Formula Used
Nyquist sampling rate: Fs(min) = 2 × fmax
Time figure frequency: fmax = counted cycles ÷ total measured time
Total measured time: horizontal divisions × time per division
Spectrum grid frequency: fmax = frequency per division × divisions to highest component
Recommended rate: Fs(recommended) = safety factor × fmax
Sampling interval: Ts = 1 ÷ Fs(recommended)
How to Use This Calculator
- Select the figure reading method that matches your graph.
- Enter the values read from the waveform or spectrum.
- Use consistent units from the figure labels.
- Choose a safety factor of at least 2.
- Press Calculate to show results above the form.
- Download the result as CSV or PDF when needed.
Example Data Table
| Figure Type |
Reading |
Highest Frequency |
Minimum Sampling Rate |
Recommended Note |
| Time waveform |
4 cycles over 2 ms |
2 kHz |
4 kHz |
Use more margin for noisy plots. |
| Spectrum axis |
Peak ends at 3.2 kHz |
3.2 kHz |
6.4 kHz |
Use highest visible component. |
| Spectrum grid |
500 Hz per division, 6 divisions |
3 kHz |
6 kHz |
Check axis scale carefully. |
Understanding Figure Based Sampling
A figure often shows a waveform, a period, or a frequency spectrum. Each view can lead to the same sampling decision. The key is finding the highest frequency that must be preserved. Once that value is known, the Nyquist rule gives the minimum sampling rate.
Why Nyquist Rate Matters
Sampling turns a continuous signal into measured points. If points are too far apart, different waves can look the same. That error is called aliasing. It can move high frequency content into lower ranges. The result may look valid, yet it is false. A proper sampling rate protects the shape, timing, and spectrum of the signal.
Reading A Time Figure
For a time waveform, count the cycles shown in the figure. Then measure the total time across those cycles. The frequency is cycles divided by time. If the figure uses divisions, multiply divisions by the time per division. This gives the time span. The calculator then computes the highest frequency from that span.
Reading A Spectrum Figure
For a spectrum, locate the highest visible frequency component. Use the value on the axis if it is labeled. If the axis is gridded, multiply the number of divisions by the frequency per division. This works well for plots, oscilloscope screenshots, and textbook figures.
Using A Safety Factor
The exact Nyquist rate is twice the highest frequency. It is the theoretical minimum. Real systems often need more margin. Filters are not perfect. Figure readings can also be approximate. A safety factor, such as 2.5 or 4, provides a more practical recommended rate. The calculator also shows the sampling interval. This interval is the time between samples.
Practical Notes
Use consistent units before comparing results. Avoid rounding early. Read the figure carefully, especially when the curve is small. If several components appear, use the highest one. For reports, save the result table. It records the method, units, minimum rate, recommended rate, and interval. That record makes your sampling choice easier to review.
When To Recheck
Recheck the reading when the figure uses mixed units or compressed axes. A small mistake near the highest component doubles inside the final rate. Conservative settings are usually safer for capture, analysis, and filtering work.
FAQs
What is the Nyquist sampling rate?
It is the minimum sampling rate needed to represent a signal without ideal aliasing. It equals two times the highest frequency present in the signal.
How do I find frequency from a time figure?
Count the cycles shown. Measure the total time across those cycles. Divide cycles by total time to get the signal frequency.
How do I use a spectrum figure?
Find the highest frequency component that appears in the spectrum. Use that value as the maximum frequency for the Nyquist calculation.
Why is a safety factor included?
The Nyquist rate is a theoretical minimum. A safety factor gives extra room for filter limits, reading errors, and practical measurement needs.
Can I use divisions from a graph?
Yes. Multiply the number of divisions by the value per division. Use time divisions for waveforms and frequency divisions for spectrum plots.
What happens if I sample below Nyquist rate?
Aliasing can occur. High frequency content may appear as false lower frequency content, which can distort analysis and recorded data.
Is the recommended rate always required?
No. It is a practical guide. Some systems need more margin, while carefully filtered signals may work near the theoretical minimum.
What unit should I enter?
Use the same unit shown on your figure. The calculator converts values internally before displaying the final sampling rate.