Dear Samuel,

welcome,

If i understood your question you have one data aggregate per month, that is one value per month. You have this monthly data for a period from year 1900 to 2016, which is  a period of 116 or 117 including year 1900. Assume 116 year excluding year 1900, then the number of data points N= 12x116=1392, Then the highest possible frequency will be one cycle per two months = 1/6 year per cycle. The lowest frequency will be one cycle per 1392 monthes which will be 116 year per cycle. The data is already sampled in one sample per month.  The limit frequencies will be the inverse of the given minimum and maximum periods. The intermediate frequencies will be multiples of fmim= 1/116  cycle/year up to the highest frequency 6 cycles per year.

Best wishes

Thanks very much Addelhalim Zekry. My period is 117 years, that gives me 1404 data points. I am using the Matlab function : pwelch(x, [], [], [], FS). where x is precipitation and FS is sample rate.

Per your explanation, is FS equal to 1/6 or 6? and again is there a special way you came by the highest possible frequency of one cycle per two months? Thank for your help.

Oops :)

FS = 12 (/ year) !

The maximum frequency detectable is a mathematical property. You may e.g. consult wikipedia, starting with the "Nyquist Shannon Sampling Theorem"

( https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem ).

 Samuel,

I would like to cite my first comment:The data is already sampled in one sample per month, so the sampling frequency FS is one sample per month, which is 12 samples per year as the colleague Dreher gave in his answer.

This is for the sampling frequency formally.

However, i considered the samples as lattice points. And to form a periodicity, the minimum periodicity will be a maximum followed by a minimum and so on. Therefore i considered the highest frequency to be observed will be 6 per year or one per two months.

So, I am interested to see your spectral density function.

Best wishes

Thanks so much for your help Abdelhalim Zekry and U. Dreher. I have attached a plot of my signal after using Fs=12. I had three peaks. one that occurs one time per year, the second one occurs two times per year and the third one occurs three times per year.

I was wondering if the interpretation of my results  is right. What if I wanted to know if it has a monthly pattern as well as a yearly pattern, Is there a way to verify that?