# How could one can say that frequency spectrum having Nyquist frequency 'x' is the most appropriate representation of a given signal?

I have a sinusoidal signal which has a period of 2 and I want to find the frequencies that are present.I assumed sampling interval as 0.01 and based on this I sampled the signal.The Nyquist frequency i got from this is suppose 'x'.Now if I change my sampling interval to 0.001, Nyquist frequency in this case is '10*x' So my question is,which frequency spectrum will represent the signal correctly, the one with Nyquist frequency 'x' or the one one with Nyquist frequency '10*x'

• Why is your sampling interval so small? Is this a homework problem? – Amal May 10 '16 at 16:18

The most important thing is to sample at more than twice your signal's bandwidth; the period is largely irrelevant. Say your signal with period 2 is a square wave -- its bandwidth is infinite and you'll never be able to sample it correctly (at least in theory). If your signal is a sine wave, then a period of 2 means its bandwidth is 0.5 and you'll easily sample it adequately.

Personally, whenever possible, I'd sample:

• a bit above Nyquist (say, at $2.2B$, where $B$ is the signal bandwidth), to maximize the number of useful frequency bins, and
• for as long as possible, to increase the spectral resolution.
• i don't think using 2.2 to calculate the nyquist criterion is going to get this guy the correct answer to his homework question – panthyon Oct 12 '15 at 23:16
• The only thing that I know about my signal is the lowest frequency and the period.So bandwidth concept won't work in my case. – ashu sharma Oct 12 '15 at 23:22
• that is false. you know a lot about the available bandwidth given the sampling period. – panthyon Oct 12 '15 at 23:24
• I don't have much knowledge about bandwidth.is there any other way? – ashu sharma Oct 12 '15 at 23:31
• what does your textbook say about the relationship between sampling period and sampling rate? and then what about the available bandwidth given the sampling rate? – panthyon Oct 12 '15 at 23:36