Sampling Rate Calculator
Determine the optimal sampling frequency based on the Nyquist-Shannon Theorem.
Understanding the Sampling Rate
In digital signal processing, the sampling rate (or sampling frequency) defines how many times per second an analog signal is measured to convert it into a digital representation. Choosing the correct sampling rate is critical to ensure that the original signal can be reconstructed without distortion.
The Nyquist-Shannon Sampling Theorem
The fundamental rule of digital sampling is the Nyquist-Shannon Theorem. It states that to perfectly capture a signal, the sampling rate must be at least twice the highest frequency present in the signal. This minimum threshold is known as the Nyquist Rate.
If you sample at a rate lower than this, a phenomenon called aliasing occurs, where higher frequencies "fold back" into lower frequencies, creating audible or visible artifacts that were not in the original source.
Why do we use 44.1 kHz for CDs?
The human ear can typically hear frequencies up to 20,000 Hz (20 kHz). According to Nyquist, we need at least 40 kHz. The additional 4.1 kHz acts as a "guard band" to allow for anti-aliasing filters to roll off gradually without affecting the audible spectrum. This explains why our calculator's "2.2x" safety factor is a common industry standard.
| Application | Common Sampling Rate | Bit Depth |
|---|---|---|
| Telephony / Voice | 8,000 Hz | 8-bit |
| FM Radio / Pro Audio | 32,000 Hz | 16-bit |
| CD Audio | 44,100 Hz | 16-bit |
| Professional Video / DVD | 48,000 Hz | 24-bit |
| High-Res Audio | 96,000 – 192,000 Hz | 24-bit |
Bitrate and Storage Impact
Higher sampling rates and bit depths result in better audio fidelity but require significantly more storage and bandwidth. Bitrate is calculated as:
Bitrate = Sampling Rate × Bit Depth × Number of Channels
For example, standard CD audio (44.1kHz, 16-bit, 2 channels) has a bitrate of approximately 1,411 kbps.