# What is the LOW frequency resolution rule analogous to Nyquist?

If I'm analyzing a signal in the frequency domain, I know about the well known Nyquist criteria that the sample frequency must be > 2x of the highest component present in the signal.

However, there are very few references related to the lowest frequency I can analyze. This problem comes up in a lot of natural data where we have limited windows of observation because the instruments to do so were only invented or in wide spread use in the last 50-100 years, and natural cycles can be decades, centuries, or longer.

One would think that you could analyze a component where at least one period was in the sample window, but I find because of required windowing to prevent edge effects that the signal often disappears (it depends on the phase). I then thought it was a mirror of Nyquist and I could resolve any signal with at least 2 periods in a window, but actual analysis shows that to not be true when there's a another overlying signal whose period is similar.

I found through experiment that I needed at least 5 periods to resolve a signal where there's another signal near the same frequency.

Is there a formal way of representing this problem or a definitive reference I can use?

Would the same issue apply to wavelet analysis in the same manner?

• I think you may need to study your signal in the DFT domain and increase the resolution (the number of points per sample). Have a look to this question: electronics.stackexchange.com/questions/12407/… Commented Mar 13, 2016 at 6:26
• I forgot to mention that I padded like crazy. It just makes the FFT smoother, it doesn't add any information. There's a lower frequency information limit. You can't use a 10 second window to detect a 1/100000000000000 HZ signal for example, even if you pad with billions of zeroes. But what is that formal limit, formally? is the question here Commented Mar 13, 2016 at 14:00
• From the answers in that thread "EDIT: There is also a trick to pad the input with zeros and taking a bigger FFT. It will not improve your differentiation ability but may make the spectrum more readable. It is basically a trick similar to antialiasing in vector graphics." Commented Mar 13, 2016 at 14:01