Vibration measurement setup and FFT calculator
If you want a measurement setup that can separate two close frequencies in the spectrum without taking unnecessarily long: enter Fmax and the number of lines to see time and resolution, or enter the frequencies you need to separate and get the required number of lines.
Reverse calculation: separating two frequencies
With the Fmax and window above, the lines needed to see two frequencies as separate peaks.
Measurement setup
- Sampling frequency (Fs = 2.56 · Fmax)
- 2,560 Hz
- Nyquist frequency (Fs / 2)
- 1,280 Hz
- Frequency resolution (Δf)
- 0.313 Hz
- Record length (T)
- 3.2 s
- Samples per block (N)
- 8,192 samples
- Total measurement time
- 8 s
- Effective noise bandwidth
- 0.469 Hz
- Closest resolvable frequencies (≈)
- 1.25 Hz
Example check: separating 2× line frequency
Can you separate the electrical 2× line frequency (100 / 120 Hz) component from the nearest running-speed multiple?
Fs = 2.56·Fmax · Δf = Fmax / lines · T = lines / Fmax · N = 2.56·lines · T_total = T·(1 + (M−1)(1−overlap))
This calculation follows the common analyser practice (Fs = 2.56·Fmax); your instrument's own rule may differ. The ENBW factors and separation rule are approximate; check the current instrument manual. This is a preliminary assessment.
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How to use it
A
Enter Fmax directly or have it calculated from a target frequency (e.g. BPFI × 3.5); choose lines, window, averages and overlap.
B
Read the sampling frequency, Δf, record length and total measurement time.
C
Enter the two frequencies you must separate in the reverse calculation to see the lines required.
02
How do Fmax, lines and time relate?
The analyser shows the spectrum up to Fmax with as many lines as you choose. The line spacing is Δf = Fmax / lines and the record length is T = lines / Fmax = 1 / Δf. So better resolution (smaller Δf) costs a longer record; doubling the lines doubles the record length.
Most analysers use a sampling frequency of Fs = 2.56 × Fmax, so a block holds 2.56 × lines samples (1024 for 400 lines, 8192 for 3200 lines). The theoretical minimum is 2 × Fmax; the extra margin is for the roll-off of the anti-aliasing filter.
03
Window, ENBW and resolvability
The FFT assumes the finite record is periodic; the window reduces the leakage this causes. Hanning is general purpose (ENBW ≈ 1.5 bins). Flat top favours amplitude accuracy but has a wide main lobe (ENBW ≈ 3.77 bins), which makes close frequencies harder to separate. Uniform (rectangular) has the narrowest lobe but high leakage; it is used for impacts and transients.
To see two lines as separate peaks, their spacing must be larger than roughly the main-lobe width of the window: about 2 Δf for Uniform, 4 Δf for Hanning, 10 Δf for Flat top. Example: if the 2× running-speed component of a 2-pole motor and the mains 2× component (100 / 120 Hz) are close together, the small difference calls for a high number of lines.
04
Aliasing, anti-aliasing and averaging
Aliasing (frequency folding): if the signal contains components above the Nyquist frequency (Fs / 2), they appear as a lower frequency that is not really there. The anti-aliasing low-pass filter before the ADC prevents this; because the filter cannot cut off sharply, Fs is taken as 2.56 × Fmax and the region between Fmax and 1.28 × Fmax is not displayed.
Block overlap: the window edges suppress the signal; overlapping consecutive blocks (50% – 67% for Hanning) recovers that loss and gets more averages from the same raw record, but the gain is limited because the blocks are not fully independent. Averaging: linear averaging gives all blocks equal weight (reduces noise in steady state); rolling (exponential) averaging weights recent blocks more and suits watching for change.
FAQ
- Is the data I enter sent anywhere?
- No. The calculation runs entirely in your browser; values are not sent to any server or stored.
- Why Fs = 2.56 × Fmax?
- The theoretical minimum is 2 × Fmax. Because a real anti-aliasing filter cannot cut off sharply, analysers leave a margin such as 2.56; the part above Fmax is not displayed. Your instrument's rule may differ.
- How many lines should I choose?
- Choose by the closest two frequencies you want to separate: required Δf ≈ spacing / main-lobe factor. For general monitoring 400 – 1600 lines is often enough; separating close peaks from gears or electrical sources can take 3200 and more.
- Hanning or Flat top?
- Hanning for finding frequencies and separating close peaks; Flat top for measuring the amplitude of a single component accurately. Flat top's wide main lobe makes it unsuitable for separating close frequencies.
- How do averages and overlap affect measurement time?
- With M averages the total time is T × (1 + (M − 1)(1 − overlap)). Four averages at 50% overlap take about 62% as long as four averages without overlap.
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