After taking the frequency spectrum of an impulse force (from a shaker, sampled from a vibration analysis test), there are noticeable peaks at 50 and 150 Hz (presumably due to some electrical/electronic artefacts or some mismatch impedance between the shaker's coil and its structure). This specific experiment aims to study the effect of frequency resolution on the spectrum.
When the frequency resolution is smaller (same bandwidth, or F_max - F_min, is used, and more spectral/FFT lines are used), these sudden peaks start to appear. It should be noted that the original input signal is the same. The question is why this happens?
Thanks for your help
I am guessing that with a frequency resolution of 6.25Hz you do not "see" the 50Hz peak, typical in a data acquisition system not properly isolated from the power line frequency, its third harmonic at 150Hz and, for what it matters, also the the seventh at 350Hz and the ninth at 450Hz, because the "jumps" in the frequency values will hide those peaks due to the low resolution.
I suggest that you look at the array of frequency values used to make the plot with the lowest number of FFT lines. For example, if the array values jump from 47.5Hz to 53.75Hz, your spectrum analyzer does not have enough frequency resolution to "see" the 50Hz peak nor the other ones. They will only appear if you use a higher frequency resolution as is the case with the higher number of FFT lines.
This does not mean that the frequencies are not in the signal, it is the low frequency resolution that hides them and you cannot see the corresponding peaks.
Paulo Candeias
Thanks for your answer, but we have a problem. The index 50 Hz (and 150 Hz) are available in both all case:
- Frequency resolution 6.25 Hz: 50 Hz is the 8th index, 150 Hz is the 24th
- Frequency resolution 3.125 Hz: 50 Hz is the 16th index
- Frequency resolution 1.5625 Hz: 50 Hz is the 32nd index
- Frequency resolution 781.25 mHz: 50 is the 64th index
- Frequency 390.625 mHz: 50 Hz is the 128th index
So in all case, there is always a FFT line running through 50 Hz (this is also confirmed with checking with the raw numerical file)
So, my first argument does not hold but the second one still does. Low frequency resolution means that the energy at the 50Hz frequency is spread over 6.25Hz in the FFT analyzer (the same thing happens to the higher harmonics). With higher resolution the energy is concentrated around the frequencies contained in the signal and therefore the peaks start showing.
You mention that the signal is the same, only it is processed with different frequency resolution? What is the signal sampling? What is the time duration of the signal? It seems that when the frequency resolution increases the energy contained in the signal gets smaller (lesser and lesser dB values).
The graph shows the conversion of a "knocking force" (man-made impulse) from time to the frequency domain. Thus, the peaks should not be there in the first place. Time duration of the signal or the measurement time (defined by the software) is 1/delta f (inverse of the frequency resolution).
About the different heights, it can be contributed to the different coefficients in Fourier transform (this is made by having different frequency resolution)
Edit: The coefficients can be seen (or at least, mentioned) by Hartin and Belanus in 1997
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