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# What is Sample Rate? [Explained]

Audio Basis - articles about audio

Read an easy explanation, of what is sample rate and Nyquist–Shannon sampling theorem.

updated

Author: Yuri Korzunov,
Audiophile Inventory's developer with 25+ year experience in digital signal processing,
author of the articles that make audio easy for beginners

## What is sample rate?

Sample rate is a number of digital signal's samples per second.

More sample rate - more samples per second.

### What is sample

Sound is air pressure oscillation.

The oscillation is a fast changing of air pressure in time.

Air oscillations impact to a microphone. Changings of the air pressure are transformed into oscillations of electrical voltage. The last one is an analog waveform.

Analog-to-digital converter makes instant measurements of voltage. Measurements are placed at even intervals on the time.

Sample is the measurement.

Digital signal (digital form of analog waveform) is the sample sequemce.

Also, we can same that sampling rate is the measurement number per second.

Digital signal has own sampling rate.

## What is sine signal?

Sine signal is a periodic waveform. Changing of analog-audio voltage repeats over time period. Here we can look at the reference points of the waveform during a period.

values 0 → amplitude → 0 → -amplitude, or

GROUND → UP → GROUND → DOWN

Period repeats during time.

It's like periodical swing of the pendulum. Period is repeatable movement.

Period 0: center → left → center → right,

Period 1: center → left → center → right.

. . .

Period N: center → left → center → right.

Amplitude is how far the pendulum deviates from the central position.

Frequency of sine is a number of periods per second.

More sine frequency more high sound. Bass is low frequencies. Birdsong is high frequencies with plenty of the periods.

## What is Nyquist–Shannon sampling theorem?

We have a time between the samples.

Designate this time as sampling period.

Imagine sine with the one repeating during the two sampling periods.

Nyquist–Shannon sampling theorem says:

Highest sound frequency, which be able to converted to digital form, is half of sampling rate.

Example: If sampling rate is 44100 Hz, such digital signal can contains maximum frequency 22050 Hz = 44100 / 2.

## Sample rate and "stairs"

At first sight, digital signal like to "stairs". But, really, it is not so.

"Stairs" exists after conversion digital values to electrical voltage.

But next stage is analog filtering.

The filtering smooth stairs (interpolate). It is like to connecting voltage values by steel ruler.

## Why sample rate above 44.1 kHz is need

Sample rate 44100 Hz:

• cover audible band 0 ... 20 000 Hz and
• have 2050 Hz reserve for the transient band of low-frequency filter (in ADC and DAC).

However, the reserve is abstractly considered. Real-life filters are analog. They have a wide transient band.

To solve the wide transient band issue, filters on a chip, higher sample rates, oversampling are used.

But these filters are not ideal and have:

• ringing audio (property of digital filters);
• limitation of the minimal size of the transient band (due to limited computing resources for example).

To reduce "hard" efforts to achieve a proper filter transient band, higher sample rates (including DSD) may be used.

Read details issues of sample rate and filters:

### What is a good sampling rate?

There is no "good" or "bad" sampling rates. Higher sampling rates allows solving issuies that are inherent in low diskretization frequencies.