Configure the Sampling Analysis
Choose one focused mode or run comprehensive analysis. Blank optional fields are skipped.
Core Formulas
| Quantity | Formula | Purpose |
|---|---|---|
| Nyquist frequency | fN = fs / 2 | Highest unaliased baseband frequency. |
| Nyquist rate | fs ≥ 2fmax | Minimum ideal real-sampling rate. |
| Oversampling ratio | OSR = fs / (2fmax) | Measures sampling margin above Nyquist. |
| Samples per cycle | SPC = fs / fsignal | Measures waveform sampling density. |
| FFT bin width | Δf = fs / N | Estimates frequency resolution. |
| Bandpass sampling | 2fH/m ≤ fs ≤ 2fL/(m−1) | Finds non-overlapping spectral-image ranges. |
How to Use
- Select a focused mode or comprehensive analysis.
- Enter frequencies and choose matching measurement units.
- Set practical margins for filters and clock accuracy.
- Add FFT or recording values when spectral analysis matters.
- Press Calculate and review warnings before choosing hardware.
Example Data
| Application | Highest frequency | Typical sampling rate | Nyquist frequency | Comment |
|---|---|---|---|---|
| Telephone speech | 3.4 kHz | 8 kHz | 4 kHz | Small transition band remains. |
| Compact-disc audio | 20 kHz | 44.1 kHz | 22.05 kHz | Filter margin exceeds two kilohertz. |
| Professional audio | 20 kHz | 48 kHz | 24 kHz | Additional transition margin is available. |
| Vibration monitoring | 10 kHz | 25.6 kHz | 12.8 kHz | Common analyser sampling choice. |
| Biomedical waveform | 150 Hz | 1 kHz | 500 Hz | Strong oversampling supports filtering. |
Assumptions and Limitations
- Ideal Nyquist limits assume band-limited input signals.
- Real filters require a nonzero transition region.
- Clock jitter can degrade high-frequency conversion accuracy.
- I/Q results use a simplified complex-sampling bandwidth rule.
- Bandpass ranges require suitable analogue filtering and planning.
- FFT resolution differs from true component-separation capability.
- Window choice influences leakage and amplitude accuracy.
- ADC bit depth controls quantisation, not Nyquist frequency.
Frequently Asked Questions
What is Nyquist frequency?
It equals half the sampling frequency. Frequencies above it fold into lower frequencies. Filtering helps prevent unwanted spectral aliases.
Is Nyquist frequency the same as Nyquist rate?
No, the terms describe different limits. Nyquist frequency uses a given sampling rate. Nyquist rate uses the signal bandwidth.
Why sample above exactly twice the signal frequency?
Real filters need transition space. Clock errors also consume available margin. Higher rates simplify practical reconstruction filters.
What happens when sampling is too slow?
Higher components appear at incorrect lower frequencies. This distortion is called aliasing. Digital processing cannot reliably remove it.
How is an aliased frequency calculated?
The signal repeats around sampling-rate multiples. Each repeated component folds around Nyquist boundaries. The calculator performs that spectral folding.
What is a useful samples-per-cycle target?
Two samples only meet the ideal limit. Ten or more often represent waveforms better. Required density depends on processing goals.
Can bandpass signals use lower sampling rates?
Yes, carefully selected rates can sample narrow bands. Spectral copies must not overlap. Analogue filters remain essential for success.
Does FFT size change Nyquist frequency?
No, sampling rate sets Nyquist frequency. FFT size changes frequency-bin spacing. Longer records can improve spectral resolution.
Does ADC resolution affect the Nyquist limit?
Bit depth affects amplitude quantisation. Sampling frequency controls the Nyquist limit. Both influence overall measurement quality.