# The effects of frequency resolution in FFT on the frequency spectrum

This is a section for the parameter study of my thesis (basically: why and how I did what I did in the experiments). Currently, I have to choose the fit bandwidth and FFT lines combination for the experiment (for the parameter study, it is just giving an impulse for the generator, or hitting the metal specimen with a hammer). Investigations (actual measurement) say that with frequency resolution under 0.1 Hz, the spectrum obtained would be very squishy. For example, right below is 12800 FFT lines (or 12800 FFT bins) with different bandwidths (0.5, 1, 2, 5, 10 and 20 kHz) and different frequency resolutions (39.1, 78.1, 156.3, 390.6, 781.3 and 1562.5 mHz respectively)

The spectrum with 39.1 and 78.1 mHz frequency resolution (blue and orange) are very "squishy"...

Question 1: Why do we have such squishy spectrum?

For reference: this is non-squishy spectrum

Question 2: At low-frequency range (<50 Hz), smaller FFT bin shows peak better (more data point on the same range of frequency, thus easier to spot the peaks). But why at high-frequency, smaller FFT bins lead to lower peaks (at 300 and 330 Hz)?

Question 3: Is there a "critical point" for frequency resolution? Or the trade-off between frequency resolution vs spectral/time resolution? If yes, is there any source you can point towards for me, or is this more like a rule of thumb?

Thank you for your support (This question is also posted in Electrical engineering, and per the first comment, it is put here)