is sufficient to generate a saw wave.

 

[FvM]

from what i know 3 point is sufficient to generate a saw wave

If your reconstruction filter would be a linear voltage interpolator in time domain. The sampling theorem is assuming a frequency domain filter.

 

[first7movie]

if i am using an DAC of 8 bit at 1us per sample from a 256 variable sine lookup table array. The maximum point is 256 per cycle . So my max freq 1 /(256 * 1 us)is Is there a way to calculate the minimum freq ?

 

[FvM]

Neither the maximum nor the minimum frequency is limited by the table length. You're not required to use a fixed number of samples for a sine cycle. At higher frequencies only some of the table values are used, at lower frequencies, samples are repeated. Phase respectively amplitude noise is introduced by the limited table resolution. For a method to generate variable frequencies with high resolution, refer to the NCO principle. See: Numerically-controlled oscillator - Wikipedia, the free encyclopedia

 

[flipcity]

Well, the minimum frequency is zero or DC of course. Just output a constant value all the time. But your max frequency calculation is flawed somewhat. Your maximum frequency has nothing to do with the resolution of your DAC. In fact, I believe that they now use one bit DACs to reproduce CD audio. The max frequency as you stated earlier is one half the sampling frequency. If you can sample (update your DAC) at 1 us intervals then Nyquist says you can achieve a max frequency of 500 KHz. For example, at t=0 output the min voltage from the DAC, then at t=1 us output the max voltage from your DAC, then at t=2 us output the min again and so on. This will produce a square wave at 500 KHz. An analog low pass filter can then filter out the harmonics and leave the 500 KHz fundamental sinewave.