It's not the number of samples but the sampling frequency. Here's one way to understand it -- there are three numbers important in digital signals -- the Sampling Frequency (SF), the Number of Samples (N), and the total time (T) of the sample. They are closely related by the equation N / T = SF (which makes sense, Number of Samples per Time = Samples per Time). It can also be written SF * T = N.
Now, what is the lowest, and highest, sinusoid that can be represented in the N samples? The fewest number of sinewaves you can put in is 1. 1 wave in T seconds, 1/T, is the lowest frequency that can be represented. The fewest points to define a sine wave is 2, one at the peak, one at the trough. So the highest frequency that you can extract from a waveform sampled at SF is SF/2 (or N/2 divided by T = SF/2).
In your description of the task, you mention N, but don't say anything about SF. Increasing N can allow you to represent lower frequencies, but doesn't change the maximum frequency. To do that, you need to increase the sampling frequency.
Bob Schor
