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Nyquist Sampling Theorem

#sampling#nyquist#aliasing#ADC#digital signal processing

Nyquist Sampling Theorem

The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a signal, you must sample at least twice the highest frequency component. This is fundamental to all digital signal processing and SDR systems.

fs≥2fmaxf_s \geq 2 f_{max}

Alternative Forms

Maximum Frequency
fmax=fs2f_{max} = \frac{f_s}{2}
Highest frequency that can be represented (Nyquist frequency)
With Guard Band
fs≥2.5fmaxf_s \geq 2.5 f_{max}
Practical rule including filter roll-off margin

Input Variables

MHz

Highest frequency component in the signal(Range: 0.001 – 100000 MHz)

Results

Sampling Rate (f_s)
—
Nyquist Frequency (f_{Nyquist})
—

📖 Example: Audio Sampling (CD Quality)

Determine sampling rate for audio signals up to 20 kHz

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Free Space Path Loss (FSPL)

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Wavelength-Frequency Relationship

Convert between wavelength and frequency using speed of light