Spectrum Analysis Basic Notation and Principles - Frequency and Period
The "wave length" of a sine or cosine function is typically expressed in terms of the number of cycles per unit time (Frequency), often denoted by the Greek letter nu (ν; some textbooks also use f). For example, the number of letters handled in a post office may show 12 cycles per year: On the first of every month a large amount of mail is sent (many bills come due then), then the amount of mail decreases in the middle of the month, then it increases again towards the end of the month. Therefore, every month the fluctuation in the amount of mail handled by the post office will go through a full cycle. Thus, if the unit of analysis is one year, then n would be equal to 12, as there would be 12 cycles per year. Of course, there will likely be other cycles with different frequencies. For example, there might be annual cycles (ν=1), and perhaps weekly cycles (ν=52 weeks per year).
The period T of a sine or cosine function is defined as the length of time required for one full cycle. Thus, it is the reciprocal of the frequency, or: T = 1/ν. To return to the mail example in the previous paragraph, the monthly cycle, expressed in yearly terms, would be equal to 1/12 = 0.0833. Put into words, there is a period in the series of length 0.0833 years.
In the Time Series module, the frequency is computed in terms of cycles per observations, since each observation represents one unit of time.