Sampling Theorem Calculator

Sampling Theorem Formula

Worked Example

A 4 kHz signal sampled at 6 kHz, and a 5 kHz tone in the same system:

1. Nyquist rate = 2 × 4 kHz = 8 kHz
2. Alias: |f − k fₛ| with k = round(f/fₛ) = 1 → 1 kHz

This sampling rate: is too low: frequencies above fₛ/2 alias · Tone of 5 kHz appears at: 1 kHz · Sampling interval Tₛ = 1/fₛ: 166.6666667 µs

GATE tip

For x(t) = cos(2π·f₁t) + cos(2π·f₂t)·…, the Nyquist rate is twice the HIGHEST frequency present after expanding products: cos A cos B makes sum and difference frequencies.

More Signals and Systems Calculators

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  X[k] = Σ x[n] e^(−j2πkn/N)

  k = 0 … N − 1; X[0] is the sum of the samples

  Example: The 4-point sequence x[n] = {1, 2, 3, 4}: X[0] (sum of the samples) = 10.

  Open the dft calculator →

• Convolution Calculator

  y[n] = Σₖ x[k] h[n − k]

  length of linear convolution = L_x + L_h − 1; circular wraps modulo N

  Example: x[n] = {1, 2, 3} through h[n] = {1, 1, 1}: Linear convolution y[n] = {1, 3, 6, 5, 3}.

  Open the convolution calculator →

Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.