How many periods of an analog signal are needed to be sampled ?

Hi,
supose we have an analog signal and we want to have its digital form.
Base on Nyquist Theorem our sampling speed should be at least twice the maximum frequency of analog signal.
but for having a correct process, How many periods of that analog signal are needed to be sampled ?
I heard from someone that 16 periods are needed, but i dont know why.
Can any one help me with this ?

Nyquist is a little confusing. For example, if you sample a sinusoid at just a little more than twice its frequency, you're going to get just two points of the complete sinewave. Now, you CAN reconstruct that sinewave from just those two points, but it involves a bit of math (filtering). What, exactly, are you trying to do?

For example, if you take those two points and plot them on graph, it's not going to look anything like a sinewave; it's going to look like two points.

barry said:

Nyquist is a little confusing. For example, if you sample a sinusoid at just a little more than twice its frequency, you're going to get just two points of the complete sinewave. Now, you CAN reconstruct that sinewave from just those two points, but it involves a bit of math (filtering). What, exactly, are you trying to do?

For example, if you take those two points and plot them on graph, it's not going to look anything like a sinewave; it's going to look like two points.

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Hi,
I have a 50Hz sinewave that there is a 70KHz wave on it.I need to convert this analog signal to digital form and calculate the specifications of it, like Harmonic distortion,Crest factor and etc.
My sampling frequency is about 150KSPS that it satisfy the nyquist theorem.
but know I dont know How many periods of that signal is needed to be sampled ? I heard from someone that 16 periods is required to be sampled but i dont know why and i couldnt find anything in books or articles.
Do you know anything about this ?

How many periods you need depends on what you are trying to measure exactly, but assuming that some of your measurements are going to involve either an FFT or a filter bank of some sort, you will need enough points to at least exceed the length of the FFT window or the filters impulse response.

You probably need at least a cycle at the lowest frequency of interest, so if you want to look for harmonics on the 50Hz signal (You will not see the ones on the 70KHz signal as they fall outside your bandwidth), then you need to gather at least 20ms worth of data = 3000 samples, and more makes things easier (With 3000 samples your FFT bins will each be 50Hz wide, so good luck separating the 50Hz and its second harmonic, there are ways, do a literature search).

Define what maths you are going to do, this will define the amount of data you need, 16 is a simplistic answer that may be right for some application, but will be very wrong for others.

Regards, Dan.