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I have the task:

Buildings resonance between 0.8Hz... 1Hz. These frequencies can break glass and must be avoided, so engineers need to know the exact resonance frequency.

How many FFT points are necessary for the sampling frequency 5.4Hz in order to achieve a frequency resolution of 0.001 Hz. Also determine the observation time.

Does anyone know how to start?

FFT requires N=2^k operations

The solution is 8192 points and 1517 seconds observation time.

k=13 could be derived from the solution, but that didn't really help.

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    \$\begingroup\$ Start by finding the relationship between your desired resolution and the sampling frequency. (Also "The Solution" is wrong in general, because there are many more ways of decomposing an FFT than the power of 2 approach, but if you're restricted to radix 2 then it's correct). \$\endgroup\$ Jan 15 '16 at 18:36
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FFT resolution is Fs/N for N samples. So N = Fs/0.001 = 5400. The next power of 2 is 2^13 = 8192.

At 5.4 samples/second, the time required for 8192 samples is 8192/5.4 = 1517 seconds.

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