Library / Structural dynamics and vibration testing / SDY-46
Structural dynamics and vibration testing
Number of complete Welch segments
Count of whole, possibly overlapping segments of length L that fit in a record of N samples when neighbours overlap by O samples.
- Ref
- SDY-46
- Rev
- v1
- Field
- Structural dynamics and vibration testing
- Result
- K
The number of complete segments of length L that fit in a record of N samples when neighbours overlap by O samples is K = 1 + ⌊(N − L)/(L − O)⌋. The step between segment starts is L − O. The incomplete tail is discarded. Overlapping segments are correlated, so K segments with overlap do not reduce the variance as much as K independent ones.
Count of whole, possibly overlapping segments of length L that fit in a record of N samples when neighbours overlap by O samples. The incomplete tail is discarded.
Calculator
- Step between segment starts, L − O128 samples
- Fraction of the record used0.896
- Overlap as a fraction of the segment0.5
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 1,000-sample record with 256-sample segments overlapping by 128 samples gives 6 averages.
- More overlap gives more segments, but past about 50–75 % the extra segments add little new information.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| N Record length | 256 to 100,000 samples | 1 | 780 | 779 | +1 samples | 0 % |
| L Segment length | 160 to 1,000 samples | 1 | 27 | 26 | +1 samples | 0 % |
| O Overlap | 0 to 159 samples | 3 | 8 | 5 | +1 samples | 0 % |
Sweep of Overlap
| Overlap (samples) | Number of segments |
|---|---|
| 0 | 3 |
| 19.88 | 4 |
| 39.75 | 4 |
| 59.63 | 4 |
| 79.5 | 5 |
| 99.38 | 5 |
| 119.3 | 6 |
| 139.1 | 7 |
| 159 | 8 |
Sweep one variable
Variables and how each one contributes
Number of segments
What the equation gives you. Everything else feeds it.
Record length
The record length, in samples. A longer record fits more segments. Raising it by 100 (to 1,100) moves the result by +16.7 %, from 6 to 7.
Segment length
The segment length, in samples. Longer segments mean fewer of them. Raising it by 16 (to 272) moves the result by +0 %, from 6 to 6.
Overlap
The overlap between neighbouring segments, in samples; it must be below L. More overlap fits more segments. Raising it by 16 (to 144) moves the result by +16.7 %, from 6 to 7.
Worked example with the values above
- Samples to cover after the first segment: N − L = 1,000 − 256 = 744.
- Step: L − O = 256 − 128 = 128; whole steps: ⌊744 / 128⌋ = 5.
- K = 1 + 5 = 6.
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