The correct answer is If we repeat P over and over again, forming an indefinitely long vector called (say) Pstar, it's obvious that the result is periodic, with period N. That is , if k = j + n*N, for any integer n, then Pstar(k) == Pstar(j).
What is the frequency of the periodic version Pstar if we consider the vector P to be a digital representation of a sound? We need to know the time Tsamp between digital samples, or more precisely, the sampling frequency Sfreq = 1/Tsamp, in order to respond to this question. Pstar has a period of N/10000 seconds and a frequency of 10000/N if Tsamp is 1/10000 seconds (Sfreq = 10000 Hertz). The sampling frequency will be primarily considered a fact about the "ditigal to analog conversion" (D/A), or the process of playing the sound, in the discussion that follows. The analog-to-digital conversion (A/D) process may also fall under this category, and the two rates need not coincide.
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