Library / Structural dynamics and vibration testing / SDY-42
Structural dynamics and vibration testing
FFT frequency-bin spacing
Spacing between neighbouring frequency bins of a transform of length Nfft taken from data sampled at fs.
- Ref
- SDY-42
- Rev
- v1
- Field
- Structural dynamics and vibration testing
- Result
- Δf [Hz]
The spacing between neighbouring frequency bins of a transform is Δf = fₛ/Nfft, the reciprocal of the record duration when no zero padding is used. Zero padding makes the bins closer by interpolating, but does not add information. The window and the length of the real data set the ability to separate nearby modes.
Spacing between neighbouring frequency bins of a transform of length Nfft taken from data sampled at fs. Zero padding makes the bins closer without adding resolution.
Calculator
- Record duration, N/fₛ2 s
- Nyquist frequency, fₛ/21,024 Hz
- Number of bins up to Nyquist2,048
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 2 s record gives bins 0.5 Hz apart, enough to separate modes 1 Hz apart or more with a Hann window.
- Doubling the record length halves the bin spacing, while doubling the sample rate doubles it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Hz) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Nfft Transform length | 64 to 65,540 | 0.03125 | 32 | 31.97 | +1 | −0.0244 % |
| fs Sample rate | 100 to 50,000 Hz | 0.02441 | 12.21 | 12.18 | +10% | +10 % |
Sweep of Transform length
| Transform length | Bin spacing (Hz) |
|---|---|
| 64 | 32 |
| 152.2 | 13.45 |
| 362 | 5.657 |
| 861.1 | 2.378 |
| 2,048 | 1 |
| 4,871 | 0.4204 |
| 11,590 | 0.1768 |
| 27,550 | 0.07433 |
| 65,540 | 0.03125 |
Sweep one variable
Variables and how each one contributes
Bin spacing
What the equation gives you. Everything else feeds it.
Sample rate
The sample rate, in Hz: samples taken per second. Sets the frequency span and scales the bandwidth in proportion. Raising it by 10 % (to 2,253) moves the result by +10 %, from 0.5 to 0.55 Hz.
Transform length
The transform length (a whole number of samples). A longer transform gives finer bin spacing. Raising it by 512 (to 4,608) moves the result by −11.1 %, from 0.5 to 0.4444 Hz.
Worked example with the values above
- Sample rate: 2,048 Hz; transform length: 4,096.
- Divide.
- Δf = 2,048 / 4,096 = 0.5 Hz.
Assumptions and limits
- A uniformly sampled, stationary record, with the window and scaling conventions stated for each entry.
- A one-sided spectrum, with the factor 2 applied only to bins that have a distinct negative-frequency partner.
Common mistakes
- Forgetting to divide by the window’s noise bandwidth or power, which scales the spectrum wrongly.
- Applying the factor 2 at DC and at the Nyquist bin.
- Assuming that zero padding adds resolution: it only interpolates the spectrum.
- Treating overlapping segments as independent: they are correlated.
Statistics and uncertainty
Windowing and averaging trade resolution against variance and leakage. Record length sets the bin spacing, and the number of segments sets how much random error remains in the estimated spectrum.
Where it is used
- Setting the record length, window and averaging for a vibration test so that nearby modes can be told apart.
- Scaling windowed FFT output to correct amplitudes and spectral densities.
Maths you need
- Discrete Fourier transform: frequency content of a sampled record
- Window function: a taper applied to reduce spectral leakage
- Power spectral density: power per unit frequency