What is the Nyquist sampling rate?

The Nyquist rate is f_s = 2 × f_max — the absolute minimum sampling frequency required to reconstruct a signal without aliasing. In practice, control systems use 10–20× the bandwidth to ensure adequate phase margin and disturbance rejection.

Why do control systems sample at 10–20× bandwidth instead of 2×?

The 2× Nyquist minimum assumes an ideal anti-aliasing filter and is too slow for closed-loop control. A rule of thumb for control is f_s ≥ 10 × BW for acceptable performance and f_s ≥ 20 × BW for tight control, providing enough phase margin and fast disturbance rejection.

What is the sampling period T?

T = 1 / f_s (in seconds). For example, a 100 Hz sampling rate gives T = 10 ms. T is the interval between successive samples and directly sets the discrete controller update rate.

How does sampling rate affect z-transform pole stability?

Continuous-time poles in the s-plane map to z-plane poles via z = e^(sT). As T increases (slower sampling), z-plane poles migrate and can cross the unit circle, causing instability. A faster sampling rate keeps z-plane poles well inside the unit circle.

What bandwidth should I enter?

Enter the closed-loop bandwidth or the highest frequency component you need to control or measure accurately. For a PID loop, this is typically the desired bandwidth of the closed-loop response. For sensor sampling, use the highest signal frequency of interest.

Sampling Time for Control Systems

Name: Sampling Time for Control Systems
Availability: InStock
Author: Nham Vu

Calculate the required sampling period and rate for discrete control systems using the Nyquist-Shannon theorem and control system guidelines.

System Parameters

System Bandwidth / Highest Frequency

Highest significant frequency in the signal or desired closed-loop bandwidth.

Recommended Rate Multiplier

10× = minimum practical; 15× = general-purpose; 20× = tight/high-performance control.

Enter bandwidth and click Calculate

Nyquist Minimum

f_s ≥ 2 × f_max (theoretical floor — insufficient for control)

Minimum

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Sampling Rate (Hz)

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Sampling Period T (ms)

Recommended (Control Systems)

f_s = 15 × BW

Recommended

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Sampling Rate (Hz)

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Sampling Period T (ms)

Summary

Parameter	Nyquist Min	Recommended
Sampling Rate f_s	—	—
Sampling Period T	—	—
Multiplier Used	2×	—
Input Bandwidth	—

Z-Transform Pole Stability

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Summary

Calculate the required sampling period and rate for discrete control systems using the Nyquist-Shannon theorem and control system guidelines.

How it works

Enter the system bandwidth (highest significant frequency) in Hz.
Select a recommended rate multiplier (10×, 15×, or 20×) based on desired control fidelity.
The tool applies the Nyquist criterion (f_s ≥ 2 × f_max) and computes the Nyquist minimum rate.
It then computes the recommended sampling rate as multiplier × bandwidth.
Sampling period T = 1 / f_s is shown in milliseconds for both rates.
A z-transform pole stability reminder is displayed to flag aliasing risk.

Use cases

Choose a sample rate for a PID digital controller in an embedded system.
Verify that an ADC sampling rate meets Nyquist for a sensor signal bandwidth.
Compare minimum vs. recommended sampling rates when CPU load is constrained.
Teach or review Shannon-Nyquist and control system sampling theory interactively.
Quickly convert between sampling rate (Hz) and sampling period (ms) for any bandwidth.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu