How do you interpret the frequencies produced by the output of a FFT

Question

When you perform an FFT, the frequencies of each of the elements in the output array are represented by:

Frequency at element k is f(k) = k/NT

Where N is the number of samples (hence number of elements in the output array) and T is the time slide in seconds. f is measured in HZ

My question is, given that formula, the frequency of each element will always be less than 1 HZ and the FFT can never produce higher than 1HZ frequencies

So how do you operate on the higher frequencies? Like the ones the human ear can hear (20HZ to 20KHZ)

Thanks D

Answer 1

It's all about the sampling frequency. So imagine you're havin a sample rate of 48 kHz, which is pretty common. Now you are performing a FFT with N = 1024 points over your data. Then you are able to assign each n in N a specific frequency. How is this done? Just assume that N equals the sampling rate. Now you are able to retrieve an equation for every other n. The bigger you choose N the finer the spacings of the frequencies get.

Edit Also have a look at this related / similar SO question, especially the answer from Paul R is very helpful.