How to use the Nyquist Sampling Rate Calculator
- 1. Enter the frequenciesIn Hz, or in rad/s from x(t), for example 200pi.
- 2. Add your sampling rateOptional: checks each component for aliasing.
- 3. See the resultsNyquist rate, interval, alias frequencies and bit rate.
Sampling theorem and Nyquist rate
A band-limited signal with highest frequency fm can be rebuilt from its samples if fs > 2fm. The minimum rate 2fm is the Nyquist rate and 1/(2fm) is the Nyquist interval. Any component above fs/2 (the folding frequency) appears at a false lower frequency |f − k·fs|. This is aliasing.
Worked example: x(t) = cos(50πt) + cos(300πt) + cos(100πt). Dividing each ω by 2π gives 25 Hz, 150 Hz and 50 Hz. fm = 150 Hz, so the Nyquist rate is 300 Hz and the Nyquist interval is 3.33 ms. If you sample a 5 kHz tone at 8 kHz, it aliases to |5 − 8| = 3 kHz.
PCM bit rate and exam questions
For PCM, bit rate = fs × bits per sample × channels. CD audio samples at 44.1 kHz with 16 bits and 2 channels: 44,100 × 16 × 2 = 1.411 Mbps. Telephone speech uses 8 kHz × 8 bits = 64 kbps.
- Find the Nyquist rate of x(t) = 3 cos(200πt) + 5 sin(600πt) (600 Hz).
- Find the alias of a 7 kHz tone sampled at 10 kHz (3 kHz).
- Find the bit rate for a 4 kHz voice signal sampled at the Nyquist rate with 8 bits (64 kbps).
In practice, sample a bit above 2fm and use an anti-aliasing low-pass filter before the ADC.
Frequently asked questions
Is fs = 2fm enough?
In theory it is the limit, but a sine at exactly fs/2 can be sampled at its zero crossings and lost. Real systems sample faster, such as 44.1 kHz for 20 kHz audio.
How do I enter cos(200πt)?
Choose rad/s and type 200pi (or 200π). The tool divides by 2π, giving 100 Hz.
What is the folding frequency?
It is fs/2. Frequencies above it fold back into the range 0 to fs/2 and look like lower frequencies.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.