Formula used
This calculator reports two common quantities that people informally call “frequency resolution.” They are related but not identical.
- Record duration: T = N / fs
- True resolution (informal): Δf ≈ 1 / T
- FFT bin spacing: Δfbin = fs / NFFT
- Nyquist: fN = fs / 2
- Mainlobe width (first null): W ≈ k · Δf, where k depends on window
Zero padding increases NFFT, so Δfbin gets smaller. However, Δf ≈ 1/T and the window mainlobe width reflect the information content of your record.
How to use this calculator
- Select an input mode: either enter sampling rate and samples, or duration and samples.
- Set a window type to match your leakage and separation needs.
- Optionally choose a zero-padding factor to refine the plotted frequency grid.
- Click the calculate button to view results above the form.
- Use the CSV and PDF buttons to export the computed outputs.
Example data table
| Sampling rate (Hz) | Samples (N) | Duration (s) | Padding | Window | True Δf (Hz) | Bin spacing (Hz) |
|---|---|---|---|---|---|---|
| 1000 | 1024 | 1.024 | 1× | Rectangular | 0.976562 | 0.976562 |
| 2000 | 4096 | 2.048 | 4× | Hann | 0.488281 | 0.122070 |
| 48000 | 48000 | 1.000 | 2× | Blackman | 1.000000 | 0.500000 |
The second row shows how padding refines bin spacing without changing 1/T.
Why frequency resolution matters
Frequency resolution determines how finely you can distinguish nearby spectral components. In vibration tests, it helps separate structural modes. In radio monitoring, it helps isolate narrow carriers. In acoustics, it helps identify hum and harmonics. Better resolution generally requires longer observation time, not just more display points.
Core quantities reported by this tool
The calculator reports time-limited resolution and FFT bin spacing. True resolution is approximated by 1/T, where T is record duration. Bin spacing is fs/NFFT, where NFFT may include padding. Window choice adds an estimated mainlobe width that influences separability.
Record duration drives true separability
Two pure tones separated by less than about 1/T are difficult to separate from a single record, because the finite measurement time spreads energy in frequency. Extending the record from 1 s to 10 s improves 1/T from 1 Hz to 0.1 Hz. This is the most reliable lever for sharper separation.
Bin spacing and what it represents
A DFT samples the spectrum at discrete frequencies. With fs = 1000 Hz and NFFT = 1024, bins are 0.9766 Hz apart. Peaks often land between bins, so the displayed maximum can shift with bin grid placement. Smaller bin spacing improves peak localization, but does not create new information.
Zero padding in practical terms
Zero padding increases NFFT while keeping the same measured data length. It interpolates the spectrum onto a finer grid, which can make peaks look smoother and help estimate frequency by fitting around the maximum. Padding reduces bin spacing, yet 1/T stays unchanged.
Windows, leakage, and mainlobe width
Windowing reduces spectral leakage from record-edge discontinuities. The tradeoff is a wider mainlobe that can blur close components. Rectangular is narrowest but leaky. Hann and Hamming reduce sidelobes with a wider mainlobe. Blackman suppresses leakage further, with the widest mainlobe.
Planning examples with real numbers
Audio at 48 kHz: a 1.0 s record gives ~1 Hz true resolution; a 0.25 s record gives ~4 Hz. For slow sensors sampled at 200 Hz, 4096 samples cover 20.48 s, yielding ~0.0488 Hz. For 0.5 Hz, aim for T ≥ 2 s.
Common pitfalls and quick checks
Do not confuse smaller bin spacing with better physical resolution. If your record is short, features will still smear. Watch Nyquist: energy above fs/2 aliases into the band. When peaks look broad, compare mainlobe width to tone spacing. Verify units when switching between Hz and kHz.
FAQs
1) What is the difference between 1/T and fs/NFFT?
1/T reflects the time-limited ability to separate nearby components from one record. fs/NFFT is the spacing of frequency samples on the computed spectrum. Padding changes fs/NFFT, while 1/T depends on the actual record duration.
2) Does more zero padding improve resolution?
It improves the visual and numerical granularity of the spectrum by interpolating between bins. It does not add new information or overcome a short record. True separability still tracks record duration and window mainlobe width.
3) How many samples do I need for 0.5 Hz resolution?
Target T ≥ 2 seconds because 1/T ≈ 0.5 Hz. Then choose N = fs·T. For example, at fs = 1000 Hz you need about 2000 samples. Padding is optional for display refinement.
4) Which window helps distinguish two close tones?
A narrower mainlobe helps separate close tones, but low sidelobes reduce leakage. Rectangular is narrowest but leaky; Hann/Hamming often balance separation and leakage. If leakage is dominant, a stronger window can reveal weaker tones near strong ones.
5) What does Nyquist mean for my analysis?
Nyquist is fs/2, the highest frequency you can represent without aliasing. Content above Nyquist folds back into the spectrum and can mimic real low-frequency components. Use anti-alias filtering or increase sampling rate if high-frequency energy exists.
6) Why include overlap if it does not change resolution?
Overlap is used in Welch or STFT averaging to reduce variance and improve stability over time. It affects how many segments you can average and the hop size between segments. Single-record resolution is still governed mainly by record duration and windowing.
7) Why do peaks appear between bins?
A tone’s true frequency rarely aligns exactly with a bin center, so energy spreads across nearby bins. Windowing shapes that spread. Padding provides more sample points on the spectrum, which makes the peak location easier to estimate with interpolation or curve fitting.