Waveform frequency resolution for FFT – any way to increase it?

Question

This article https://www.bitweenie.com/listings/fft-zero-padding/ gives a simple relation between time-length of the input data to the FFT and the minimum distance between two frequencies that can be distinguished in the FFT. The article calls this Waveform frequency resolution.

In other words; if two input-frequencies are closer in frequency than 1/time-length_of_input_data, they will show as only one peak in the FFT-plot.

My question is: is there a way to increase this Waveform frequency resolution? I am finding it difficult to work with rather short data-series due to this limitation.

As an example, if I use a combination of sine series with periods 9.5, 10, and 11 over 240 datapoints I cannot distinguish between the different frequencies.

Answer 1

To have good frequency resultion you need a long time series.

This is a fundamental issue, called uncertainty principle . It cannot be overcome within Fourier analysis (Fourier transform, DFT, short-time Fourier transform and so on).

Also note that zero padding will not overcome this issue. It gives more points in the frequency domain, in the sense that the same spectral information is sampled more densely, but it will not make peaks sharper or more separated.

The only way to overcome the uncertainty principle is to make further assumptions on the data.

• If for example you know that there is only a single frequency component, it is possible to determine its frequency more accurately than the uncertainty principle predicts.
• Also you can use transforms such as the Vigner-Wille transform . It is not bound by the uncertainty principle, but generates "crossterms", ie frequency component artifacts. However, when you only have few frequency compoents this might be acceptable. Depends on the use-case.